THE STATISTICAL
ADVANTAGE OF STEALING BASES
written by J. F. Jarvis
September 2, 1997
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.
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
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