Stolen Bases and Caught
Stealing: A Statistical Study
John F. Jarvis
Department of Mathematical Sciences
University of South Carolina-Aiken
email:jfj@pacer1.usca.sc.edu
Stealing second base, thus advancing the runner from first to
scoring position, is one of the most visible and commented on
examples of tactics in Major League Baseball. A downside to this
is that the defense can often thwart the attempt leading to an
out. One obvious question that arises is what is the break even
point, the fraction of attempts that must succeed, allowing
successful steals to just balance the failed attempts? Success
beyond the break even point will provide a net gain in wins to a
team. The converse is also true: if the success rate is less than
the break even point the stealing tactics are reducing the team
wins.
In his 1980 Baseball Research Journal article, "Maury
Wills and the Value of a Stolen Base", David W. Smith
performs a case by case analysis of Maury Wills' base stealing
accomplishments for the 1962, 1963 and 1965 seasons. Beside
clearly indicating that base stealing was a positive force for
his team, Smith also notes that team batting average, BA, suffers
following a Wills stolen base event while team on base
percentage, OBP, is not so dramatically depressed.
Insight into the value of base stealing can be obtained from
two other lines of analysis. Starting with the full season events
files a systematic tabulation of both BA and OBP following a base
stealing event can be obtained. Simulations can provide
additional information by varying the number of team base
stealing attempts and observing the effect this has on team wins.
Preliminary results from both approaches follow.
The following table shows league BA and OBP and the the same
quantities for all plays that immediately follow or include a
stolen base, caught stealing or pick off play, collectively a SB
event. While such plays at all bases are included in the
tabulation, stealing second and caught stealing second are the
most common. Clearly, BA is significantly depressed when a SB
event occurs during an at bat. The differences between the
overall batting average (BA) and the batting average following SB
events (BA/SB) are statistically significant.
The behavior of OBC following a SB event is even more
interesting. Not only is OBC not as depressed after a SB event as
BA, beginning with the 1985 season OBP following a SB event is
larger than the season average. The larger differences are also
statistically significant for the number of events observed.
Smith observed a slightly smaller OBP following a SB event in his
paper, a pattern also seen in the earlier tabulations in Table 1.
There is a hint in this that more recent managerial tactics favor
or allow increased base on balls following a SB event. The full
season event files distinguish between intentional and non
intentional bases on balls so it will be possible to delve into
this a little more deeply.
The data for this table was extracted from the full season
events files by an enhancement of my parser.
Dave Smith kindly performed the BA calculation for the 1982
National League as a cross check on my mine.
Season BA BA/SB OBP OBP/SB Season BA BA/SB OBP OBP/SB
AL67 0.236 0.141 0.305 0.274
NL82 0.258 0.193 0.322 0.321 AL82 0.264 0.192 0.330 0.326
NL83 0.255 0.200 0.324 0.336 AL83 0.266 0.181 0.330 0.318
NL84 0.255 0.233 0.321 0.375 AL84 0.264 0.217 0.329 0.361
NL85 0.252 0.224 0.321 0.370 AL85 0.261 0.197 0.330 0.357
NL86 0.253 0.211 0.324 0.368 AL86 0.262 0.215 0.332 0.346
NL93 0.264 0.195 0.330 0.340 AL93 0.267 0.213 0.340 0.355
NL95 0.263 0.199 0.334 0.353 AL95 0.270 0.232 0.347 0.383
NL96 0.262 0.196 0.333 0.350 AL96 0.277 0.230 0.353 0.375
Table 1. League Batting Averages and On Base Percentage:
Full Season and Following SB/CS/PO
In the simulation discussion that follows stolen bases (SB)
will refer to stolen second base only. Caught stealing (CS) is
the removal of the base runner on first by either being tagged at
second or picked off of first. The result is the same in either
case so I have added successful pick offs on first to the number
of CS at second plays to get the effective CS values used in this
study.
I have used my simulator
to study the efficacy of base stealing. By varying the number of
steals (caught stealing, also) and doing an adequate number of
full season simulations, the sensitivity of wins to changes in
these parameters can be determined. The commonly accepted value
(See the Stolen Base Runs discussion in the Glossary of
Statistical Terms in Total
Baseball Fifth Ed.) is that it takes 33 SB to increase a
team's season wins by one. Similarly, 17 attempts that fail leads
to a decrease in season team wins of one. One goal of the
simulation study is determine the amount of variation in these
parameters for different teams and different seasons.
In the simulations, SB and CS plays occur strictly at random
with rates computed to reproduce the total number of the events
for a complete season. Explicitly, the simulator does not make
any game related tactical decisions about when certain plays
should occur. All events take place at season average rates. In
the case of stolen bases this means in a simulation a team is as
likely to have a SB attempt when leading by 10 runs in the top of
the ninth as it is with a tie score or losing by 10 runs. This
assumption should increase the number of events needed to win a
game. However, Table 1 above shows that batting average and on
base percentage following a SB/CS/PO event are considerably
different than the season averages. The simulator does not model
these differences. Explicitly, the simulator uses the same values
for BA and OBP following a SB event as at any other time. The two
effects would be expected to affect run production in opposite
directions. The extent that these two effects compensate each
other has not been determined in this study.
Using the Total Baseball value for SB wins the magnitude of
computational problem can be estimated. The computation requires
doing simulations with two different values for a team's season
number of SB. The average wins of one of the simulations is
subtracted from the other to get the average wins created by the
difference in SB. Specifically, consider doing two sets of
simulations, one with the teams actual season SB + 30 and the
other set with the actual SB - 30. There is a difference of 60
successes per season for the two different simulations. This will
lead to a difference of approximately 60/33 = 1.8 games per
season difference between the two simulations.
For a season of 162 games the standard deviation for season
wins is approximately 6. This value is typical of the simulation
results. It is also the value obtained by considering season wins
as being drawn from a binomial distribution. The standard error
in the estimate of the mean is the standard deviation divided by
the square root of the number of measurements being averaged.
Standard practice suggests that error estimates of 3 standard
errors be used. Since each of the simulation pairs is
independent, the expected errors of the two added together is
given as the square root of the squares of each simulation error.
In the case that both simulations have the same expected error
this is just the square root of 2 times either of the simulation
errors. Thus to measure the difference in wins to 10% accuracy
requires that:
(1) 3*sqrt(2)*6/sqrt(N) = 0.18
Solving this gives N approximately equal to 20000. Since there
are two simulations to be done, a total of 40000 season
simulations must be done to obtain 10% accuracy in the
determination of the sensitivity of team wins to changes in the
number of stolen bases. Keep in mind this estimate is based on
+/- 30 changes in stolen bases. Such is the tyranny of the
sqrt(N) convergence from Monte Carlo simulations.
Increasing the difference in stolen bases between the two
simulations helps significantly. However, there are limits on how
large this difference can be. The largest reduction in stolen
bases that can be used is a team's actual season number. A
negative number of season SB has no meaning. The largest increase
that could possible be used is to steal at every possible chance.
In practice this number of possibilities is far larger (order of
1500) than the actual number of steal attempts thus the limit on
the largest change is set by the actual numbers of stolen bases.
Explicitly I have required that both the increase and decrease
have the same magnitude be the same so that the averaging the
number of games for both simulations should result in a number of
wins equal to the season simulation averages with no modification
of the attempt rates. The need for this restriction will become
clear when the computation details are given.
Since both the effects of CS as well as SB need to be
determined, this doubles the amount of computations to be done.
Varying the parameters for both SB and CS one team at a time
would require 1120000 season simulations to be done for a 14 team
league. This approaches 8 continuous days of computing for each
league each season on my Power Mac 6100/66 system. Fortunately,
the calculation can be done in a way that saves a factor of 7 (in
a 14 team league) in time.
If two teams have their SB attempts augmented in the same
simulation, each will show slightly less success than it would
have if it were the only team in the simulation so treated. This
is because both teams face opponents that are on the average
stronger than they would have been had only one team had its SB
success rate augmented. However, if I choose a third team and
decrease its SB attempts by the amount the other two teams had
theirs increased, each of the two increased SB teams will face
opponents of the same average strength as if they were the only
team having their SB attempts increased. In a 14 team league this
argument holds when 7 teams have their SB attempts increased and
6 have theirs decreased. Consequently a set of simulations can
have half the teams with increased SB attempts. A final
refinement to this process is to choose 7 teams at random for
increased SB attempts and 6 for the opposite change in SB
attempts. A small number of season simulations are done
(typically 100-200) and the signs of the changes for all teams
are reversed and the other set of simulations done. This process
is repeated until all teams have an adequate number of season
simulations to yield the accuracy required. Constantly changing
the group of teams with augmented SB attempts helps reduce any
systematic, non stolen base, influences on the results. This
method also runs 7 times (in 14 team league) faster than doing
the computations for a single team at a time. CS is managed the
same way. This method requires that all teams use the same change
in number of SB or CS events thus the team with the fewest SB or
CS during the season limits how large a change can be used.
Applying this computation to the 1967 American league
produces:
1967 AL sb2 delta +/- 25, cs2 delta +/- 20
stolen second caught stealing season
team dwins ds/dw errs dwins dc/dw errc b.e. wfrac sb2 cs2 wins
BAL 1.10 45.3 4.3 -1.55 -25.9 2.4 0.64 0.472 50 35 -0.2
BOS 1.14 43.7 3.9 -1.55 -25.8 2.4 0.63 0.568 60 56 -0.8
CAL 1.28 39.0 3.1 -1.55 -25.8 2.2 0.60 0.522 37 32 -0.3
CHA 1.37 36.5 2.9 -1.51 -26.5 2.4 0.58 0.549 117 76 0.3
CLE 1.27 39.3 3.2 -1.47 -27.3 2.5 0.59 0.463 48 66 -1.2
DET 1.07 46.5 4.4 -1.60 -25.0 2.2 0.65 0.562 32 20 -0.1
KC1 1.14 43.7 4.1 -1.51 -26.4 2.4 0.62 0.385 113 65 0.1
MIN 1.14 44.0 4.0 -1.56 -25.6 2.3 0.63 0.562 46 34 -0.3
NYA 1.38 36.4 2.8 -1.54 -26.1 2.4 0.58 0.444 56 38 0.1
WS2 1.38 36.2 2.7 -1.49 -26.9 2.5 0.57 0.472 50 41 -0.1
41.1 -26.1 0.61 61 46 -2.5 (tot)
simulated seasons, sb: 60000, cs: 34000
Table 2: 1967 SB/CS Simulation Summary
In Table 2 the first line identifies the league, year and
lists the size of the modifications used. As always in this
series of presentations, the team names are the Project
Retrosheet and Baseball Workshop abbreviations. Column headings
are: dwins - the average change in season wins between the + and
the - modified simulations; ds/dw - is the change in stolen bases
need to create an additional win; errs is the formal error for
ds/dw. A little algebra is required to put the error estimate (1)
above into the form used in this table; dc/dw and errc are the
equivalent quantities for CS; b.e. is the break even value
(fraction of attempts that must succeed for no net gain or loss)
based on ds/dw and dc/dw values; wfrac - the actual season
fraction of games won; sb2 and cs2 are the actual season stolen
second bases and the sum of caught stealing second and picked off
of first; and wins is the net value of the team's base stealing
efforts given the simulation ds/dw and dc/dw values and the
actual season number of SB and CS. The ds/dw, dc/dw, b.e. and
season sb2 and cs2 columns are averaged and the wins column is
totaled. The average number of season simulations used in the
calculation of these values is given on the final line of the
table.
In the following table the quantities are league season
averages except for wins which is the total league wins or losses
due to attempts to steal second base.
Season ds/dw dc/dw Av. b.e. Av sb2 Av cs2 wins
1967 AL 41.1 -26.1 0.61 61 46 -2.5
1982 NL 41.2 -24.8 0.62 136 69 6.7
1982 AL 43.7 -25.7 0.63 89 55 -1.2
1983 NL 41.1 -25.0 0.62 136 69 7.0
1983 AL 42.7 -25.7 0.62 97 52 3.7
1986 NL 42.7 -25.3 0.63 137 68 6.6
1986 AL 44.6 -25.3 0.64 95 52 1.5
1993 NL 46.2 -25.4 0.64 104 53 2.4
1993 AL 45.3 -25.0 0.64 96 57 -2.1
1995 NL 46.3 -24.8 0.65 95 44 3.8
1995 AL 49.5 -25.5 0.66 80 41 -0.0
1996 NL 46.8 -24.7 0.65 107 46 5.7
1996 AL 52.0 -25.3 0.67 89 43 0.8
Table 3. Season Stolen Base and Caught Stealing Summary
Considering all the data several observations are pertinent.
There are variations of ds/dw and dc/dw in excess of +/- 10% of
the mean for individual seasons. Similarly, within a season there
are variations as large as +/- 20% from the best to worst teams
in the SB calculation. Smaller values of ds/dw and break even
values indicate better base stealing results for a team. The
values for dc/dw are more uniform between different seasons and
within a league. The negative sign for dc/dw values indicates
increased CS decreases wins, as it should. While close to the
values given in Total Baseball the average values for ds/dw and
dc/dw in Table 3 are systematically larger . This may reflect the
absence of game state tactical decisions in the simulator. Still,
all seasons are treated uniformly and the trends should be
significant.
The total wins values indicates very little net gain from base
stealing. The results in the summary table are suggestive in
other ways. The American league consistently shows less from base
stealing than does the National League. Also apparent in the
summary is a slight decrease in the effectiveness of base
stealing in recent seasons. Values for the break even point and
for ds/dw are generally larger in the most recent seasons.
Other season results follow and are in the same format as
Table 2:
1982 NL sb2 delta +/- 60, cs2 delta +/- 30
stolen second caught stealing season
team dwins ds/dw errs dwins dc/dw errc b.e. wfrac sb2 cs2 wins
ATL 2.51 47.9 3.2 -2.48 -24.2 1.6 0.66 0.549 133 77 -0.4
CHN 3.04 39.4 2.1 -2.37 -25.3 1.7 0.61 0.451 120 72 0.2
CIN 3.40 35.3 1.7 -2.29 -26.2 1.8 0.57 0.377 121 76 0.5
HOU 2.91 41.3 2.3 -2.42 -24.8 1.7 0.62 0.475 128 63 0.6
LAN 2.76 43.4 2.6 -2.39 -25.1 1.7 0.63 0.543 145 59 1.0
MON 2.89 41.5 2.2 -2.35 -25.5 1.8 0.62 0.531 147 53 1.5
NYN 2.86 42.0 2.5 -2.31 -26.0 1.9 0.62 0.401 125 58 0.7
PHI 2.86 42.0 2.5 -2.42 -24.8 1.7 0.63 0.549 108 67 -0.1
PIT 2.86 42.0 2.5 -2.40 -25.0 1.7 0.63 0.519 149 77 0.5
SDN 3.04 39.5 2.1 -2.45 -24.5 1.7 0.62 0.500 156 77 0.8
SFN 2.87 41.8 2.2 -2.40 -25.0 1.7 0.63 0.537 119 54 0.7
SLN 3.20 37.5 1.9 -2.56 -23.5 1.4 0.62 0.568 183 90 1.0
41.1 -25.0 0.62 136 69 7.0 (tot)
simulated seasons, sb: 25000, cs: 25000
1982 AL sb2 delta +/- 35, cs2 delta +/- 25
stolen second caught stealing season
team dwins ds/dw errs dwins dc/dw errc b.e. wfrac sb2 cs2 wins
BAL 1.52 46.0 3.3 -2.03 -24.6 1.8 0.65 0.580 46 37 -0.5
BOS 1.62 43.1 3.1 -2.09 -24.0 1.7 0.64 0.549 39 39 -0.7
CAL 1.54 45.4 3.4 -1.99 -25.2 1.9 0.64 0.574 48 53 -1.0
CHA 1.48 47.1 3.6 -2.01 -24.9 1.8 0.65 0.537 131 64 0.2
CLE 1.70 41.3 2.9 -1.96 -25.5 1.9 0.62 0.481 136 67 0.7
DET 1.46 48.0 3.7 -2.01 -24.9 2.0 0.66 0.512 81 64 -0.9
KCA 1.62 43.1 3.1 -2.01 -24.8 1.8 0.63 0.556 124 52 0.8
MIL 1.44 48.7 4.0 -2.00 -24.9 1.9 0.66 0.586 80 51 -0.4
MIN 1.59 44.1 3.2 -1.82 -27.5 2.3 0.62 0.370 37 27 -0.1
NYA 1.63 42.9 3.1 -1.94 -25.8 2.0 0.62 0.488 66 45 -0.2
OAK 1.56 45.0 3.4 -1.91 -26.2 1.9 0.63 0.420 182 68 1.4
SEA 1.83 38.3 2.4 -1.86 -26.8 2.1 0.59 0.469 110 77 0.0
TEX 1.79 39.1 2.5 -1.75 -28.5 2.4 0.58 0.395 61 40 0.2
TOR 1.78 39.4 2.6 -1.92 -26.0 1.9 0.60 0.481 105 84 -0.6
43.7 -25.7 0.63 89 55 -1.2 (tot)
simulated seasons, sb: 31000, cs: 31000
1983 NL sb2 delta +/- 60, cs2 delta +/- 30
stolen second caught stealing season
team dwins ds/dw errs dwins dc/dw errc b.e. wfrac sb2 cs2 wins
ATL 2.88 41.7 2.1 -2.24 -26.7 1.7 0.61 0.543 135 85 0.1
CHN 2.68 44.9 2.5 -2.41 -24.9 1.6 0.64 0.438 78 38 0.2
CIN 2.95 40.7 2.0 -2.26 -26.5 1.8 0.61 0.457 145 72 0.8
HOU 2.58 46.4 2.6 -2.57 -23.3 1.3 0.67 0.525 156 97 -0.8
LAN 2.95 40.7 2.1 -2.37 -25.3 1.5 0.62 0.562 155 72 1.0
MON 2.98 40.3 2.1 -2.37 -25.3 1.6 0.61 0.506 131 44 1.5
NYN 3.16 38.0 1.7 -2.30 -26.0 1.7 0.59 0.420 129 67 0.8
PHI 2.77 43.4 2.2 -2.47 -24.3 1.4 0.64 0.556 133 70 0.2
PIT 3.16 37.9 1.7 -2.45 -24.5 1.5 0.61 0.519 116 75 -0.0
SDN 3.29 36.4 1.7 -2.40 -25.0 1.5 0.59 0.500 162 65 1.8
SFN 3.00 40.0 2.0 -2.36 -25.4 1.6 0.61 0.488 139 67 0.8
SLN 2.93 40.9 2.1 -2.49 -24.1 1.5 0.63 0.488 194 86 1.2
40.9 -25.1 0.62 139 70 7.6 (tot)
simulated seasons, sb: 30000, cs: 30000
1983 AL sb2 delta +/- 25, cs2 delta +/- 20
stolen second caught stealing season
team dwins ds/dw errs dwins dc/dw errc b.e. wfrac sb2 cs2 wins
BAL 1.13 44.1 4.9 -1.56 -25.7 2.1 0.63 0.605 57 36 -0.1
BOS 1.15 43.5 4.7 -1.55 -25.8 2.1 0.63 0.481 29 25 -0.3
CAL 1.16 42.9 4.7 -1.48 -27.1 2.4 0.61 0.432 41 37 -0.4
CHA 1.08 46.2 5.7 -1.58 -25.4 2.0 0.65 0.611 158 52 1.4
CLE 1.34 37.2 3.5 -1.54 -26.0 2.1 0.59 0.432 100 77 -0.3
DET 1.14 43.8 4.7 -1.53 -26.1 2.3 0.63 0.568 80 49 -0.1
KCA 1.18 42.5 4.6 -1.64 -24.4 1.9 0.64 0.488 171 52 1.9
MIL 1.13 44.4 5.0 -1.67 -24.0 1.8 0.65 0.537 94 44 0.3
MIN 1.16 42.9 4.8 -1.55 -25.8 2.2 0.62 0.432 41 34 -0.4
NYA 1.09 45.8 5.6 -1.59 -25.1 2.0 0.65 0.562 73 31 0.4
OAK 1.23 40.8 4.3 -1.50 -26.7 2.3 0.60 0.457 178 81 1.3
SEA 1.30 38.5 3.7 -1.45 -27.6 2.4 0.58 0.370 120 76 0.4
TEX 1.22 41.0 4.5 -1.60 -25.0 1.9 0.62 0.475 100 54 0.3
TOR 1.15 43.6 4.6 -1.64 -24.5 1.9 0.64 0.549 116 81 -0.7
42.7 -25.7 0.62 97 52 3.7 (tot)
simulated seasons, sb: 40000, cs: 40000
1986 NL sb2 delta +/- 60, cs2 delta +/- 30
stolen second caught stealing season
team dwins ds/dw errs dwins dc/dw errc b.e. wfrac sb2 cs2 wins
ATL 2.91 41.2 1.1 -2.32 -25.8 0.9 0.61 0.447 88 75 -0.8
CHN 2.76 43.5 1.3 -2.31 -25.9 0.9 0.63 0.438 127 61 0.6
CIN 2.77 43.3 1.3 -2.36 -25.5 0.9 0.63 0.531 148 54 1.3
HOU 2.96 40.5 1.1 -2.37 -25.3 0.9 0.62 0.593 156 80 0.7
LAN 3.07 39.0 1.0 -2.39 -25.1 0.8 0.61 0.451 136 59 1.1
MON 2.71 44.2 1.3 -2.39 -25.1 0.9 0.64 0.484 172 90 0.3
NYN 2.55 47.0 1.5 -2.32 -25.9 0.9 0.65 0.667 105 48 0.4
PHI 2.56 47.0 1.5 -2.47 -24.3 0.8 0.66 0.534 139 68 0.2
PIT 3.05 39.4 1.0 -2.35 -25.6 0.9 0.61 0.395 129 61 0.9
SDN 2.84 42.2 1.2 -2.33 -25.8 0.9 0.62 0.457 84 64 -0.5
SFN 2.63 45.6 1.4 -2.42 -24.8 0.8 0.65 0.512 141 83 -0.3
SLN 3.06 39.3 1.1 -2.43 -24.7 0.8 0.61 0.491 219 71 2.7
42.7 -25.3 0.63 137 68 6.6 (tot)
simulated seasons, sb: 100000, cs: 100000
1986 AL sb2 delta +/- 40, cs2 delta +/- 30
stolen second caught stealing season
team dwins ds/dw errs dwins dc/dw errc b.e. wfrac sb2 cs2 wins
BAL 1.96 40.8 3.1 -2.30 -26.1 1.7 0.61 0.451 55 35 0.0
BOS 1.71 46.9 3.9 -2.47 -24.3 1.5 0.66 0.590 40 37 -0.7
CAL 1.75 45.7 3.8 -2.43 -24.6 1.5 0.65 0.568 97 40 0.5
CHA 2.13 37.5 2.6 -2.30 -26.1 1.7 0.59 0.444 96 55 0.5
CLE 1.91 42.0 3.2 -2.47 -24.3 1.4 0.63 0.519 132 54 0.9
DET 1.61 49.6 4.8 -2.43 -24.7 1.5 0.67 0.537 122 55 0.2
KCA 1.77 45.1 3.9 -2.33 -25.8 1.7 0.64 0.469 94 47 0.3
MIL 1.85 43.3 3.2 -2.37 -25.4 1.6 0.63 0.478 92 49 0.2
MIN 1.80 44.4 3.4 -2.33 -25.7 1.6 0.63 0.438 75 58 -0.6
NYA 1.81 44.1 3.5 -2.37 -25.3 1.6 0.64 0.556 118 47 0.8
OAK 1.82 43.9 3.8 -2.36 -25.4 1.6 0.63 0.469 123 54 0.7
SEA 1.63 49.0 4.7 -2.34 -25.7 1.6 0.66 0.414 91 68 -0.8
TEX 1.78 44.9 3.8 -2.36 -25.4 1.5 0.64 0.537 90 67 -0.6
TOR 1.68 47.5 3.9 -2.36 -25.4 1.6 0.65 0.531 106 55 0.1
44.6 -25.3 0.64 95 52 1.5 (tot)
simulated seasons, sb: 30000, cs: 30000
1993 NL sb2 delta +/- 50, cs2 delta +/- 25
stolen second caught stealing season
team dwins ds/dw errs dwins dc/dw errc b.e. wfrac sb2 cs2 wins
ATL 2.07 48.2 3.1 -1.91 -26.1 1.8 0.65 0.642 115 44 0.7
CHN 2.21 45.2 2.5 -2.11 -23.7 1.4 0.66 0.519 91 41 0.3
CIN 2.26 44.3 2.5 -1.93 -26.0 1.8 0.63 0.451 115 56 0.4
COL 2.08 48.2 3.1 -1.79 -27.9 2.0 0.63 0.414 119 83 -0.5
FLO 2.41 41.5 2.1 -1.96 -25.4 1.6 0.62 0.395 106 54 0.4
HOU 2.23 44.8 2.7 -1.97 -25.3 1.6 0.64 0.525 87 55 -0.2
LAN 2.29 43.7 2.4 -1.97 -25.4 1.6 0.63 0.500 103 59 0.0
MON 1.97 50.7 3.2 -2.07 -24.2 1.5 0.68 0.580 197 48 1.9
NYN 2.24 44.6 2.4 -2.00 -25.0 1.6 0.64 0.364 70 50 -0.4
PHI 1.88 53.2 3.6 -2.07 -24.2 1.5 0.69 0.599 82 28 0.4
PIT 2.22 45.0 2.5 -1.90 -26.4 1.7 0.63 0.463 77 51 -0.2
SDN 2.13 47.0 2.8 -1.94 -25.8 1.6 0.65 0.377 70 40 -0.1
SFN 2.18 45.9 2.7 -1.96 -25.5 1.6 0.64 0.636 97 63 -0.4
SLN 2.27 44.0 2.5 -2.02 -24.8 1.6 0.64 0.537 133 74 0.0
46.2 -25.4 0.64 104 53 2.4 (tot)
simulated seasons, sb: 40000, cs: 40000
1993 AL sb2 delta +/- 30, cs2 delta +/- 25
stolen second caught stealing season
team dwins ds/dw errs dwins dc/dw errc b.e. wfrac sb2 cs2 wins
BAL 1.29 46.4 4.3 -1.95 -25.6 1.8 0.64 0.525 64 59 -0.9
BOS 1.41 42.5 3.8 -2.06 -24.3 1.5 0.64 0.494 65 45 -0.3
CAL 1.32 45.5 4.5 -1.96 -25.5 1.6 0.64 0.438 143 89 -0.3
CHA 1.41 42.6 3.8 -1.92 -26.0 1.6 0.62 0.580 99 53 0.3
CLE 1.45 41.5 3.6 -2.06 -24.3 1.5 0.63 0.469 133 49 1.2
DET 1.05 57.4 7.0 -2.05 -24.3 1.5 0.70 0.525 90 57 -0.8
KCA 1.40 42.8 3.9 -2.05 -24.4 1.5 0.64 0.519 88 70 -0.8
MIL 1.36 44.2 4.2 -1.93 -25.9 1.6 0.63 0.426 115 79 -0.5
MIN 1.38 43.4 4.0 -1.93 -25.9 1.7 0.63 0.438 77 56 -0.4
NYA 1.34 44.9 4.5 -2.04 -24.6 1.5 0.65 0.543 34 31 -0.5
OAK 1.29 46.7 4.5 -1.93 -25.9 1.7 0.64 0.420 110 54 0.3
SEA 1.34 44.8 4.2 -2.08 -24.0 1.5 0.65 0.506 82 59 -0.6
TEX 1.39 43.3 4.0 -2.10 -23.8 1.4 0.65 0.531 104 57 0.0
TOR 1.23 48.7 5.0 -1.93 -25.9 1.7 0.65 0.586 141 42 1.3
45.3 -25.0 0.64 96 57 -2.1 (tot)
simulated seasons, sb: 40000, cs: 40000
1995 NL sb2 delta +/- 40, cs2 delta +/- 20
stolen second caught stealing season
team dwins ds/dw errs dwins dc/dw errc b.e. wfrac sb2 cs2 wins
ATL 1.72 46.5 2.4 -1.57 -25.5 1.4 0.65 0.625 64 39 -0.2
CHN 1.62 49.3 2.7 -1.62 -24.6 1.3 0.67 0.507 96 40 0.3
CIN 1.68 47.7 2.5 -1.53 -26.2 1.5 0.65 0.590 145 58 0.8
COL 1.55 51.7 3.0 -1.68 -23.8 1.3 0.68 0.535 90 51 -0.4
FLO 1.73 46.1 2.4 -1.59 -25.2 1.4 0.65 0.469 106 49 0.4
HOU 1.67 47.8 2.5 -1.64 -24.4 1.3 0.66 0.528 150 48 1.2
LAN 1.71 46.8 2.5 -1.65 -24.2 1.3 0.66 0.542 114 43 0.7
MON 1.96 40.9 1.8 -1.54 -26.0 1.5 0.61 0.458 101 52 0.5
NYN 1.93 41.4 2.0 -1.67 -24.0 1.3 0.63 0.479 48 36 -0.3
PHI 1.85 43.4 2.1 -1.64 -24.3 1.3 0.64 0.479 59 25 0.3
PIT 1.63 49.0 2.7 -1.61 -24.8 1.4 0.66 0.403 73 49 -0.5
SDN 1.89 42.4 2.0 -1.63 -24.6 1.4 0.63 0.486 96 41 0.6
SFN 1.50 53.5 3.2 -1.61 -24.8 1.3 0.68 0.465 125 41 0.7
SLN 1.93 41.4 1.9 -1.59 -25.2 1.4 0.62 0.434 66 46 -0.2
46.3 -24.8 0.65 95 44 3.8 (tot)
simulated seasons, sb: 82000, cs: 83000
Two 40000 season simulations were done for the the 1995 NL as
a consistency test. The results were consistent within the
calculated error limits. Both simulation were combined in the
above table.
1995 AL sb2 delta +/- 40, cs2 delta +/- 15
stolen second caught stealing season
team dwins ds/dw errs dwins dc/dw errc b.e. wfrac sb2 cs2 wins
BAL 1.66 48.1 4.7 -1.14 -26.4 4.0 0.65 0.493 84 45 0.0
BOS 1.66 48.1 5.1 -1.17 -25.5 3.4 0.65 0.597 93 44 0.2
CAL 1.66 48.2 5.1 -1.20 -25.0 3.4 0.66 0.538 51 37 -0.4
CHA 1.51 53.1 5.5 -1.20 -24.9 3.2 0.68 0.472 93 39 0.2
CLE 1.53 52.3 5.7 -1.17 -25.6 3.6 0.67 0.694 109 52 0.1
DET 1.51 53.0 5.6 -1.14 -26.4 3.7 0.67 0.417 63 39 -0.3
KCA 1.69 47.2 4.3 -1.34 -22.3 2.9 0.68 0.486 94 48 -0.2
MIL 1.63 49.0 4.8 -1.19 -25.3 3.6 0.66 0.451 92 39 0.3
MIN 1.72 46.5 4.6 -1.11 -27.1 4.2 0.63 0.389 93 58 -0.1
NYA 1.71 46.8 4.6 -1.16 -25.9 3.6 0.64 0.549 46 26 -0.0
OAK 1.53 52.4 5.6 -1.19 -25.3 3.4 0.67 0.465 83 41 -0.0
SEA 1.63 49.0 4.9 -1.08 -27.8 4.1 0.64 0.545 83 41 0.2
TEX 1.68 47.5 4.5 -1.20 -25.0 3.6 0.66 0.514 71 52 -0.6
TOR 1.57 51.1 5.5 -1.12 -26.9 4.0 0.66 0.389 61 17 0.6
49.4 -25.7 0.66 80 41 -0.0 (tot)
simulated seasons, sb: 24000, cs: 24000
1996 NL sb2 delta +/- 60, cs2 delta +/- 30
stolen second caught stealing season
team dwins ds/dw errs dwins dc/dw errc b.e. wfrac sb2 cs2 wins
ATL 2.69 44.6 2.2 -2.39 -25.1 1.3 0.64 0.593 73 41 0.0
CHN 2.66 45.1 2.1 -2.45 -24.5 1.3 0.65 0.469 90 45 0.2
CIN 2.29 52.3 3.0 -2.45 -24.5 1.3 0.68 0.500 133 55 0.3
COL 2.21 54.3 3.3 -2.39 -25.1 1.4 0.68 0.512 173 47 1.3
FLO 2.77 43.3 1.9 -2.37 -25.3 1.3 0.63 0.494 86 45 0.2
HOU 2.58 46.6 2.2 -2.44 -24.6 1.3 0.65 0.506 142 60 0.6
LAN 2.65 45.2 2.1 -2.47 -24.3 1.2 0.65 0.556 111 39 0.8
MON 2.68 44.7 2.2 -2.43 -24.7 1.2 0.64 0.543 96 35 0.7
NYN 2.88 41.6 1.9 -2.50 -24.0 1.2 0.63 0.438 78 49 -0.2
PHI 2.46 48.8 2.6 -2.46 -24.4 1.3 0.67 0.414 99 42 0.3
PIT 2.42 49.6 2.6 -2.49 -24.1 1.2 0.67 0.451 106 42 0.4
SDN 2.85 42.1 1.9 -2.35 -25.6 1.4 0.62 0.562 87 48 0.2
SFN 2.36 50.9 2.7 -2.34 -25.7 1.4 0.66 0.420 103 51 0.0
SLN 2.64 45.4 2.1 -2.51 -23.9 1.2 0.66 0.543 126 49 0.7
46.8 -24.7 0.65 107 46 5.7 (tot)
simulated seasons, sb: 40000, cs: 40000
1996 AL sb2 delta +/- 40, cs2 delta +/- 20
stolen second caught stealing season
team dwins ds/dw errs dwins dc/dw errc b.e. wfrac sb2 cs2 wins
BAL 1.56 51.2 4.7 -1.63 -24.5 2.3 0.68 0.543 67 40 -0.3
BOS 1.45 55.4 5.4 -1.56 -25.6 2.3 0.68 0.525 83 43 -0.2
CAL 1.67 47.9 4.1 -1.58 -25.3 2.3 0.65 0.435 47 40 -0.6
CHA 1.51 53.2 5.5 -1.53 -26.1 2.5 0.67 0.525 94 44 0.1
CLE 1.51 53.0 5.2 -1.56 -25.7 2.5 0.67 0.615 122 52 0.3
DET 1.41 56.9 6.1 -1.35 -29.6 3.2 0.66 0.327 74 51 -0.4
KCA 1.99 40.2 3.0 -1.61 -24.8 2.2 0.62 0.466 161 73 1.1
MIL 1.54 51.9 4.8 -1.73 -23.1 1.9 0.69 0.494 86 44 -0.2
MIN 1.77 45.2 3.8 -1.57 -25.4 2.4 0.64 0.481 133 49 1.0
NYA 1.69 47.3 4.0 -1.61 -24.9 2.3 0.65 0.568 83 41 0.1
OAK 1.37 58.3 6.2 -1.64 -24.4 2.2 0.70 0.481 55 34 -0.4
SEA 1.38 58.1 6.5 -1.61 -24.9 2.4 0.70 0.528 71 36 -0.2
TEX 1.40 57.1 5.8 -1.65 -24.2 2.2 0.70 0.556 76 24 0.3
TOR 1.51 53.1 5.4 -1.59 -25.1 2.2 0.68 0.457 92 35 0.3
52.0 -25.3 0.67 89 43 0.8 (tot)
simulated seasons, sb: 30000, cs: 30000
Copyright 1997, John F. Jarvis
comments to: jfj@pacer1.usca.sc.edu
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