Learning by Dying: Combat Performance in the Age of Sail

968

Learning by Dying: Combat Performance

in the Age of Sail

DANIEL K. BENJAMIN AND ANCA TIFREA

Between 1660 and 1815 the combat fatality rate among British navy captains

fell by 98 percent, even as the combat success of the British Navy rose dra-

matically. Both developments can be explained as a result of learning by do-

ing among British commanders. This learning was importantly driven by the

extensive wartime experience accumulated over this period, combined with

the unparalleled financial incentives for combat success offered to British

commanders.

etween 1650 and 1680 there was a revolution in naval warfare. The

great battle fleets that were to dominate the age of sail were cre-

ated; state navies replaced armed merchantmen with highly specialized

warships; the line of battle was introduced; and the broadside became

the dominant method of dispensing firepower. These developments

were the product of a rapid maturation of the state as an organization of

taxation and control, and led to state monopolization of force at sea.

They also yielded a struggle at sea sufficiently intense and protracted to

be labeled the “Second Hundred Years War.”1 Despite massive naval

investment by the French and Dutch in the late seventeenth century, and

by the Spanish and French after 1720, Britain ultimately established it-

self as the undisputed ruler of the world’s oceans—a position it main-

tained into the twentieth century.

The Journal of Economic History, Vol. 67, No. 4 (December 2007). © The Economic

History Association. All rights reserved. ISSN 0022-0507.

Daniel K. Benjamin is Alumni Distinguished Professor, Department of Economics, Clemson

University, Clemson, SC 29634-1309; and Senior Fellow, PERC, 2048 Analysis Drive, Boze-

man, MT 59715. E-mail: [email protected]. Anca Tifrea is Senior Associate, KPMG

LLP, 303 Peachtree St., Atlanta, GA 30308. E-mail: [email protected].

Financial support from the Earhart Foundation and from the Spiro Center of Clemson Univer-

sity is gratefully acknowledged. We thank Jan Glete for providing us with unpublished data,

Roger Knight for many helpful discussions, and N. A. M. Rodger for his criticisms of an earlier

draft. None is responsible for what follows. William R. Dougan, James Foreman-Peck, David

Haddock, P. J. Hill, Philip Hoffman, Patrick Minford, two anonymous referees, and seminar

participants at Clemson University, Cardiff University, and the London School of Economics

also provided useful comments. Tom Evans, Paul Seufert, and Ruthira Naraidoo performed ad-

mirably as research assistants. Part of this research was conducted while Benjamin was a visit-

ing professor at Cardiff University, Wales and an Honorary Caird Research Fellow at the Na-

tional Maritime Museum, Greenwich; the research support of both institutions is gratefully

acknowledged, as is the encouragement and assistance of Patrick Minford of Cardiff University,

Nigel Rigby and Janet Norton of the National Maritime Museum, and Sarah Palmer of Green-

wich University. 1 See, for instance, Lavery, Ship and Line; Glete, Navies; Palmer, “‘Military Revolution’” ;

Tunstall, Naval Warfare; and Rodger, Command.

B

Learning by Dying 969

The narrative history of this struggle has been well documented and

ably told by naval historians.2

Our intent is to supplement the literature

in three ways. First, the existing historical narratives are qualitative in

nature; we seek to quantify the process by which Britain took command

of the ocean. Second, we hope to show that despite British setbacks

(such as those suffered during the War of American Independence) the

origins of the process that culminated in victory over Napoleon in 1815

can be traced to the First Dutch War 150 years before. Most impor-

tantly, we show that Britain’s ultimate dominance at sea was the culmi-

nation of a long process of learning, one in which both experience and

incentives played crucial roles.

We do not seek to rewrite British naval history. Nothing that follows

denies the importance of the geographical, political, and financial forces

that long have been central to the histories of this period. Indeed, as we

shall make clear, many of the familiar themes, including Britain’s island

status and the backdrop of continental land wars, are essential to our

story. We focus on the mechanism by which these larger forces mani-

fested themselves in the outcomes of warfare at sea, and thus show in

fairly precise terms the fundamental continuity of the underlying process.

The hallmark of the sea battles fought in the decades after 1650 was

widespread carnage. Comprehensive casualty counts are not readily

available, but casualties among commanding officers in the Royal Navy

were reliably recorded, and they speak unequivocally. In a single en-

gagement, the Four Days’ Battle in June 1666, 10 Royal Navy post-

captains died in combat; this was nearly 8 percent of all English post-

captains afloat at the time.3 During the two wars with the Dutch in the

1660s and 1670s, more than 60 English post-captains were killed in ac-

tion, a time when there were an average of but 114 rated ships in the

English navy. Published battle narratives plus the limited casualty data

available in published sources suggest that the butcher’s bill on the

quarterdeck had its counterpart between decks.4

There are many reasons for the high casualty rates of these years, in-

cluding the close quarters of the North Sea and the English Channel,

2 James, Naval History; Mahan, Sea Power; Clowes, Royal Navy; Creswell, British Admirals;

Glete, Navies; Lavery, Nelson’s Navy and Nelson and the Nile; Lewis, Navy; Marcus, Naval

History; Palmer, “‘Military Revolution’” and “‘Soul’s Right Hand’”; and Rodger, Wooden

World and Command.3 To oversimplify: Post-captains commanded “rated” or “post” ships—those that, for most of

the period, were officially armed with 20 guns or more. The commander of a smaller naval ves-

sel commonly was addressed as “captain,” but his official title was “master and commander.”

We generally use “English” for the period before the 1707 legislative union of Scotland and

England, and “British” for the period after 1707, but we also use “British” as a generic descrip-

tor when little harm is done by the imprecision. 4 See, for example, Clowes, Royal Navy; Tunstall, Naval Warfare; and Rodger, Command.

970 Benjamin and Tifrea

where the key battles took place, and the fact that the English and Dutch

were eager to stand and fight. We argue that one other factor was at

work. Between 1650 and 1680, firepower became concentrated as never

before, and delivered by ships built to administer and withstand more

punishment than ever before. Commanders erred often in dispensing

this firepower and avoiding its adverse consequences, mistakes that

proved fatal for them and their crews. The result was high casualty

rates. As tactics were learned and improved, fewer mistakes were made

and casualties declined. Among British captains, who are the focus of

our study, much of the learning took place rapidly, but it continued well

into the eighteenth century. By the Great Wars of 1793–1815, although

ships were at least twice as powerful as their predecessors of a century

before, combat at sea was far less deadly for British captains: they had

learned how to win—or lose—without killing nearly as many of them-

selves or their men.

The learning that reduced fatality rates among captains is also evident

in the combat success of the Royal Navy. Over the 150 years covered

by our study, the British navy markedly increased the losses it inflicted

on enemy fleets, relative to the combat losses it suffered. And although

the performance of the navy’s command structure improved most rap-

idly in the first half of our sample, improvement continued throughout

the period we study. The culminating triumph of the Napoleonic wars is

thus traceable in the data back to the initial engagements of the first

Anglo-Dutch war, more than 150 years before.

We focus on the British navy for two reasons. First, systematic data

on battle outcomes during this period are of higher quality for it than for

other navies—perhaps because Britain succeeded, and thus more avidly

recorded its activities. Second, by 1815 no one doubted Britain’s domi-

nance at sea, yet in 1650 no one could have predicted that outcome. In

quantifying the process by which Britain prevailed we also suggest fac-

tors we believe should be given more weight in discussions of this pe-

riod. Specifically, we argue that the ability of British captains to trans-

form experience into success stemmed from two key facts: the officers

and men of the British navy had far more opportunity than enemy crews

to develop their combat skills, and they were given unparalleled finan-

cial incentives to succeed. This combination of opportunity and motive

thus helped fuel the Royal Navy’s rise to greatness.

HISTORICAL PERSPECTIVE

The execution of King Charles on 30 January 1649 marked the cul-

mination of the English Revolution and presaged the dawn of a new era


in naval warfare. The Revolutionary government of England saw the

navy as a means of solidifying its rule and accomplishing a variety of

political and religious objectives. Mercantile interests were ardent back-

ers of a stronger navy, for they sought a greater share of world trade,

perhaps even the displacement of the Netherlands as the world’s domi-

nant carrier of goods at sea. The efforts of the new government and its

mercantilist supporters led in passage of the Navigation Act of 1651,

which helped precipitate the first Anglo-Dutch war of 1652/53.5

The Dutch navy at this time consisted chiefly of cruisers, speedy ves-

sels optimized for convoy escort duty and keeping open the sea lanes vi-

tal to trade. Most English vessels were comparably sized, but the Eng-

lish also had a small contingent of “great ships,” battleships optimized

for firepower and the ability to withstand intense combat. Perhaps most

crucially, the English discovered the line of battle, which was an effec-

tive defense against the Dutch melee tactics, and a devastating means of

delivering concentrated firepower.6 Despite unremitting willingness of

the Dutch to fight, the English tactics and battleships tipped the balance,

and the Battle of Scheveningen in 1653 sealed an English victory.

The war brought several lessons. Both sides relied heavily on armed

merchantmen to supplement their state navies, standard practice at that

time.7

But in this war, the weaknesses of the armed merchant ships were

painfully obvious: they were slower and less maneuverable than spe-

cialized warships, and too lightly armed and built to inflict or withstand

intense firepower. Moreover, the small warships of the Dutch were no

match for the English battleships. And finally, as the English demon-

strated at Gabbard Shoals in 1653, the tactic of fighting in line-ahead—

what was to become known as the line of battle—was an enormously

effective means of concentrating firepower.

These lessons induced the Dutch to cut their reliance on armed mer-

chant ships in favor of specialized warships, and to increase the number

of battleships in their fleet. Meanwhile, political turmoil in England at-

tenuated the English response to the war’s lessons. Thus, by the onset of

5 On the government’s view of the navy, see Glete, Navies, p. 180. Israel, Dutch Republic,

pp. 714–15; and Rodger, Command, pp. 8–12, emphasize the religious and political forces that

led to war. 6 In forming a line of battle, the ships of a fleet lined up bow to stern, with the commanding

officer’s ship roughly in the center of the line. This formation made it more difficult for enemy

ships to attack the vulnerable bow and stern of one’s vessels; and because most of each ship’s

cannons were arrayed along its sides, the line of battle concentrated firepower against an enemy,

and ensured that one did not fire into one’s own ships. The line of battle replaced melee tactics,

in which ships had clustered around their commander’s ship and sailed into the midst of the en-

emy fleet that was similarly arrayed, firing at will at a convenient target, which hopefully be-

longed to the enemy. See Rodger, Wooden World; and Palmer, “‘Military Revolution’.” 7 See Glete, Navies; and Rodger, Safeguard.


the second war in 1664, although both fleets were more powerful than

in 1652, the Dutch were no longer at a substantial disadvantage. Most

importantly, by the Four Days’ Battle of June 1666 the Dutch finally

concluded that the line of battle was superior to melee tactics. By the

war’s end in 1667, it was clear that specialized warships, headed by

powerful battleships arrayed in the line of battle, were the future of na-

val warfare.8

Mindful of these events, France was transforming its navy into a

modern force, investing heavily in ships, particularly battleships, and

creating a permanent officer corps and a series of permanent naval

dockyards.9

These developments in turn set the stage for Samuel

Pepys’s successful campaign to upgrade the British fleet through a

large-scale building program.10

On a smaller scale, Denmark-Norway

and Sweden were also strengthening their state navies, both in number

and average size of ships.

Widespread warfare in the 1670s put the new fleets and their tactics

to the test, with England, France, and Sweden allied against Spain,

Netherlands, and Denmark-Norway. The battles proved to be tactically

indecisive, but they cemented the lessons of the first two Anglo-Dutch

wars: Coordinated, concentrated firepower and the ability to withstand

it were the keys to victory. By 1680 the major powers of Europe had es-

tablished the character of the ships and tactics that dominated naval

warfare for the next century and a half. It was a world that the captains

of 1650 would have had trouble recognizing.

All of this had come at substantial cost. Aside from the resources de-

voted to the unprecedented ship-building programs, the battles of this era

had been bloody and destructive. Numerous Dutch ships had been sunk in

the first two Anglo-Dutch wars, an outcome routinely fatal for many of

the crew. During the second Anglo-Dutch war of 1664–1667, more Brit-

ish post-captains were killed in combat than were to die in combat during

all of the Great Wars of 1793–1815, and the carnage during the third An-

glo-Dutch war of 1672/73 fully matched that of the years 1793–1815.

How would the British commanders of the future put to work their ships,

their tactics, and their knowledge of both during future wars?

THE COMBAT DECISION

Contact between hostile sailing vessels did not always result in com-

bat. Except in conditions of greatly reduced visibility, vessels did not

8 See Palmer, “‘Military Revolution’”; and Tunstall, Naval Warfare, chapter 1. 9 Glete, Navies, pp. 187–88. 10 Ibid., pp. 192–95.


TABLE 1

THE OUTCOMES OF COMMAND DECISIONS

Decision

Fight Flee

Correct Survival; capture or sinking

of enemy vessel

Survival; retention of command

Result

Incorrect Death; loss of ship by capture

or sinking

Court martial; disgrace and loss of

command; perhaps execution

Note: See the text for discussion.

simply materialize next to one another. Instead, they sighted each other

from a distance of several miles, well beyond the range of their can-

nons. For combat to occur, at least one commanding officer (admiral or

commodore of a fleet or squadron, or captain of an individual vessel)

had to choose it. Even this was only a necessary condition. If one com-

mander demurred and was properly situated (e.g., to windward), even a

determined effort by the other to engage might prove futile.

We characterize the combat decision of a commanding officer as a

binary choice to “fight” or “flee.” We also treat the outcome as binary:

either “correct” or “incorrect.” The 2 x 2 matrix in Table 1 summarizes

this view. The entries in the interior are the consequences of the com-

manding officer’s decision and whether it was correct. Thus, as shown

in the northwest quadrant, the choice to fight, if correct, resulted in sur-

vival for the commanding officer and victory for his ship, squadron, or

fleet. The other entries are to be interpreted similarly (see Appendix I

for a more complete analysis).

Clearly, there are potential ambiguities. A commander might “de-

cide” to flee, yet be compelled to engage in combat by an enemy com-

mander who chose to fight. What we observe is combat and its out-

come, not the mental states of the participants, so we record an entry in

the left column of the table. Similarly, the decision to fight could yield

survival for the commanding officer, despite the loss of his ship, just as

it could lead to his demise, despite victory for his ship or fleet (as in the

famous case of Nelson at Trafalgar). In our empirical work, we thus

treat the individual outcomes of decision-making (survival or death)

separately from the tactical outcomes (victory or defeat).

In the early years of the revolution in naval warfare, commanders

made numerous mistakes, fighting when they should have fled, and

fleeing when they should have fought. But for those who survived, there

was an opportunity to learn: from their own mistakes and those of their

predecessors. Learning could even be institutional, as in the creation of


Fighting Instructions, official documents that summarized the general

principles according to which combat should be conducted. As knowl-

edge accumulated, the error rate of commanders should have fallen. The

result would be fewer combat fatalities and greater success in combat.

Another type of learning surely occurred during the century and a

half covered by our data, namely a rise in the effective strength (combat

ability) of a vessel or fleet of any given nominal strength. Indeed, his-

torical accounts suggest that British commanders were sharpening those

skills relevant once combat was imminent or underway. For example,

improvements were clearly discernable in ship handling, gunnery, tac-

tics, navigation, signaling, fleet command and control, and victualing

and health.11

In each case, the ability of British commanders to adminis-

ter, concentrate, and avoid lethal firepower was enhanced. If such learn-

ing occurred at a rate faster than among Britain’s enemies the result

would be an increase in the relative strength of British ships, and grow-

ing British combat success.

LEARNING BY DOING

Productivity increases have been seen in some industries even absent

explicit investment in physical or human capital. The explanation for

such observations has been that as firms produce more goods they learn

to improve the production process, i.e., there is accumulation of knowl-

edge as a side effect of economic activity. Such knowledge accumula-

tion is known as learning by doing.

Learning is the product of experience and takes place during or as a

result of an activity.12

The first explicit empirical work on learning by

doing was by T. P. Wright, who observed that labor-hours necessary to

produce an airframe was a decreasing function of the cumulative num-

ber of airframes produced in prior periods. Allan Searle investigated

learning in the shipbuilding industry. Kenneth Arrow developed a theo-

retical model of the process, emphasizing that learning by doing is the

product of experience, and is subject to sharply diminishing returns.

Subsequent studies have elaborated on Arrow’s model, and extended

our empirical knowledge. Armen Alchian analyzed airframe production,

and Leonard Rapping focused on shipbuilding; both used data from

World War II. Paul David and Jeffrey Williamson assessed the extent of

learning by doing in the American textile industry during the early nine-

11 See Cordingly, Billy Ruffian; Marcus, Naval History; Creswell, British Admirals; Sobel,

Longitude; Tunstall, Naval Warfare; Palmer, “‘Soul’s Right Hand’”; Rodger, “Image” and

Wooden World; and Harbron, Trafalgar.12 Learning may also take place as a result of observing, a fact to which we return later.


teenth century. More recent papers by Byong-Hyong Bahk and Michael

Gort and by Lanier Benkard have examined in more detail the empirical

findings of earlier studies.13

Learning by doing can be analyzed by assuming a production func-

tion as simple as the Cobb-Douglas, tttt ELAKy , where A is tech-

nology, yt is production at time t, Kt is capital, Lt is labor, and Et is a

measure of experience. The most common measures of experience have

been cumulative output, cumulative investment, or time elapsed since

the beginning of the activity.14

In examining learning by doing, it is possible to investigate how the

firm obtains more output from given inputs or how it reduces the costs

of producing a given output. In our case, the available data dictate the

approach we take. The records of failure—captains who were killed in

combat and ships that were either sunk or captured in combat—are

available, so we use them. We think of the cost of production (combat)

as being the loss of a captain or ship, and the experience that helps de-

termine this cost as being the cumulative sum of such losses in the past.

Thus, we view the captains of the Royal Navy as collectively learning

from the past failures of their predecessors. Although individual cap-

tains surely did learn from their own experiences, the learning in which

we are interested here took place over a great span of time (a century

and a half) and was the product of the experiences of the thousands of

Royal Navy captains who served over this period. That is, we view the

captains of 1800 as benefiting from their own experience, and from the

experience of the captains of 1740 and those of 1680. Some of this

knowledge was passed along formally in the Fighting Instructions. But

more importantly, it was accumulated and transmitted through the ex-

traordinary mentoring and evaluation process of the Royal Navy, as we

discuss below. In essence, the command structure of the navy, from

Admiralty Board to midshipman, was organized to ensure that the nec-

essary elements of success—and survival—were passed from one gen-

eration of commanders to the next.15

13 Wright, “Factors”; Searle, “Productivity”; Arrow, “Economic Implications”; Alchian, “Air-

frame Production Functions”; Rapping, “Learning”; David, “Learning”; Williamson, “Embodi-

ment”; Bahk and Gort, “Decomposing Learning”; and Benkard, “Learning.” 14 Some authors, such as Benkard, “Learning,” have investigated whether forgetting—decay

in the stock of knowledge—may occur. When forgetting is possible, the empirical specification

is readily modified. Given that Et = Yt, where t goes from 0 to T–1 (one period before the ref-

erence period), to adjust for forgetting, one simply specifies Et = Et–1 + Yt–1, where Yt is output

at time t, and (1 – ) is the rate of depreciation of knowledge. 15 An alternative approach would entail a survival analysis on individual commanders or ships,

examining how the cumulative combat experience of commanders influenced their survival or that

of their vessels and crew in combat. As a practical matter this is not likely to be feasible, because

such information is available only spread across many thousands of log books and muster books.


COMBAT FATALITIES

Published data on total casualties are sporadic, even for the British

navy during the well-documented wars of 1793–1815, so our focus is on

two measures for which data are available—fatalities among captains

and ships captured or sunk in action. Nevertheless, there are compelling

reasons why our measures are informative and valuable. Warships were

the most complex and costly pieces of capital extant during this period.

The capture or sinking of one in combat was an important accomplish-

ment for the victor and a serious loss for the vanquished. Successful

captains were valuable instruments of war, and their skills arguably had

the largest effects on the outcomes of battles. Given their exposed posi-

tions directing combat from the quarterdeck, captains had strong incen-

tives to learn more effective means of combat, and we expect their

learning—or lack thereof—to show up in their combat fatality rates.

We argue that three factors determine combat fatalities among cap-

tains: their exposure to combat, the stock of knowledge possessed by

them, and the intensity of the wars in which they fought. To construct

fatalities we aggregate data on captains killed in action over five year

periods, because reliable data on rated ships is available only at five

year intervals, evenly divisible by five.16

For a given year of ship data,

fatalities are thus the combat fatalities during the five years centered on

the year in question. As an alternative measure of the combat outcomes

of captains we also examine the combat hazard rate among them, which

we define as fatalities divided by the number of rated ships in the Brit-

ish fleet. Summary statistics on this and other key variables are shown

in Table 2.

The exposure of captains to combat is the product of the number of

rated ships and the number of years of combat during the five years cen-

tering on each observation. When exposure to the hazards of war is

higher, the number of captains killed in action should be higher,

whether the added exposure is due to more ships in action, or to a

longer period of war during the five year span of measurement.

The captains of 1690, we argue, knew more about modern combat

techniques than did their predecessors who fought in the 1660s or

1670s. They were thus less likely to fight when they should flee, and

hence less likely to errantly die in combat. They also knew better how

to conduct their combat, and thus were more likely to be victorious over

16 Interpolating the ship data between the available dates would nominally give us more data,

but any such interpolation would be fundamentally arbitrary. For the years 1720–1815, see

Glete, Navies, tables 23-3, 23-9, 23-17, and 23-43; for 1820 and for the years before 1720, Pro-

fessor Glete provided us with his unpublished estimates.


TABLE 2

SUMMARY STATISTICS, 1670–1815

(N = 30)

Variable Mean Std. Dev. Minimum Maximum

Fatalities 4.7 5.4 0 16

Combat hazard rate 0.028 0.041 0 0.152

Knowledge 111.7 35.3 33 170

Exposure 524.6 554.4 0 1,770

British fleet 201 70 92 354

Foreign fleet* 166.5 101.8 2 393

British losses 5.3 7.5 0 26

Foreign losses 28.9 42.5 0 150

Loss ratio* 0.19 0.18 0 0.65

* Foreign fleet and the ratio of British to combined British and foreign losses are defined only

during time of war, so N = 22 for these variables.

Note: The minimum reported value of 2 for foreign fleet refers to the American fleet in 1775,

prior to France’s entry into the war.

Sources: See the text and Appendix 2.

their enemies. As our measure of the growing stock of knowledge about

modern combat, we compute the cumulative fatalities prior to the ob-

servation in question.17

Not all wars are the same, and hard-fought wars are likely to produce

more casualties. Measuring the intensity of combat is not easy, and we

have tried several alternatives. The measure of intensity on which we

have settled is, for each five year period, the log of the number of pages

of combat descriptions in William Laird Clowes’s seven-volume history

of the Royal Navy. Although this measure is crude and imperfect, it is

statistically superior to the other measures we have examined.18

It also

has conceptual reasons to recommend it. For example, more important

battles are likely to be more fiercely contested and also are likely to be

more closely examined and extensively written about by historians.

17 An alternative measure of knowledge is the cumulative number of British ships lost in prior

combat. Such a measure is inferior to the measure of knowledge discussed in the text, in the

sense that the fatality measure yields a higher log-likelihood ratio, and when the ship-loss meas-

ure is added to a regression equation that contains the fatality measure, the coefficient of the

ship-loss variable is not statistically different from zero, while the coefficient and standard error

of the fatality measure are substantively unaffected. As we note in Appendix 2, only about 20

percent of the time is the combat loss of a ship accompanied by the death of its captain, and vice

versa.18 The lengths of the Clowes narratives also depend on the duration of the war during the five

year period and perhaps on the size of the navy, so our interpretation of this variable as “inten-

sity” is only correct if we control for these other factors—which we do. Other measures of in-

tensity we have examined include the log of real expenditures on the navy and the log of the

number of pages devoted to “operations” in Rodger, Command. The measure we use is superior

in two ways: when included alone as a measure of intensity it yields the largest value of the log-

likelihood function, and when included with other measures of intensity, only it is statistically

significant among them.


Moreover, even if a protracted, intensive engagement turns out that way

simply by chance, it is still likely to produce both more casualties and

damage, and more material suitable for historical narrative.

Estimates

The data on captains killed in action are a classic example of count

data. Like much count data, ours exhibit over-dispersion relative to a

Poisson distribution, with a variance about six times the mean. To esti-

mate the determinants of captains killed in action, fatalities, we thus use

negative binomial (rather than Poisson) regression. The results are shown

in column (1) of Table 3.19

The signs of the estimated coefficients of ex-

posure and knowledge are clearly consistent with the combat decision

model: exposure to greater hazards led to higher fatalities, yet over time

captains were building on the accumulated knowledge of their predeces-

sors, so the fatalities associated with any given combat exposure were fal-

ling.20

The estimated coefficient of intensity is also as one would expect:

fatalities were higher in wars in which combat was more intense.21

An alternative measure of the risks of combat is the hazard rate, de-

fined as ratio of captains killed in each period to the number of rated

ships in the British fleet during that period. Thus, in column (2) of Ta-

ble 3, using fractional logit regression, we examine how the hazard rate

was affected by knowledge, exposure, and intensity.22

Again we see that

exposure to more combat led to a higher hazard rate, yet over time the

hazard rate was falling as captains built on the accumulated knowledge

of their predecessors.23

19 Because our fatality data do not begin until 1660, rather than impose an arbitrary initial

value of zero for cumulative fatalities, we exclude 1660 from the estimates that follow. Includ-

ing the initial observation does not substantively alter the results, although its does generate

considerably more overdispersion. 20 Dickey-Fuller tests reveal that all four of our key variables are stationary. Knowledge is the

sum of fatalities over time, so it might be thought that it is nonstationary. In fact it is stationary.

To see why, let Ft be fatalities in time t and Kt, the sum of fatalities from t – N to t – 1, be

knowledge. According to our theory, Ft = Kt + et, and by construction it must be true that Kt =

Ft–1, where is the difference operator. This implies that Ft = Kt + et = Ft – 1 + et. Thus,

we can write Ft = (1 + ) Ft–1 + et = et / [1 – (1 + )L], where L is the lag operator. Cumulat-

ing Ft from t – N to t – 1, we find that [1 – (1 + )L]Kt = ( et– 1) = (et–1 – et–N–1), implying that

knowledge is stationary. The intuition here is simple. As learning occurs, fatalities decline, so

increments to knowledge also decline over time. As experience grows, knowledge acts as

though it is approaching an asymptotic value (perfection, one presumes), so its variance is finite. 21 Using the test statistics recommended by Cameron and Trivedi, Regression Analysis,

pp. 227–30, we cannot reject the hypothesis of no serial correlation in the residuals associated

with our estimates. 22 Wooldridge, Econometric Analysis, pp. 661–63. 23 It is possible (and certainly suggested by the narratives of the period) that, at the onset of

war, captains and their crews were less efficient than they became as the war progressed. Hence,


TABLE 3

FATALITY AND HAZARD RATE ESTIMATES

Fatalities

(negative binomial regression)

Dependent Variable: Five Year Combat

Fatalities among British Post Captains

(standard errors in parentheses)

Hazard Rates

(fractional logit regression)

Dependent Variable: Five Year Ratio of

British Post Combat Fatalities to Rated Ships

(robust standard errors in parentheses)

(1)

1670–1815

(2)

1670–1815

Knowledge –0.035

(0.004)

Knowledge –0.044

(0.004)

Exposure 0.0014

(0.0004)

Exposure 0.001

(0.0004)

Intensity 0.66

(0.16)

Intensity 0.81

(0.18)

Constant 1.70

(0.45)

Constant –2.76

(0.48)

N 30 N 30

Log likelihood –50.4 Log pseudo-likelihood –2.44

Notes: Estimates are substantively unaffected if linear, quadratic, or cubic functions of time are

included in the regressions, or if estimates are performed for subsamples 1690–1815 or 1710–

1815. See the text for discussion.


Knowledge is highly correlated with time (r = 0.97), so we have re-

estimated the regressions in columns (1) and (2) with linear, quadratic,

and cubic functions of time included. In each case, the estimated values

of the coefficients of knowledge, intensity, and exposure are substan-

tively unaffected, and the coefficients of these variables remain statisti-

cally significant at conventional levels (p < 0.05). In no case are any of

the coefficients of the time variables statistically different from zero.24

observations preceded by peace might be systematically different from those preceded by war.

We have created an indicator variable that takes a value of one for observations preceded by

peace and zero else, and re-estimated our key regressions to test for differences in intercept or

slope coefficients for observations preceded by peace. We find no differences, but this is not too

surprising, given that enemy captains and their crews typically were also emerging from peace;

with the small number of observations we have, the power of a test such as this is likely to be

low.24 It is possible that it is the mere cumulative exposure to combat, rather than losses in combat,

that is responsible for learning, perhaps because observing combat is as good as engaging in com-

bat as a means of learning. To test this, we have cumulated past values of our exposure variable

and re-estimated the regressions in columns (1) and (2) with this cumulative exposure variable in-

cluded. The coefficient of the cumulative exposure variable is not statistically different from zero,

and its inclusion has no substantive effect on the coefficient of knowledge in either regression. It is

also possible that Britain’s growing success was because it was devoting ever more resources to

naval warfare, relative to her enemies. To test this hypothesis, we have computed the ratio of the

British fleet to the combined fleets of her enemies in each period and included this as regressor in

our key regressions. The estimated coefficient of this variable is statistically insignificant, and it

inclusion does not substantively affect the estimated coefficients of the other variables.


0

3

6

9

12

15

18

1670 1690 1710 1730 1750 1770 1790 1810

Fat

alit

ies

Captains killed in action Predicted killed in action

FIGURE 1

ACTUAL AND PREDICTED COMBAT FATALITIES, 1670–1815

Note: Predicted values are based on column (1), Table 3.


The high fatality rates of the early years of our sample account for an

important component of the variance in the observed fatalities; indeed,

36 percent of the fatalities in our sample occur before 1680. We have

therefore re-estimated the regressions in columns (1) and (2) excluding

all of the seventeenth century data. Doing so has substantively no effect

on the estimates of either equation. We infer that the early, high-fatality

years of our sample were not fundamentally different from later years—

except that captains initially had little knowledge of how to survive the

rigors of modern combat, and so were much more likely to be killed for

their efforts.25

Empirical Implications

The regression results in column (1) enable us to predict the expected

fatalities for each five year period, and thus compare these predictions

with the observed data. Figure 1 shows the results of doing so. Despite

the abrupt and large period-to-period swings in fatalities, it is evident

that the estimated model closely tracks both the timing and magnitude

of those changes.

25 The elasticities reported in Table 4 are also substantively unaffected when, as discussed in

the text, we truncate the data to exclude the early, high-fatality-rate data.


TABLE 4

IMPLIED ELASTICITIES OF FATALITIES WITH RESPECT TO KNOWLEDGE,

EXPOSURE, AND INTENSITY

Independent Variable Elasticity

Knowledge –3.9

Exposure 0.8

Intensity 0.7

Note: Estimates are based on column (1), Table 3.

We can also use the estimates in column (1) to deduce the implied

elasticities of fatalities with respect to knowledge, exposure, and inten-

sity. These elasticities, evaluated at the sample means, are shown in Ta-

ble 4. Although intensity and exposure each have only modest effects

on fatalities, knowledge has quite a large impact. The importance of

learning in determining fatalities can be confirmed by considering a

simple counterfactual experiment: Ceteris paribus, if the captains of the

Revolutionary and Napoleonic Wars (1793–1815) had possessed the

same combat knowledge as their counterparts of 100 years before

(1693–1715), how many would have died in combat? The answer is that

instead of 27 being killed, 208 would have died.26

It is also useful to isolate the effects of learning on hazard rates over

time. Using the estimates shown in column (2) of Table 3, we set the val-

ues of exposure and intensity equal to their means for our full sample, and

predict hazard rates as a function of the varying stock of knowledge over

the period. We average these predictions over each of the 20 year subpe-

riods of our era. As the first row of Table 5 reveals, during the early years

of our sample a post-captain had about a 16 percent chance of being

killed in any five year time period in which exposure and intensity were

at their means. As is apparent from the steep initial declines in the hazard

rate, roughly 90 percent of the captains’ learning took place during the

first 60 years of our sample. Nevertheless, learning continued through the

eighteenth century, albeit at a much slower rate. The last row of Table 5

reveals that by the Napoleonic War, the combat hazard rate for captains

had fallen to about one chance in a thousand.27

26 In doing this calculation we hold exposure and intensity at their 1793–1815 values and re-

place the values of knowledge with its mean for 1693–1715. 27 The quality of British guns improved relative to those of her enemies during the last years

of our period, due to a new gun design by Bloomfield, the introduction of the gunlock, and the

invention of the carronade. (Rodger, Command, pp. 377–78, 420–21.) Although these innova-

tions would all be expected to improve British performance during the years 1793–1815 relative

to the past, we can find no statistical support for this. As a practical matter, the number of fatali-

ties and the combat hazard rate (and our measures of combat success, discussed below) are all

quite close to their predicted values during the French Revolutionary and Napoleonic Wars.

This is not to say that the improvements were not important, only that we cannot discern their

effects in our data.


TABLE 5

THE EFFECTS OF LEARNING ON HAZARD RATES, 1670–1810

Period Predicted Hazard Rate

1670–1690 0.160

1690–1710 0.047

1710–1730 0.010

1730–1750 0.009

1750–1770 0.005

1770–1790 0.003

1790–1810 0.001

Notes: Hazard rates are obtained from column (2), Table 3, by setting intensity and exposure

equal to their mean values and allowing knowledge to vary over time. For each 20 year block of

time, the predicted five year hazard rates are averaged to yield the numbers shown here.

Sources: See the text.

THE OUTCOMES OF BATTLE

The results thus far must be tempered by two considerations. We

cannot reliably observe instances in which captains correctly chose to

flee in the face of a superior enemy force (the northeast quadrant of

Table 1). If there were many such encounters for our period, then a

declining fatality rate among captains would be of little value to the

Crown. Moreover, aside from draws, every observable contact be-

tween two enemies results in a victory or defeat. Skillful, knowledge-

able captains are more likely to survive even unsuccessful combat than

are unskilled, ignorant captains, because able captains will refrain

from errantly extending losing combat. Yet one of the two captains

must lose, regardless of ability. When it comes to victories and losses,

it is relative skill or ability that is important, and over time it is rela-

tive rates of learning that determine the ebb and flow of victories and

losses. Even if British captains were learning—and learning rapidly—

if their enemies (most notably the French) were learning even faster,

combat fatality rates among British captains could be declining, even

though they were losing more often.

Countering such a view is that this period of falling British fatalities

culminated with record-low levels of combat hazard rates, and a crush-

ing British victory at sea over her enemies—and a subsequent century

of hegemony at sea. Indeed, M. A. J. Palmer characterizes the eight-

eenth century as a era in which the Royal Navy won “victory after vic-

tory.”28

Still, it is useful to examine other evidence.

28 Palmer, “‘Soul’s Right Hand’,” p. 692.


TABLE 6

BRITISH COMBAT LOSSES AS A FRACTION OF TOTAL COMBAT LOSSES

(fractional logit regressions)

Dependent Variable: Ratio of British Losses to Combined Losses

(robust standard errors in parentheses)

(1)

1670–1815

(2)

1670–1815

Knowledge –0.031

(0.010)

–0.024

(0.006)

Exposure 0.0013

(0.0009)

Intensity –0.34

(0.57)

Constant 2.22

(1.32)

1.31

(0.77)

N 22 22

Log pseudo-likelihood –6.2 –6.3

Notes: Observations are weighted by total ships (British plus foreign) lost in combat.


Victory at Sea

Most of the ships lost at sea during the age of sail were victims of ad-

verse weather or navigational errors. As with combat fatalities, we focus

here solely on losses that were the direct result of combat. As discussed

in Appendix 2, there was little overlap between British ships lost in

combat and combat fatalities among British captains, making combat

ship losses a largely independent measure of the learning process.29

For

each five year period we sum the British post ships sunk or captured by

the enemy, and for Britain’s enemies we sum their ships of 20 guns or

more sunk or captured in combat.30

We then compute the loss ratio as

British combat losses in combat divided by the total combat losses

(British plus foreign), a number that can range from zero to one (see

Table 2); hypotheses regarding the determinants of this ratio can be

tested using fractional logit.

Although the theory implies that knowledge should reduce British

losses relative to foreign losses, the theory is silent on whether exposure

or intensity should affect this ratio, so we estimate the effects of knowl-

edge both including and excluding these variables. The resulting frac-

tional logit estimates are in Table 6, where we see that knowledge im-

portantly enhanced British success in combat. Because neither intensity

29 Indeed, the correlation between the two measures (r = –0.21) is not statistically different

from zero (p = 0.25). 30 British losses are from Hepper, British Warship Losses; and foreign losses are from

Clowes, Royal Navy.


TABLE 7

PREDICTED BRITISH SHARE OF COMBAT SHIP LOSSES, 1670–1810

Period British Share of Total Combat Ship Losses

1670–1690 0.449

1690–1710 0.378

1710–1730 0.211

1730–1750 0.189

1750–1770 0.166

1770–1790 0.133

1790–1810 0.084

Notes: Predictions are based on estimates in column (2), Table 6, with the predicted British

share of losses averaged for each 20 year period.

Sources: See the text.

nor exposure have statistically significant effects on British success, we

exclude them in column (2). The results are the same: as the knowledge

of British captains grew, their success improved.

There are some noteworthy features of this measure of learning, high-

lighted in Table 7. The right hand column shows the predicted propor-

tion of the ships lost in combat that would be British. Thus a number

equal to 0.5 would imply that Britain would be expected to suffer losses

equal to those she inflicted on her enemies, because half of all losses

would be British ships. We see in the first row that during the early

years of our period, England was in fact suffering almost the same

number of ship losses as she was inflicting. By the 1710–1730 period,

however, learning had brought Britain almost a four-to-one advantage

in combat outcomes. By the Napoleonic War, Britain was inflicting

losses more than ten times as great as she was suffering. If we compare

these numbers with those in Table 5 showing fatality rates we see an-

other feature. Although most of the decline in fatality rates comes dur-

ing the first third of our period, the improvement in relative combat per-

formance is spread more evenly over the entire period 1670 to 1810.

Comparing Combat Losses

The results thus far are consistent with a process in which British

captains were learning faster than their foreign counterparts. Here we

separately investigate British losses and foreign losses, in an effort to

refine our understanding of this process. We begin with a simple ques-

tion: Does our measure of knowledge, which we claim reflects the state

of knowledge among British captains, have an effect on foreign

losses?31

We then construct an alternative measure of knowledge, based

31 If our measure of British knowledge cut foreign losses at the same rate as British losses, we

would have doubts about what it was measuring. Ideally, we would have constructed a foreign


TABLE 8

COMBAT LOSSES OF RATED SHIPS

(negative binomial regressions)

Dependent Variable: Rated Ships Sunk or Captured in Battle

(standard errors in parentheses)

(1)

British Losses

1670–1815

(2)

Foreign Losses

1670–1815

(3)

British Losses

1670–1815

(4)

Foreign Losses

1670–1815

Knowledge:

fatalities

–0.023

(0.006)

–0.002

(0.005)

— —

Knowledge:

ship losses

— — –0.019

(0.005)

–0.001

(0.001)

Exposure 0.0023

(0.0007)

0.0001

(0.0006)

0.0022

(0.0006)

0.0001

(0.0006)

Intensity 0.41

(0.27)

1.32

(0.24)

0.46

(0.23)

1.38

(0.24)

Constant 0.77

(0.84)

–1.84

(0.75)

0.46

(0.54)

–2.04

(0.65)

N 30 30 30 30

Log likelihood –61.1 –94.4 –59.7 –93.6


Notes: In columns (1) and (2) our measure of knowledge is the lagged sum of fatalities among

British captains, as it was in our estimates of combat fatalities. In columns (3) and (4) our meas-

ure of knowledge is the lagged sum of past ships lost in combat—cumulative British losses in

column (3) and cumulative foreign losses in column (4). See text for discussion.

on data that is available for both British and foreign fleets. Under both

approaches, our dependent variable is the number of ships lost in com-

bat (British or foreign), and our measures of exposure and intensity are

the same, except that the measure of foreign exposure entails multiply-

ing the size of foreign fleets by the duration of the war.

The dependent variables in Table 8 are the number of ships lost in

combat by Britain (columns (1) and (3)) and by her enemies (columns (2)

and (4)). In columns (1) and (2) our measure of knowledge is the lagged

sum of fatalities among British captains, as it was in our estimates of

combat fatalities. This measure has a large statistical and substantive im-

pact on British losses, but effectively no impact on foreign losses, either

numerically or statistically. Given our interpretation of this measure of

British knowledge, this is not surprising, but it is reassuring.32

analogue of our British fatality-based measure, but that was impossible, because there is no

source of combat fatalities among foreign captains. 32 Improved British knowledge might even increase foreign losses. That it does not do so may

reflect a conscious decision by the enemy to keep its fleets out of harm’s way. Certainly Napo-

leon placed a high weight on maintaining a “fleet in being,” even one in port, rather than risk

annihilation by the British. This interpretation is consistent with the fact that exposure does not

have a statistically significant effect on foreign losses; if foreign ships were at anchor rather

than at sea, our exposure variable would do a poor job of measuring their actual exposure to

combat. See also our discussion of the innovation process, below, as well as Appendix 2.


In columns (3) and (4) knowledge is the lagged sum of past ships lost

in combat—cumulative British losses in column (3) and cumulative for-

eign losses in column (4). Again, we see strong evidence of learning by

doing in the British estimates: as knowledge accumulates over time, ex-

pected losses fall.33

In sharp contrast, although there is a hint of learning

among foreign commanders, the evidence is weak. The coefficient of

knowledge in equation (4) is one-twentieth the magnitude found in

equation (3), and although negative, it is not statistically different from

zero at conventional levels. If we pool the data on ship losses for British

and foreign, and estimate a combined ship-loss regression, allowing for

clustering of residuals by year, we confirm the results of Table 8: the

coefficient of knowledge is not statistically different from zero for for-

eign nations, while the coefficient of knowledge for Britain is negative

and statistically different from zero and from the coefficient of knowl-

edge for foreign nations: Britain was learning faster than her enemies.34

We have examined two other approaches to foreign losses. The for-

eign nations we treat as Britain’s enemies sometimes battled among

themselves, engaged in warfare against other nations, and (as with the

Anglo-Dutch alliance against the French in the 1690s) sometimes allied

themselves with Britain. Potentially, they gained valuable knowledge in

such endeavors, knowledge not reflected in the estimates of column (4)

of Table 8. Hence, we have collected foreign ship losses from engage-

ments other than those in which Britain was the foe.35

Cumulating these

with the losses suffered against Britain gives us an alternative and more

comprehensive measure of the knowledge of foreign commanders. Nev-

ertheless, even when we use this potentially superior measure in re-

estimating equation (4) of Table 8, the results are substantively and sta-

tistically the same: there is essentially no evidence of learning on the

part of foreign commanders.36

We also have created a panel data set in

33 The elasticity of ship losses with respect to this measure of knowledge is –1.8, somewhat

below the elasticity of –2.4 implied by using fatalities as the measure of knowledge. Although

not shown explicitly here, estimates for the subperiods 1690–1815 and 1710–1815 are quite

similar. 34 As discussed in note 24, it is possible that observing (in addition to doing) was an effective

means of learning. But including either cumulative British exposure or cumulative foreign ex-

posure has no substantive effect on the impact of knowledge and neither of these cumulative ex-

posure variables have coefficients statistically different from zero. 35 We have supplemented the material in Clowes, Naval History, with data from Sanderson,

Sea Battles; Tunstall, Naval Warfare; Jenkins, History; Glete, Navies; and Lyon, Sea Battles. It

is possible that we have missed some minor engagements in compiling the supplemental foreign

losses, but cross-checking of sources suggests that nothing we have missed will alter our results

in any meaningful way. 36 The similarity between the conclusions produced by the two measures of foreign knowl-

edge is not entirely surprising. Foreign nations were fighting Britain in a very large proportion


which there are three comparison foreign fleets: French, Spanish, and

“all other” enemies. The results are substantively identical to those re-

ported in Table 8: Britain was learning, while her enemies were not.

THE INNOVATION PROCESS

Naval warfare is a complex endeavor and the 150 years covered by

our study witnessed political, administrative, and logistical changes on a

huge scale. We have developed important new quantitative measures of

the progress of naval warfare over this period, and presented compelling

evidence that Britain’s success may be viewed as the proximate result

of learning by doing over a long span of time. We cannot hope to illu-

minate every element of why Britain succeeded where her enemies did

not. But we can suggest two key factors that have not received suffi-

cient attention in the existing literature: opportunity and motive.

Opportunity

The British navy spent more time at war than did any of her enemies,

and did so actively at sea, rather than bottled up in port by continental

strategic considerations, inadequate finances, or enemy blockade. Year

after year of convoy, patrol, blockade duty, and combat in all seasons

enabled the commanders and sailors of the British fleet to master

the real essentials of naval tactics . . . , the well drilled line of battle and such

flexibility as would enable advantage to be taken of any opportunities the enemy

might offer.37

The line of battle was both the supreme offensive and defensive

weapon of the era; hence, it was prone to yield inconclusive encounters,

particularly when one of the fleets was French, for a fundamental

French strategy of much of the era was to avoid decisive combat.38

As

Admiral Sir John Jervis, writing when he was a post captain, remarked

after the battle of Ushant in 1778:

of the battles in which appreciable numbers of rated ships were lost, so the correlation between

the two measures of foreign knowledge is 0.99. 37 Creswell, British Admirals, p. 39. 38 One section of the French Fighting Instructions of the eighteenth century is entitled “To

Avoid an Engagement.” There is no mention, nor even a suggestion, of any such notion in the

British Fighting Instructions. As Creswell, British Admirals, p. 48, remarks, “It is perhaps rea-

sonable to detect here a difference in outlook that had a continuous effect throughout the eight-

eenth century.”


. . . two fleets of equal force can never produce decisive events, unless they are

equally determined to fight it out, or the commander-in-chief of one of them

bitches it so as to misconduct his line.39

In Jervis’s view (shared by others) decisiveness required avoiding mis-

takes and capitalizing on the enemy’s mistakes. The way to do both was

practice and more practice: learning by doing.

The British were at war at sea during 77 of the 156 years between

1660 and 1815, some 20 percent more than France or Spain, and vastly

more than any of her other enemies. Britain also enjoyed a relatively

stable political system and a strong financial system, and her two chief

opponents of the eighteenth century were hamstrung by other factors.

Crucially, in all of the wars with Britain except the War of American

Independence, the resources of the continental powers were drained by

the necessity of fielding large land forces; conflict at sea was only part

of a larger struggle. The realities of geography meant that island Britain

could—indeed had to—focus much more of her resources on the sea.

This not only meant a larger navy; it also meant a navy that spent much

more of its time at sea.40

Spain’s position was complicated by the fact that it had let its navy

sink into ruin during the seventeenth century. A concerted effort to re-

build during the eighteenth century brought the Spanish fleet much

closer to parity with the British. Yet Spain suffered from chronic man-

ning problems that sharply hampered her ability to bring an experi-

enced, effective fighting force to bear against Britain.41

France had

enlarged and modernized its fleet late in the seventeenth century, and

quickly adopted the line of battle, but financial exigencies in the 1690s

caused it to redirect resources to the army; by 1720 the French navy was

a shadow of its former self. A renewed French commitment to its navy,

particularly after the debacle of the Seven Years War, finally bore fruit

during the War of American Independence, when it was freed of the

demands of large-scale continental conflict.42

But French designs for

39 Cited in Palmer, “‘Soul’s Right Hand’,” p. 695, emphasis in original. 40 See Glete, Navies, pp. 212–20; and Rodger, Command.41 Mühlmann, Die reorganization der Spanischen Kreigsmarine, pp. 123–59. 42 Palmer, “‘Soul’s Right Hand’,” argues that British success against the French from 1739

onwards was in part due to the decentralized command and control structures adopted by

Vernon, Anson, Hawke, and Nelson. This decentralization was reversed under Howe during the

American Revolution—years of malaise for the British fleet. It is worth noting that Figure 1 re-

veals that more than the predicted number of British captains were killed during the War of

American Independence; Britain’s losses of ships were also higher than would be expected,

given the estimates of Tables 6 and 8. Whether the relatively poor performance of Britain during

the American Revolution was because it was distracted by land operations while France and

Spain were not, or because of some other factor, we cannot determine. But this episode does

raise an interesting question: if the French and Spanish had been able at other times to concen-


parity were dashed early in the French Revolution, when the mostly aris-

tocratic officers of the French navy were either chased out of the service

or executed, eliminating much of that navy’s collective experience.43

Overall, Britain’s advantage measured by years of combat thus un-

derstates the British edge in relevant experience, because financial, stra-

tegic, and manning considerations sharply cut the sea time of enemy

fleets. In addition, the British navy did its best—with some success in

the Seven Years War, and much more success from 1793 onwards—to

keep enemy fleets bottled up in port. As John Creswell notes:

Here, in respect of experience, British admirals usually had advantages over

their enemies. In the fifty years up to Trafalgar the British and French had been

at war during twenty-three of them and during those years the British fleets had

often been at sea for long periods while the enemy remained blockaded in Brest

or Toulon even when they were more numerous than their blockaders.44

Blockade duty, combined with the incessant requirements of patrol

and convoy duty, took a tremendous toll, injuring and killing men and

damaging ships; but it built the British navy into a formidable fighting

machine, with “the self-confidence nurtured by long months at sea, of-

ten in foul weather.”45

Crews became expert at handling their vessels

and training for combat, while the squadrons and fleets were drilled into

ruthless efficiency. The Spanish and French, meanwhile, were sitting at

anchor. When battle was joined, the fight was between men and ships

honed and hardened to the task at hand, against opponents who had

barely gained their sea legs. The outcomes are clear in the data.46

Motive

It is not obvious that a fleet long at sea would consistently win

against a freshly provisioned fleet manned by well-rested crews.47

Sea

duty was hard on ships and men; a fleet emerging from port with well-

maintained ships and fresh crews might have found—and defeated—

worn-out ships and disgruntled sailors in the fleet long at sea. The gen-

ius of the British Navy in preventing this lay in an incentive system that

trate on the sea with as much focus as they did during the War of American Independence,

would Britain have gained command of the ocean? 43 Creswell, British Admirals, p. 197; and Rodger, Command, p. 532. 44 Creswell, British Admirals, p. 254. 45 Ibid., p. 116. 46 And apparent to observers at the time. See, for example, ibid., pp. 177, 183–84. 47 For example, Hawke’s successful blockade of Brest in 1759 was made possible only by

major advances in the system of victualing the fleet. Hayward, For God, chapter 3, addresses

the difficulties in maintaining the Toulon blockade during 1803–1805, illustrating the lengths to

which commanders had to go to ensure that their fleets were combat ready.


supplied its officers and men with the motivation needed to outperform

their foes. 48

Officers and men of the Royal Navy received pay from two sources.

During both war and peace, they were paid monthly wages that were

highly skewed by rank and, except at the very lowest ranks, higher on

larger ships. During war, wages were supplemented with a prize system

in which rewards included the economic value of enemy vessels cap-

tured, and “head money” paid for the capture or death of sailors aboard

enemy warships. Prize earnings were even more sharply skewed than

wages. For example, although a captain’s wages averaged perhaps 20

times that of an able bodied seaman, a captain’s share of prize money

was typically more than 200 times the share going to a seaman.49

Benjamin and Christopher Thornberg have shown that the shipboard

organization of the lower deck of the Royal Navy in the age of sail use-

fully may be thought of as a hierarchical tournament: Noncommis-

sioned officers competed for promotions that brought sharply higher

wages and larger prize shares. Tom Wareham makes clear there was

also a tournament among commissioned officers, in which superior per-

formance yielded promotion, which in turn led to opportunities for sub-

stantially higher income.50

All authorities agree that patronage was essential to the promotion

system of the Royal Navy.51

But one must recognize its meaning in this

context. It is normal today to think in terms of political patronage, in

which individuals are granted choice positions because they have politi-

cally powerful allies. Such “interest” (as it was called) was no stranger

to the Royal Navy. Indeed, during the 1650s, loyalty to the new Repub-

lic was essential, and this was reflected in Cromwell’s choice of cap-

tains.52

But as early as the 1660s, the casualties of the first Anglo-Dutch

war made it possible for command openings to be filled with men who

had distinguished themselves in action. The growing professionalism of

the navy was enhanced by Charles II’s 1677 decision to require candi-

dates for lieutenant not merely to pass an examination in seamanship

conducted by senior officers, but to have served at least three years at

48 For more detail, see Benjamin and Thornberg, “Comment” and “Organization.” 49 These ratios depend on the rate of the ship. See Hill, Prizes; and Benjamin, “Golden Har-

vest,” for details. 50 Benjamin and Thornberg, “Organization”; Wareham, Star Captains; and Benjamin and

Thornberg, “Comment.” See Lazear and Rosen, “Rank-Order Tournaments”; and Rosen, “Au-

thority” and “Prizes,” on tournaments as efficient compensation systems. 51 Lewis, Navy; Rodger, Wooden World, pp. 273–303; Lavery, Nelson’s Navy, pp. 94–98;

Wareham, Star Captains, pp. 110–12; Rodger, Command, pp. 52–55, 112–22, 388–89, 512–22;

and Knight, Pursuit, p. 14. 52 Rodger, Command, pp. 52–55.


sea, including one as a midshipman, before being allowed to stand for

the exam.

Notwithstanding some well-publicized exceptions, during the height

of Britain’s success in the age of sail, political patronage played a role

chiefly in speeding (rather than creating) promotions. Even more impor-

tant, when it came to command, the Admiralty was zealous in ensuring

that only naval patronage—that is, the influence of superior officers—

was relied upon.53

An essential ingredient in the promotion process was the certification

of officers as being prepared for advancement and command. Crucially,

the certifying senior officers put their own reputations on the line. If the

officers they recommended did not live up to expectations, their future

recommendations were heavily discounted by the Admiralty. Because

the best men were drawn to serve under those officers who could further

their careers, loss of credibility with the Admiralty could seriously

hamper the subsequent career of the senior officer in question.54

Quite apart from honor and pride, there were large financial stakes

involved when men made promotion recommendations or decisions.

Success in battle—and thus prize money—depended on the quality of

the men one commanded. At each critical stage in the evaluation and

recommendation process, the decision-makers had compelling self-

interests to ensure that the best men were promoted and given command

responsibility.

Successful command was substantively the only way that a com-

moner could expect to rise in British society. And time at sea was the

only way a man could earn prize money. Over the years 1793–1815,

captains could expect to earn prize money two to five times greater than

their monthly wages.55

But—and this is critical—it was command of a

vessel or squadron that offered the promise of riches, not merely rank,

and command was given only in the expectation of superior perform-

ance.56

Long-term retention of command was heavily dependent on a

53 Wareham, Star Captains, makes the point about speed; Rodger, Wooden World and Com-

mand, address the general issue at length. 54 The discussion by Rodger, Wooden World, pp. 273–303, on this point is explicit and exten-

sive. Rodger, Wooden World; and Wareham, Star Captains, both note that this evaluation proc-

ess started early in officers’ careers: Midshipmen avidly sought the ships of influential com-

manders, and promising lieutenants were often given slots on flagships, where a local

commander-in-chief could monitor their careers. 55 See Hill, Prizes; and Benjamin, “Golden Harvest.” 56 To put the distinction in perspective, roughly 30 percent of all men promoted to post cap-

tain during the Napoleonic wars never received a vessel to command, and many of those cap-

tains who commanded a vessel at some point spent only a few months in command. Wareham,

Star Captains, p. 21. There would seem little point in promoting an officer and then not employ-

ing him, but Wareham, Star Captains, p. 78, suggests the Admiralty sometimes used promotion

as a form of superannuation.


captain’s continued performance in accomplishing the specific objec-

tives of the Crown.57

Captains who performed well were rewarded with

prize money, honors, and the continued command necessary to ensure

future prize money and honors. Those who did not were returned to the

shore and half pay. For island Britain, survival was possible only by

victory at sea, and all elements of the Royal Navy’s organization and

incentives were structured accordingly.58

CONCLUSIONS AND IMPLICATIONS

When Spain’s 1796 declaration of war forced the Royal Navy to

withdraw from the Mediterranean, the notion that Britain soon would

crush her adversaries would have seemed wishful thinking, even to the

eternally optimistic Nelson. Yet less than 20 years later, victory was so

complete that Britain’s worldwide dominance at sea went unchallenged

for a century. If our evidence is correct, the gloom of 1796 was unwar-

ranted in the historical context that preceded it.

The Royal Navy did not win every battle in which it engaged during

the modern age of combat sail, and its performance during the War of

American Independence was less than spectacular. Moreover, in the

waning years of the Napoleonic Wars, losing engagements with the

radical new American super-frigates (such as the Constitution) gave

British commanders pause. Yet the final resolution of the “Second

Hundred Years War” was no fluke. It was instead the cumulative effect

of decades of experience, hard-won in the crucible of combat.

Over the years from 1660 to 1815—spanning the height of modern

combat under sail—commanders in the British navy learned how to

fight and win, one engagement at a time, one war at a time. As British

commanders learned from their past mistakes, their combat fatality rate

declined dramatically, on such a sustained basis that between 1660 and

57 Wareham, Star Captains, pp. 128–51. 58 Of course a key question is the organization, incentive, and control system of the British

navy relative to those systems employed by its enemies. Although the evidence on those other

systems is scanty, some points are clear. First, the structure of pay in the French, Spanish, and

Dutch navies was considerably flatter than in the British navy, suggesting the absence of the

type of tournament present in the British navy. Second, the command structure in the French

and Spanish navies was largely determined on the basis of factors other than ability as a naval

commander. French officers were heavily drawn from the ranks of the aristocracy, with less re-

gard for their ability than in Britain, and the command structure of the French navy was further

weakened during the French Revolution, because many (aristocratic) officers were executed or

run out of the navy. Britain was an island with a relatively weak army, so (compared to France

and Spain) the Crown might have felt that external threats were more severe than any internal

threat posed by the aristocracy or the army, and so felt more inclined to heed the wishes of the

Admiralty. See Davids, “Maritime Labour”; Jenkins, History; Mühlmann, Die reorganization

der Spanischen Kreigsmarine; and Harbron, Trafalgar, for more.


1815 it fell 98 percent. Moreover, this learning manifested itself in other

measures of combat performance: British combat losses relative to the

losses they inflicted on their enemies declined by 80 percent.

These developments were no accident. Britain was compelled by its

insular status to devise successful strategies for combat at sea. This en-

tailed keeping ships at sea, on convoy, patrol, and blockade duty.

Meanwhile, enemy fleets were bottled up by financial and strategic con-

siderations of their own—and eventually by British blockade. The com-

bination enabled British crews to hone their skills, even as the enemy’s

were atrophying. But what made this tactic possible was the other ele-

ment of British strategy—a compensation and promotion system that

gave commander and crewman alike the incentive to behave as though

he were the King himself. Driven by the demands of nearly incessant

warfare, and encouraged by organizational supremacy and financial in-

centives, British commanders outperformed their enemy counterparts

because in learning by doing they accumulated a stock of combat

knowledge that made them the best in the world.

Appendix I: Types of Learning

Learning When to Fight

The implications of learning can be seen with the aid of Appendix Figure 1. Con-

sider a commander with a force of known fighting strength Si, where i = L, H, and the

value L indicates low strength and H indicates high strength. Suppose his estimate of

the enemy’s fighting strength is characterized by distribution 1, with expected value

EE and variance 12. Also assume the following:

1. the decision to fight is solely that of this commander;

2. the commander fights if he believes he is stronger than the enemy (Si > EE) and

flees otherwise;

3. a commander wins if he fights and Si > EA (where EA , the actual strength of the

enemy, is not shown in the figure) and is disgraced if he flees and Si > EA.

A commander with a relatively low level of strength, SL, will clearly flee, because

SL < EE; in doing so, he accepts the probability of disgrace shown by the area ABSL. A

commander with a high level of strength, SH, facing the same expected enemy force

would fight, because SH > EE. In doing so, he faces a probability of defeat given by

CDSH, because this is the probability that the enemy will in fact be stronger than SH.

In this context we assume that learning causes a mean-preserving reduction (to 22)

in the variance of the commander’s estimate of enemy strength. Thus, learning is

shown by the shift from distribution 1 to distribution 2. A better-informed commander

with strength SL who flees will bear a reduced probability of disgrace (A B SL < ABSL).

Similarly, a more knowledgeable commander of strength SH who fights will bear a re-

duced probability of defeat, given by C D SH < CDSH.


APPENDIX FIGURE 1

ACTUAL BRITISH STRENGTH (IS) AND THE DISTRIBUTION OF EXPECTED ENEMY

STRENGTH (E)

Because knowledge reduces the probability of defeat, two key predictions follow.

First, as commanders learned, their combat fatality rate (and, presumably, that of the

men who served under them) should have declined. Second, as combat knowledge was

accumulated, British losses (vessels sunk or captured by the enemy) should have de-

clined relative to the losses inflicted on the enemy.59

The preceding discussion treats the decision to fight as that of the British com-

mander alone. Clearly, there could be cases where British and enemy commanders

would have to “concur” before combat could commence.60 If both commanders had

unbiased beliefs about their opponents’ strengths, and if both followed a decision

rule of only fighting when they judged themselves superior to their opponent, then

no combat would have occurred. But in the age of sail, the windward ship (or fleet)

generally had the de facto option to fight or not. British commanders sought and

most often achieved the windward advantage over their opponents, implying British

59 Courts martial convictions of captains for cowardice also should have fallen. There are few

such convictions in the published record, so we are unable to test this. Also, it was often diffi-

cult for the court to discern cowardice from incompetence, and unrelated disputes among senior

flag officers were sometimes crucial in courts martial outcomes. See Hannay, Naval Courts

Martial; Rodger, Wooden World; and Byrn, Crime.60 If agreement by both commanders is required for a fight to occur, it is possible that a game

theoretic approach to combat decisions could be fruitful. See Benjamin and Cojuc, “‘Til Death

Do Us Part’,” for one such attempt.

E

Distribution 1

Distribution 2

A

B

A'

B'C

D

C'D'

SL

SHE


commanders generally made the decision whether and when to engage combat.61

Hence, our characterization of the combat decision as one made by British com-

manders is likely to be a good approximation of the circumstances in which we test

our theory.

There is an interesting implication of this behavior of British commanders. Given

our presumed decision rule, a commander in the windward position chooses to fight

only if Si > EE. Assuming commanders’ expectations were unbiased, British com-

manders would win more than half the time, even if a randomly selected British ship

or fleet were no better than a randomly selected enemy ship or fleet. This “selection

bias” in the outcomes of battles likely accounts for some of the observed advantage of

the windward position in combat under sail; moreover, because the British most often

sought and obtained the weather gage, the observed performance of British ships in

combat was an upward-biased measure of the combat effectiveness of a randomly se-

lected British ship.

Learning How to Fight

There is another type of learning that surely took place during the period of our

data, and that is a rise in the average combat ability (effective strength) of a vessel or

fleet of any given nominal strength. Indeed, historical accounts suggest that British

commanders were sharpening those skills that were relevant once combat was immi-

nent or underway, and the main text offers specific examples of such learning.

If such learning occurred faster than among Britain’s enemies, this would have

raised the strength of British ships relative to the enemy’s. In terms of Appendix Fig-

ure 1, Si would move to the right relative to the distribution of E. Several implications

follow. First, for encounters in which a British ship previously would have fought

(Si > EE), a rise in strength increased the probability of British victory: the area be-

tween EE and Si rises. Second, a rise in the effective strength of British ships implies

that some encounters for which Si < EE prior to learning now have Si > EE. Hence,

British ships should have become more aggressive, choosing to fight more often, and

choosing to fight ships (or fleets) that were increasingly powerful relative to their own

nominal strength. Third, the Admiralty should have raised the standard to which Brit-

ish captains were held: for encounters in which Si < EE, a rise in Si due to learning

would have produced a higher probability of disgrace in the event of flight.

Learning without Choice

The discussion in the text supposes that British commanders unilaterally decided

whether to fight. How did learning affect outcomes when enemy commanders made

this choice? In such cases the British commander’s expectations were irrelevant; all

61 A vessel in the windward position (which was said to have the “weather gage”) was the one

first touched by the wind. Thus, if the wind was blowing out of the north, the vessel farthest

north had the weather gage. Because sailing vessels cannot sail directly into the wind, it was

possible for the windward vessel to position itself so that the enemy literally could not—as a

matter of physics—get close enough to engage. But at all times, the windward vessel had the

option of sailing downwind to engage the enemy. This advantage could be used to feed the men

before battle, finish final preparations of the ship, await reinforcements, or even wait for

weather conditions to change in favor of the windward vessel. See Benjamin and Thornberg,

“Comment,” for more extensive discussion, including an analysis of the strategic circumstances

that made the weather gage more valuable to the British.


that mattered was the strength of the British commander’s force relative to the actual

strength of the enemy. If Si > EA, the British won; if the inequality was reversed, so too

was the outcome.

Any British ship (or fleet) of actual strength Si could be expected to encounter some

distribution of enemy vessels, whose commanders would have expectations regarding

the strength of the British. We let Si* represent the expected strength of the British, as

perceived by the enemy. We assume that enemy estimates of British strength are unbi-

ased, i.e., that E(Si) = Si*, but we also recognize that some British ships (50 percent if

the distribution is symmetric) will turn out to be stronger than anticipated by the en-

emy. If enemy ships follow the rule of fighting only when their strength is greater than

the expected strength of their British opponent, then all enemy ships weaker than Si*

will decline to fight. Remaining enemy ships will fight and expect to win, but not all

of them will in fact win, because half of their British opponents will turn out to be

stronger than anticipated.

As the British become stronger over time due to learning, they will win an increas-

ing proportion of the battles in which they are engaged, even though the enemy are

aware of Britain’s growing strength and are altering their behavior accordingly. This

result is most easily seen in Appendix Figure 2, under the assumption that enemy

strength is distributed uniformly over the range from E1 to E2, with a mean of Em. The

strength of a British opponent, as perceived by the enemy, is distributed over the range

from S1 to S2, with a mean of Sm. Given that the enemy declines to engage if its

strength is less than Sm, the only foreign ships that fight will have strengths ranging

from Sm up to E2. Overlap of British strength over enemy strength (and thus British

victory) occurs with probability Pb = (S2 – Sm ) / (E2 – Sm). We assume that when Brit-

ish strength increases, the entire distribution of S shifts up, implying that both S2 and

Sm change. Given this assumption, the marginal effect of a change in British strength is

given by

dPb / dS = (S2 – Sm) / (E2 – Sm)2 > 0

Thus, as the British grew stronger, they would win an increasing proportion of the bat-

tles in which they were engaged, even thought the enemy was quite sensibly declining

a growing proportion of the opportunities for engagement.

Appendix 2: Data Sources

David Syrett and R. L. DiNardo track careers of commissioned officers of the Royal

Navy. In addition to recording dates of commission and promotion, they record those

officers killed in combat, including the dates on which these men were killed. There

are four commissioned ranks: admiral (including vice admiral and rear admiral), post-

captain, commander, and lieutenant. We focus exclusively on fatalities among post-

captains, because it is possible to measure their potential combat exposure with the

greatest precision. For the years 1660–1815, some 173 British post-captains died in

combat, an average of about one per year. In most years, none were killed; in the most

lethal year (1666), 16 were killed in action, ten of them in the same battle.62

Post-captains commanded “rated” ships, which for most of our period were ships

carrying 20 or more cannons (referred to as guns). These ships were grouped into six

62 Syrett and DiNardo, Commissioned Sea Officers. We used Clowes, Royal Navy; James,

Naval History; and Hepper, British Warship Losses to cross-check combat fatalities.


APPENDIX FIGURE 2

DISTRIBUTIONS OF ACTUAL ENEMY STRENGTH (E) AND EXPECTED BRITISH

STRENGTH (S)

rates, the largest of which, the first rates, carried at least 100 guns; the smallest of the

rated ships, the sixth rates, carried 20 to 28 guns. The standard source on the size of

the British fleet, and the fleets of its enemies, is Jan Glete, who records this informa-

tion at five year intervals, in years evenly divisible by five.63 As shown in Table 2 of

the text, the fleet of rated British ships—and thus the number of British captains and

ships who might have been subjected to combat—averaged 201 during our sample pe-

riod, ranging from a low of 92 in 1670 to a high of 354 in 1810. On average, the Brit-

ish fleet grew at a rate of about 0.7 percent per year during our period (t = 11.1), rising

sharply during war and declining during peace.

David Hepper records dates of combat between Britain and her various enemies

during the years of our study.64 Britain was at war for 77 of the 156 years between

1660 and 1815. Historical accounts suggest that these wars differed in their intensity,

which we take into account as noted in the text.

Losses of British ships are summarized by Hepper, whose data we cross-checked

with that of Clowes, being careful to distinguish combat losses from the far more nu-

merous losses due to storm, navigational error, or other accidents.65 We examine

losses of rated ships, because the data are most reliable, and these ships were com-

manded by post-captains. There was only about 20 percent overlap between British

63 Glete, Navies. Until 1714, only a subset of vessels, carrying more than 28 guns, were rated,

and our count of the number of rated vessels before that date reflects this fact. 64 Hepper, British Warship Losses. At the urging of a referee, we exclude seventeenth-century

conflicts with the various states along the Barbary Coast, although treating these conflicts as

war leaves our results substantively unaffected. 65 Hepper, British Warship Losses; and Clowes, Royal Navy.

E S E ES S 2 m1 1 2m


ships lost in combat and combat fatalities among British captains, so combat losses of

ships provides a largely independent measure of the process of learning in the Royal

Navy.66 Finally, Clowes has compiled combat vessel losses (captured or sunk) for na-

tions engaged in combat with Britain, and we have extracted these for all ships of 20

or more guns. Again, Glete enables us to determine fleet sizes for the various combat-

ant navies, albeit with some imprecision, a matter discussed in the text.67

66 Popular lore has it that the captain “goes down with the ship,” but some captains died victo-

rious, and others died on vanquished but still floating vessels. Only about 10 percent of the ves-

sels lost in combat in our period sank; the rest were captured. Prior to the development of the

fused shell in the mid-nineteenth century, it was difficult to damage a warship enough to sink it.

Incentives were also at work: a captured warship meant prize money to the victorious crew,

whereas the (largely nonswimming) crew of a vessel that sank faced a high risk of drowning or

hypothermia. 67 As Glete, Navies, notes, not all ships were in commission at all times, so the numbers of

ships subject to the hazards of combat are somewhat lower than we show. On balance, the effec-

tive number of ships in national fleets surely rose over our period, because ships were getting

larger and more seaworthy and navies thus moved a larger proportion of their fleets to year

round (rather than just summer) service. As noted in the text, we supplemented our regression

with various time trends, none of which had any effect. We also created a variable based on the

number of different months in a year that ships were lost in combat. Including this in our regres-

sions also has no effect. Hence, we believe the gradual move to year-round operations does not

influence any of our estimates.

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Learning by Dying: Combat Performance in the Age of Sail

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