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 th
extensive wartime experience accumulated over this period, combined wi
the unparalleled financial incentives for combat success offered to Briti
commanders.
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 development
were the product of a rapid maturation of the state as an organization o
taxation and control, and led to state monopolization of force at sea
They also yielded a struggle at sea sufficiently intense and protracted t
be labeled the "Second Hundred Years War."1 Despite massive naval
investment by the French and Dutch in the late seventeenth century, an
by the Spanish and French after 1 720, 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: wahoo@clemson.edu. Anca Tifrea is Senior Associate, KPMG
LLP, 303 Peachtree St., Atlanta, GA 30308. E-mail: atifrea@kpmg.com.
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 We thank Jan Glete for providing us with unpublished data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 earlie
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 semina
participants at Clemson University, Cardiff University, and the London School of Economic
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.
See, for instance, Lavery, Ship and Line; Glete, Navies; Palmer, "'Military Revolution'" ;
Tunstall, Naval Warfare; and Rodger, Command
968
Learning by Dying 969
The narrative history of this struggle has been well do
ably told by naval historians.2 Our intent is to supplement
in three ways. First, the existing historical narratives are
nature; we seek to quantify the process by which Britain
of the ocean. Second, we hope to show that despite Br
(such as those suffered during the War of American Ind
origins of the process that culminated in victory over Na
can be traced to the First Dutch War 150 years before
tantly, we show that Britain's ultimate dominance at sea w
nation of a long process of learning, one in which both e
incentives played crucial roles.
We do not seek to rewrite British naval history. Nothin
denies the importance of the geographical, political, and f
that long have been central to the histories of this period
shall make clear, many of the familiar themes, including
status and the backdrop of continental land wars, are ess
story. We focus on the mechanism by which these large
fested themselves in the outcomes of warfare at sea, and
fairly precise terms the fundamental continuity of the under
The hallmark of the sea battles fought in the decades a
widespread carnage. Comprehensive casualty counts ar
available, but casualties among commanding officers in t
were reliably recorded, and they speak unequivocally.
gagement, the Four Days' Battle in June 1666, 10 Roy
captains died in combat; this was nearly 8 percent of all
captains afloat at the time.3 During the two wars with th
1660s and 1670s, more than 60 English post-captains wer
tion, a time when there were an average of but 114 rated
English navy. Published battle narratives plus the limited
available in published sources suggest that the butche
quarterdeck had its counterpart between decks 4
There are many reasons for the high casualty rates of th
cluding the close quarters of the North Sea and the Engl
2 James, Naval History; Mahan, Sea Power; Clowes, Royal Navy; Creswell,
Glete, Navies; Lavery, Nelson 's Navy and Nelson and the Nile; Lewis, Nav
History; Palmer, '"Military Revolution'" and "'Soul's Right Hand'"; and
World and Command.
To oversimplify: Post-captains commanded "rated" or "post" ships - those
the period, were officially armed with 20 guns or more. The commander of
sel commonly was addressed as "captain," but his official title was "master
We generally use "English" for the period before the 1 707 legislative uni
England, and "British" for the period after 1 707, but we also use "British" a
tor when little harm is done by the imprecision.
4 See, for example, Clowes, Royal Navy; Tunstall, Naval Warfare; and Rodge
970 Benjamin and Tifrea
where the key battles took place, and the fact that the Englis
were eager to stand and fight. We argue that one other fac
work. Between 1650 and 1680, firepower became concentrat
before, and delivered by ships built to administer and with
punishment than ever before. Commanders erred often in
this firepower and avoiding its adverse consequences, m
proved fatal for them and their crews. The result was hi
rates. As tactics were learned and improved, fewer mistake
and casualties declined. Among British captains, who are th
our study, much of the learning took place rapidly, but it co
into the eighteenth century. By the Great Wars of 1793-181
ships were at least twice as powerful as their predecessors o
before, combat at sea was far less deadly for British captain
learned how to win - or lose - without killing nearly as man
selves or their men.
The learning that reduced fatality rates among captains is
in the combat success of the Royal Navy. Over the 150 year
by our study, the British navy markedly increased the losses
on enemy fleets, relative to the combat losses it suffered. A
the performance of the navy's command structure improved
idly in the first half of our sample, improvement continued
the period we study. The culminating triumph of the Napole
thus traceable in the data back to the initial engagements o
Anglo-Dutch war, more than 150 years before.
We focus on the British navy for two reasons. First, syst
on battle outcomes during this period are of higher quality for
other navies - perhaps because Britain succeeded, and thus m
recorded its activities. Second, by 1815 no one doubted Brit
nance at sea, yet in 1650 no one could have predicted that o
quantifying the process by which Britain prevailed we also s
tors we believe should be given more weight in discussions
riod. Specifically, we argue that the ability of British captain
form experience into success stemmed from two key facts: t
and men of the British navy had far more opportunity than ene
to develop their combat skills, and they were given unparal
cial incentives to succeed. This combination of opportunity
thus helped fuel the Royal Navy's rise to greatness.
HISTORICAL PERSPECTIVE
The execution of King Charles on 30 January 1649 marked the c
mination of the English Revolution and presaged the dawn of a new
Learning by Dying 97 1
in naval warfare. The Revolutionary government of Englan
navy as a means of solidifying its rule and accomplishing a
political and religious objectives. Mercantile interests were a
ers of a stronger navy, for they sought a greater share of w
perhaps even the displacement of the Netherlands as the w
nant carrier of goods at sea. The efforts of the new governm
mercantilist supporters led in passage of the Navigation Ac
which helped precipitate the first Anglo-Dutch war of 1 652/53
The Dutch navy at this time consisted chiefly of cruisers,
sels optimized for convoy escort duty and keeping open the
tal to trade. Most English vessels were comparably sized, bu
lish also had a small contingent of "great ships," battleship
for firepower and the ability to withstand intense combat. P
crucially, the English discovered the line of battle, which w
tive defense against the Dutch melee tactics, and a devastatin
delivering concentrated firepower.6 Despite unremitting w
the Dutch to fight, the English tactics and battleships tipped
and the Battle of Scheveningen in 1653 sealed an English vic
The war brought several lessons. Both sides relied heavily
merchantmen to supplement their state navies, standard pra
time.7 But in this war, the weaknesses of the armed merchan
painfully obvious: they were slower and less maneuverab
cialized warships, and too lightly armed and built to inflict o
intense firepower. Moreover, the small warships of the Du
match for the English battleships. And finally, as the Engl
strated at Gabbard Shoals in 1653, the tactic of fighting in
what was to become known as the line of battle - was an en
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.
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'."
See Glete, Navies', and Rodger, Safeguard.
972 Benjamin and Tifrea
the second war in 1664, although both fleets were more pow
in 1652, the Dutch were no longer at a substantial disadvant
importantly, by the Four Days' Battle of June 1666 the Dut
concluded that the line of battle was superior to melee tact
war's end in 1667, it was clear that specialized warships,
powerful battleships arrayed in the line of battle, were the f
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
bat. Except in conditions of greatly reduced visibility, vessels d
8 See Palmer, "'Military Revolution'"; and Tunstall, Naval Warfare, chapter 1.
y Glete, Navies, pp. 187-88.
w Ibid., pp. 192-95.
Learning by Dying 973
Table 1
Decision
Fight Flee
Correct Survival; capture or sinking Survival; retention of command
of enemy vessel
Result
Incorrect Death; loss of ship by capture Court martial; disgrace and loss of
or sinking 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 2x2 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
974 Benjamin and Tifrea
Fighting Instructions, official documents that summarized
principles according to which combat should be conducted.
edge accumulated, the error rate of commanders should have
result would be fewer combat fatalities and greater success i
Another type of learning surely occurred during the cent
half covered by our data, namely a rise in the effective stren
ability) of a vessel or fleet of any given nominal strength.
torical accounts suggest that British commanders were sharp
skills relevant once combat was imminent or underway. For
improvements were clearly discernable in ship handling, gu
tics, navigation, signaling, fleet command and control, and
and health.11 In each case, the ability of British commanders
ter, concentrate, and avoid lethal firepower was enhanced. If
ing occurred at a rate faster than among Britain's enemies
would be an increase in the relative strength of British ships
ing British combat success.
LEARNING BY DOING
Productivity increases have been seen in some industries even ab
explicit investment in physical or human capital. The explanation
such observations has been that as firms produce more goods they
to improve the production process, i.e., there is accumulation of kn
edge as a side effect of economic activity. Such knowledge accumu
tion is known as learning by doing.
Learning is the product of experience and takes place during or
result of an activity.12 The first explicit empirical work on learnin
doing was by T. P. Wright, who observed that labor-hours necessa
produce an airframe was a decreasing function of the cumulative
ber of airframes produced in prior periods. Allan Searle investi
learning in the shipbuilding industry. Kenneth Arrow developed a
retical model of the process, emphasizing that learning by doing i
product of experience, and is subject to sharply diminishing retur
Subsequent studies have elaborated on Arrow's model, and exte
our empirical knowledge. Armen Alchian analyzed airframe product
and Leonard Rapping focused on shipbuilding; both used data f
World War II. Paul David and Jeffrey Williamson assessed the exten
learning by doing in the American textile industry during the early ni
11 See Cordingly, Billy Ruffian', Marcus, Naval History; Creswell, British Admirals;
Longitude; Tunstall, Naval Warfare; Palmer, "'Soul's Right Hand'"; Rodger, "Image
Wooden World; and Harbron, Trafalgar.
Learning may also take place as a result of observing, a fact to which we return later.
Learning by Dying 975
teenth century. More recent papers by Byong-Hyong B
Gort and by Lanier Benkard have examined in more det
findings of earlier studies.13
Learning by doing can be analyzed by assuming a pro
tion as simple as the Cobb-Douglas, yt = AK"I?tEYt , w
nology, yt is production at time /, Kt is capital, Lt is
measure of experience. The most common measures of
been cumulative output, cumulative investment, or tim
the beginning of the activity.14
In examining learning by doing, it is possible to inve
firm obtains more output from given inputs or how it
of producing a given output. In our case, the available
approach we take. The records of failure - captains wh
combat and ships that were either sunk or captured
available, so we use them. We think of the cost of pro
as being the loss of a captain or ship, and the experien
termine this cost as being the cumulative sum of such l
Thus, we view the captains of the Royal Navy as collec
from the past failures of their predecessors. Although
tains surely did learn from their own experiences, the l
we are interested here took place over a great span of
and a half) and was the product of the experiences of
Royal Navy captains who served over this period. That
captains of 1 800 as benefiting from their own experien
experience of the captains of 1740 and those of 168
knowledge was passed along formally in the Fighting I
more importantly, it was accumulated and transmitted
traordinary mentoring and evaluation process of the Ro
discuss below. In essence, the command structure of
Admiralty Board to midshipman, was organized to ensu
essary elements of success - and survival - were passed
eration of commanders to the next.15
13 Wright, "Factors"; Searle, "Productivity"; Arrow, "Economic Implicati
frame Production Functions"; Rapping, "Learning"; David, "Learning"; W
ment"; Bahk and Gort, "Decomposing Learning"; and Benkard, "Learning
Some authors, such as Benkard, "Learning," have investigated whether
in the stock of knowledge - may occur. When forgetting is possible, the e
is readily modified. Given that E, = YYh where t goes from 0 to T-\ (one
erence period), to adjust for forgetting, one simply specifies Et = SEt_\ +
at time t, and (1 - 3) is the rate of depreciation of knowledge.
An alternative approach would entail a survival analysis on individual c
examining how the cumulative combat experience of commanders influenced
of their vessels and crew in combat. As a practical matter this is not likely
such information is available only spread across many thousands of log book
976 Benjamin and Tifrea
COMBAT FATALITIES
Published data on total casualties are sporadic, even for the B
navy during the well-documented wars of 1793-1815, so our focu
two measures for which data are available - fatalities among
and ships captured or sunk in action. Nevertheless, there are com
reasons why our measures are informative and valuable. Warshi
the most complex and costly pieces of capital extant during this
The capture or sinking of one in combat was an important acco
ment for the victor and a serious loss for the vanquished. Su
captains were valuable instruments of war, and their skills argua
the largest effects on the outcomes of battles. Given their expos
tions directing combat from the quarterdeck, captains had strong
tives to learn more effective means of combat, and we expe
learning - or lack thereof - to show up in their combat fatality rate
We argue that three factors determine combat fatalities amon
tains: their exposure to combat, the stock of knowledge possess
them, and the intensity of the wars in which they fought. To c
fatalities we aggregate data on captains killed in action over fiv
periods, because reliable data on rated ships is available only
year intervals, evenly divisible by five.16 For a given year of sh
fatalities are thus the combat fatalities during the five years cen
the year in question. As an alternative measure of the combat ou
of captains we also examine the combat hazard rate among them,
we define as fatalities divided by the number of rated ships in t
ish fleet. Summary statistics on this and other key variables are
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.
Learning by Dying 977
Table 2
SUMMARY STATISTICS, 1670-1815
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
during time of war, so N= 22
Note: The minimum reported
prior to France's entry into the
Sources'. See the text and App
their enemies. As our
modern combat, we co
servation in question.17
Not all wars are the s
more casualties. Measu
have tried several alte
have settled is, for eac
of combat descriptions
of the Royal Navy. Al
statistically superior t
has conceptual reasons
battles are likely to be
more closely examine
17 An alternative measure of
combat. Such a measure is in
sense that the fatality measur
ure is added to a regression eq
ship-loss variable is not statist
of the fatality measure are su
percent of the time is the com
versa.
18 The lengths of the Clowes narratives also depend on the duration of the war du
year period and perhaps on the size of the navy, so our interpretation of this variab
sity" is only correct if we control for these other factors - which we do. Other m
tensity we have examined include the log of real expenditures on the navy and t
number of pages devoted to "operations" in Rodger, Command. The measure we use
in two ways: when included alone as a measure of intensity it yields the largest valu
likelihood function, and when included with other measures of intensity, only it i
significant among them.
978 Benjamin and Tifrea
Moreover, even if a protracted, intensive engagement turns
simply by chance, it is still likely to produce both more ca
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?2 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.
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.
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 Kh the sum of fatalities from /- N to /- 1, be
knowledge. According to our theory, F, = aKt + eh and by construction it must be true that &Kt =
F,_b where A is the difference operator. This implies that AF, = aAKt + Ae, = aFt_ x + Aet. Thus,
we can write Ft = (1 + a) F,_i + Aet = Aet I [1 - (1 + a)L], where L is the lag operator. Cumulat-
ing Ft from / - Nto t - 1, we find that [1 - (1 + a)L]Kt = (IAe,_ x) = (et_\ - e,-.N_\), 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.
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.
Wooldridge, Econometric Analysis, pp. 661-63.
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,
Learning by Dying 979
Table 3
Fatalities Hazard Rates
(negative binomial regression) (fractional logit regression)
Dependent Variable: Five Year Combat Dependent Variable: Five Year Ratio of
Fatalities among British Post Captains British Post Combat Fatalities to Rated Ships
(standard errors in parentheses) (robust standard errors in parentheses)
(1) (2)
1670-1815 1670-1815
Knowledge -0.035 Knowledge -0.044
(0.004) (0.004)
Exposure 0.0014 Exposure 0.001
(0.0004) (0.0004)
Intensity 0.66 Intensity 0.81
(0.16) (0.18)
Constant 1.70 Constant -2.76
(0.45) (0.48)
N 30 TV 30
Log likelihood -50.4 Log pseudo-likelihood -2.44
Notes: Estimates are substantively unaffected if linear, quadratic, or cu
included in the regressions, or if estimates are performed for subs
1815. See the text for discussion.
Sources'. See the text and Appendix 2.
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.
980 Benjamin and Tifrea
Figure 1
ACTUAL AND PREDICTED COMBAT FATALITIES, 1670-1815
Note: Predicted values are based on column (1), Table 3.
Sources: See the text and Appendix 2.
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.
Learning by Dying 981
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
We can also use the
elasticities of fatalitie
sity. These elasticities
ble 4. Although inten
on fatalities, knowle
learning in determini
simple counterfactual
Revolutionary and N
same combat knowle
(1693-1715), how man
instead of 27 being ki
It is also useful to iso
time. Using the estima
ues of exposure and int
predict hazard rates as
the period. We average
riods of our era. As the
of our sample a post
killed in any five year
at their means. As is ap
rate, roughly 90 perce
first 60 years of our sa
eighteenth century, al
reveals that by the Na
had fallen to about one
26 In doing this calculation w
place the values of knowledge
27 The quality of British gun
of our period, due to a new g
invention of the carronade.
tions would all be expected to
to the past, we can find no sta
ties and the combat hazard r
quite close to their predicte
This is not to say that the im
effects in our data.
982 Benjamin and Tifrea
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 obtain
equal to their mean values and
time, the predicted five year h
Sources: See the text.
THE OUTCOMES OF BATTLE
The results thus far must be tempered by two consideratio
cannot reliably observe instances in which captains correctly ch
flee in the face of a superior enemy force (the northeast quadra
Table 1). If there were many such encounters for our period,
declining fatality rate among captains would be of little value t
Crown. Moreover, aside from draws, every observable cont
tween two enemies results in a victory or defeat. Skillful, know
able captains are more likely to survive even unsuccessful comba
are unskilled, ignorant captains, because able captains will r
from errantly extending losing combat. Yet one of the two c
must lose, regardless of ability. When it comes to victories and
it is relative skill or ability that is important, and over time it
tive rates of learning that determine the ebb and flow of victo
losses. Even if British captains were learning - and learning rap
if their enemies (most notably the French) were learning even f
combat fatality rates among British captains could be declining,
though they were losing more often.
Countering such a view is that this period of falling British fa
culminated with record-low levels of combat hazard rates, and a
ing British victory at sea over her enemies - and a subsequent c
of hegemony at sea. Indeed, M. A. J. Palmer characterizes the
eenth century as a era in which the Royal Navy won "victory aft
tory."28 Still, it is useful to examine other evidence.
28 Palmer, "'Soul's Right Hand'," p. 692.
Learning by Dying 983
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) (2)
1670-1815 1670-1815
Knowledge -0.031 -0.024
(0.010) (0.006)
Exposure 0.0013
(0.0009)
Intensity -0.34
(0.57)
Constant 2.22 1.31
(1.32) (0.77)
N 22 22
Log pseudo-likelihood -6.2 -6.3
Notes: Observations are weighted by total ship
Sources: See the text and Appendix 2.
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).
British losses are from Hepper, British Warship Losses; and foreign losses are from
Clowes, Royal Navy.
984 Benjamin and Tifrea
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 ar
share of losses averag
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
Learning by Dying 985
Table 8
COMBAT LOSSES OF RATED SHIPS
(negative binomial regressions)
Dependent Variable: Rated Ships Sunk or Captured in Battle
(standard errors in parentheses)
(1) (2) (3) (4)
British Losses Foreign Losses British Losses Foreign Losses
1670-1815 1670-1815 1670-1815 1670-1815
Knowledge: -0.023 -0.002 - -
fatalities (0.006) (0.005)
Knowledge: - - -0.019 -0.001
ship losses (0.005) (0.001)
Exposure 0.0023 0.0001 0.0022 0.0001
(0.0007) (0.0006) (0.0006) (0.0006)
Intensity 0.41 1.32 0.46 1.38
(0.27) (0.24) (0.23) (0.24)
Constant 0.77 -1.84 0.46 -2.04
(0.84) (0.75) (0.54) (0.65)
N 30 30 30 30
Log likelihood -61.1 -94.4 -59.7 -93.6
Sources'. See the text and Appendix 2.
Notes'. In columns (1) and (2) our measure of knowledg
British captains, as it was in our estimates of combat f
ure of knowledge is the lagged sum of past ships lost
column (3) and cumulative foreign losses in column (4).
on data that is available for both British a
approaches, our dependent variable is the
bat (British or foreign), and our measures
the same, except that the measure of fore
ing the size of foreign fleets by the duratio
The dependent variables in Table 8 are
combat by Britain (columns (1) and (3)) an
and (4)). In columns (1) and (2) our measur
sum of fatalities among British captains,
combat fatalities. This measure has a large
pact on British losses, but effectively no i
numerically or statistically. Given our int
British knowledge, this is not surprising, bu
analogue of our British fatality-based measure, but t
source of combat fatalities among foreign captains.
Improved British knowledge might even increase for
reflect a conscious decision by the enemy to keep its fl
leon placed a high weight on maintaining a "fleet in bei
annihilation by the British. This interpretation is consis
have a statistically significant effect on foreign losses;
than at sea, our exposure variable would do a poor job
combat. See also our discussion of the innovation proces
986 Benjamin and Tifrea
In columns (3) and (4) knowledge is the lagged sum of past
in combat - cumulative British losses in column (3) and cum
eign losses in column (4). Again, we see strong evidence of l
doing in the British estimates: as knowledge accumulates ove
pected losses fall.33 In sharp contrast, although there is a hin
among foreign commanders, the evidence is weak. The coef
knowledge in equation (4) is one-twentieth the magnitud
equation (3), and although negative, it is not statistically dif
zero at conventional levels. If we pool the data on ship losses
and foreign, and estimate a combined ship-loss regression,
clustering of residuals by year, we confirm the results of
coefficient of knowledge is not statistically different from z
eign nations, while the coefficient of knowledge for Britain
and statistically different from zero and from the coefficien
edge for foreign nations: Britain was learning faster than her en
We have examined two other approaches to foreign losses.
eign nations we treat as Britain's enemies sometimes bat
themselves, engaged in warfare against other nations, and (
Anglo-Dutch alliance against the French in the 1690s) somet
themselves with Britain. Potentially, they gained valuable kn
such endeavors, knowledge not reflected in the estimates o
of Table 8. Hence, we have collected foreign ship losses from
ments other than those in which Britain was the foe.35 Cumu
with the losses suffered against Britain gives us an alternati
comprehensive measure of the knowledge of foreign comman
ertheless, even when we use this potentially superior me
estimating equation (4) of Table 8, the results are substantive
tistically the same: there is essentially no evidence of learn
part of foreign commanders.36 We also have created a pane
33 The elasticity of ship losses with respect to this measure of knowledge is -1
below the elasticity of -2.4 implied by using fatalities as the measure of know
not shown explicitly here, estimates for the subperiods 1690-1815 and 1710-
similar.
As discussed in note 24, it is possible that observing (in addition to doing) wa
means of learning. But including either cumulative British exposure or cumulati
posure has no substantive effect on the impact of knowledge and neither of these
posure variables have coefficients statistically different from zero.
We have supplemented the material in Clowes, Naval History, with data fro
Sea Battles', Tunstall, Naval Warfare', Jenkins, History, Glete, Navies', and Lyon
is possible that we have missed some minor engagements in compiling the supple
losses, but cross-checking of sources suggests that nothing we have missed will a
in any meaningful way.
The similarity between the conclusions produced by the two measures of f
edge is not entirely surprising. Foreign nations were fighting Britain in a very la
Learning by Dying 987
which there are three comparison foreign fleets: French,
"all other" enemies. The results are substantively identica
ported in Table 8: Britain was learning, while her enemies
THE INNOVATION PROCESS
Naval warfare is a complex endeavor and the 150 years cov
our study witnessed political, administrative, and logistical chan
huge scale. We have developed important new quantitative meas
the progress of naval warfare over this period, and presented com
evidence that Britain's success may be viewed as the proximate
of learning by doing over a long span of time. We cannot hope
minate every element of why Britain succeeded where her ene
not. But we can suggest two key factors that have not received
cient attention in the existing literature: opportunity and motive.
Opportunity
The British navy spent more time at war than did any of her e
and did so actively at sea, rather than bottled up in port by con
strategic considerations, inadequate finances, or enemy blockad
after year of convoy, patrol, blockade duty, and combat in all
enabled the commanders and sailors of the British fleet to master
the real essentials of naval tactics . . . , the well drilled line of battle and
flexibility as would enable advantage to be taken of any opportunities the e
might offer.37
The line of battle was both the supreme offensive and def
weapon of the era; hence, it was prone to yield inconclusive enco
particularly when one of the fleets was French, for a fund
French strategy of much of the era was to avoid decisive comb
Admiral Sir John Jervis, writing when he was a post captain, re
after the battle of Ushant in 1778:
of the battles in which appreciable numbers of rated ships were lost, so the correlati
the two measures of foreign knowledge is 0.99.
37 Creswell, British Admirals, p. 39.
One section of the French Fighting Instructions of the eighteenth century is ent
Avoid an Engagement." There is no mention, nor even a suggestion, of any such no
British Fighting Instructions. As Creswell, British Admirals, p. 48, remarks, "It is pe
sonable to detect here a difference in outlook that had a continuous effect throughout
eenth century."
988 Benjamin and Tifrea
. . . two fleets of equal force can never produce decisive events, unless
equally determined to fight it out, or the commander-in-chief of on
bitches it so as to misconduct his line.39
In Jervis's view (shared by others) decisiveness required av
takes and capitalizing on the enemy's mistakes. The way to
practice and more practice: learning by doing.
The British were at war at sea during 77 of the 156 years
1660 and 1815, some 20 percent more than France or Spain
more than any of her other enemies. Britain also enjoyed a
stable political system and a strong financial system, and he
opponents of the eighteenth century were hamstrung by ot
Crucially, in all of the wars with Britain except the War o
Independence, the resources of the continental powers wer
the necessity of fielding large land forces; conflict at sea w
of a larger struggle. The realities of geography meant that i
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.
4U See Glete, Navies, pp. 212-20; and Rodger, Command.
Muhlmann, Die reorganization der Spanischen Kreigsmarine, pp. 123-59.
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-
Learning by Dying 989
parity were dashed early in the French Revolution, when th
tocratic officers of the French navy were either chased out
or executed, eliminating much of that navy's collective expe
Overall, Britain's advantage measured by years of comba
derstates the British edge in relevant experience, because f
tegic, and manning considerations sharply cut the sea tim
fleets. In addition, the British navy did its best - with som
the Seven Years War, and much more success from 1793 o
keep enemy fleets bottled up in port. As John Creswell not
Here, in respect of experience, British admirals usually had advanta
their enemies. In the fifty years up to Trafalgar the British and Fren
at war during twenty-three of them and during those years the Briti
often been at sea for long periods while the enemy remained blockad
or Toulon even when they were more numerous than their blockaders
Blockade duty, combined with the incessant requirement
and convoy duty, took a tremendous toll, injuring and kil
damaging ships; but it built the British navy into a formid
machine, with "the self-confidence nurtured by long mont
ten in foul weather."45 Crews became expert at handling
and training for combat, while the squadrons and fleets we
ruthless efficiency. The Spanish and French, meanwhile, w
anchor. When battle was joined, the fight was between m
honed and hardened to the task at hand, against oppone
barely gained their sea legs. The outcomes are clear in the d
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?
Creswell, British Admirals, p. 197; and Rodger, Command, p. 532.
Creswell, British Admirals, p. 254.
45 Ibid., p. 116.
And apparent to observers at the time. See, for example, ibid., pp. 177, 183-84.
For example, Hawke's successful blockade of Brest in 1759 was made possible only by
major advances in the system of victualing the fleet. Hay ward, 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.
990 Benjamin and Tifrea
supplied its officers and men with the motivation needed to
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 IPs 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."
These ratios depend on the rate of the ship. See Hill, Prizes; and Benjamin, "Golden Har-
vest," for details.
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.
Lewis, Navy; Rodger, Wooden World, pp. 273-303; Lavery, Nelson's Navy, pp. 94-98;
Wareham, Star Captains, pp. 1 10-12; Rodger, Command, pp. 52-55, 1 12-22, 388-89, 512-22;
and Knight, Pursuit, p. 14.
Rodger, Command, pp. 52-55.
Learning by Dying 99 1
sea, including one as a midshipman, before being allowed to
the exam.
Notwithstanding some well-publicized exceptions, during
of Britain's success in the age of sail, political patronage pla
chiefly in speeding (rather than creating) promotions. Even m
tant, when it came to command, the Admiralty was zealous i
that only naval patronage - that is, the influence of superior
was relied upon.53
An essential ingredient in the promotion process was the c
of officers as being prepared for advancement and command
the certifying senior officers put their own reputations on the
officers they recommended did not live up to expectations,
recommendations were heavily discounted by the Admiralty
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.
See Hill, Prizes', and Benjamin, "Golden Harvest."
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. 2 1 . 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.
992 Benjamin and Tifrea
captain's continued performance in accomplishing the spec
tives of the Crown.57 Captains who performed well were rew
prize money, honors, and the continued command necessary
future prize money and honors. Those who did not were retur
shore and half pay. For island Britain, survival was possib
victory at sea, and all elements of the Royal Navy's organ
incentives were structured accordingly.58
CONCLUSIONS AND IMPLICATIONS
When Spain's 1796 declaration of war forced the Royal N
withdraw from the Mediterranean, the notion that Britain soo
crush her adversaries would have seemed wishful thinking, eve
eternally optimistic Nelson. Yet less than 20 years later, victor
complete that Britain's worldwide dominance at sea went uncha
for a century. If our evidence is correct, the gloom of 1796 was
ranted in the historical context that preceded it.
The Royal Navy did not win every battle in which it engaged
the modern age of combat sail, and its performance during the
American Independence was less than spectacular. Moreover,
waning years of the Napoleonic Wars, losing engagements w
radical new American super-frigates (such as the Constitutio
British commanders pause. Yet the final resolution of the
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.
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, Muhlmann, Die reorganization
der Spanischen Kreigsmarine; and Harbron, Trafalgar, for more.
Learning by Dying 993
1815 it fell 98 percent. Moreover, this learning manifested
measures of combat performance: British combat losses r
losses they inflicted on their enemies declined by 80 percen
These developments were no accident. Britain was comp
insular status to devise successful strategies for combat a
tailed keeping ships at sea, on convoy, patrol, and blo
Meanwhile, enemy fleets were bottled up by financial and
siderations of their own - and eventually by British block
bination enabled British crews to hone their skills, even a
were atrophying. But what made this tactic possible was
ment of British strategy - a compensation and promotion
gave commander and crewman alike the incentive to beha
he were the King himself. Driven by the demands of nea
warfare, and encouraged by organizational supremacy and
centives, British commanders outperformed their enemy
because in learning by doing they accumulated a stoc
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
sider a commander with a force of known fighting strength Sh where
value L indicates low strength and H indicates high strength. Suppos
the enemy's fighting strength is characterized by distribution 1, with
EE and variance o?. 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 enem
flees otherwise;
3. a commander wins if he fights and Sj > EA (where EA , the actual
enemy, is not shown in the figure) and is disgraced if he flees and
A commander with a relatively low level of strength, SL, will clear
Sl < EE; in doing so, he accepts the probability of disgrace shown by t
commander with a high level of strength, SH, facing the same expect
would fight, because SH > EE. In doing so, he faces a probability of d
CDSH, because this is the probability that the enemy will in fact be stron
In this context we assume that learning causes a mean-preserving re
in the variance of the commander's estimate of enemy strength. Th
shown by the shift from distribution 1 to distribution 2. A better-infor
with strength SL who flees will bear a reduced probability of disgrace
Similarly, a more knowledgeable commander of strength Sh who figh
duced probability of defeat, given by CD'SH < CDSH.
994 Benjamin and Tifrea
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.
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.
Learning by Dying 995
commanders generally made the decision whether and when to e
Hence, our characterization of the combat decision as one made b
manders is likely to be a good approximation of the circumstances in
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 Sj > 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
(Sj > EE), a rise in strength increased the probability of British victory: the area be-
tween EE and 5/ rises. Second, a rise in the effective strength of British ships implies
that some encounters for which S; < EE prior to learning now have S; > 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 Sj < EE, a rise in 5/ 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.
996 Benjamin and Tifrea
that mattered was the strength of the British commander's force relativ
strength of the enemy. If 5/ > EA, the British won; if the inequality was re
was the outcome.
Any British ship (or fleet) of actual strength St could be expected to encounter some
distribution of enemy vessels, whose commanders would have expectations regarding
the strength of the British. We let S* 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(Sj) = 5, , 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 S*
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 E\ to E2, with a mean of Em. The
strength of a British opponent, as perceived by the enemy, is distributed over the range
from S\ 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.
Learning by Dying 997
Appendix Figure 2
DISTRIBUTIONS OF ACTUAL ENEMY STRENGTH (£) 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 (/ = 1 1.1), 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.
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.
Hepper, British Warship Losses; and Clowes, Royal Navy.
998 Benjamin and Tifrea
ships lost in combat and combat fatalities among British captains, so com
ships provides a largely independent measure of the process of learnin
Navy.66 Finally, Clowes has compiled combat vessel losses (captured or
tions engaged in combat with Britain, and we have extracted these for a
or more guns. Again, Glete enables us to determine fleet sizes for the va
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 capt
rious, and others died on vanquished but still floating vessels. Only about 10 per
sels lost in combat in our period sank; the rest were captured. Prior to the devel
fused shell in the mid-nineteenth century, it was difficult to damage a warship en
Incentives were also at work: a captured warship meant prize money to the v
whereas the (largely nonswimming) crew of a vessel that sank faced a high risk
hypothermia.
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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