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.


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

Return to Fun Stuff