In the first step of calculating Player Wins and Losses, baserunners, pitchers, and catchers are given credit and blame for either advancing (allowing) or failing to advance by (preventing) stolen bases (or defensive indifference) and for being caught stealing or picked off and failing to be caught stealing or picked off.

Overall, 2.2% of raw Player Decisions were accrued in this step over the entire Retrosheet era. Because stolen bases are an elective strategy, however, the share of total Player decisions earned in this Component has tended to vary more over time than other components. In the 1950s, for example, basestealing was fairly rare (until the pennant-winning 1959 Go-Go Sox); hence, Component 1 made up only 1.9% of total Player decisions during this decade. In the 1960s, spurred by the basestealing of players such as Luis Aparicio, Maury Wills, and Lou Brock, as well as the increased importance of one-run strategies due to the lower offensive levels, Component 1 grew to 2.0% of all Player decisions. Basestealing grew still more in importance in the 1970s (2.6% of total Player decisions) and peaked in the 1980s at 2.9%, thanks to a new generation of basestealers including Rickey Henderson, Tim Raines, Willie Wilson, and others. Basestealing lessened somewhat in importance in the 1990s (2.4% of total player decisions for the decade), especially the late 1990s, as offensive levels increased, making one-run strategies relatively less important. The lessening of the importance of basestealing continued into the 21st century, with Component 1 accounting for 1.9% of total Player decisions since 2000.

The probability of a stolen base is calculated based on the league-wide percentage of times a base was stolen given this particular baserunner/out state – that is, 24 probabilities are calculated, one for each base-out state (of course, the three bases-empty scenarios have no chance of a stolen base). Unique probabilities are calculated for each league-season. As an example, average probabilities over the entire Retrosheet Era (1934 - 2013) are shown below.

Overall, 2.2% of raw Player Decisions were accrued in this step over the entire Retrosheet era. Because stolen bases are an elective strategy, however, the share of total Player decisions earned in this Component has tended to vary more over time than other components. In the 1950s, for example, basestealing was fairly rare (until the pennant-winning 1959 Go-Go Sox); hence, Component 1 made up only 1.9% of total Player decisions during this decade. In the 1960s, spurred by the basestealing of players such as Luis Aparicio, Maury Wills, and Lou Brock, as well as the increased importance of one-run strategies due to the lower offensive levels, Component 1 grew to 2.0% of all Player decisions. Basestealing grew still more in importance in the 1970s (2.6% of total Player decisions) and peaked in the 1980s at 2.9%, thanks to a new generation of basestealers including Rickey Henderson, Tim Raines, Willie Wilson, and others. Basestealing lessened somewhat in importance in the 1990s (2.4% of total player decisions for the decade), especially the late 1990s, as offensive levels increased, making one-run strategies relatively less important. The lessening of the importance of basestealing continued into the 21st century, with Component 1 accounting for 1.9% of total Player decisions since 2000.

1.Credits for actual stolen bases, caught stealings, and the like are calculated simply as the change in Win Probability resulting from the change in the base/out situation (and the score, if appropriate).Calculation of Component 1 Player Game Points

The probability of a stolen base is calculated based on the league-wide percentage of times a base was stolen given this particular baserunner/out state – that is, 24 probabilities are calculated, one for each base-out state (of course, the three bases-empty scenarios have no chance of a stolen base). Unique probabilities are calculated for each league-season. As an example, average probabilities over the entire Retrosheet Era (1934 - 2013) are shown below.

Outs | Baserunners | SB | CS | Success Rate |

0 | 1 | 5.8% | 3.3% | 63.9% |

0 | 2 | 1.2% | 0.5% | 70.3% |

0 | 3 | 0.2% | 0.2% | 58.0% |

0 | 1-2 | 1.5% | 1.4% | 52.9% |

0 | 1-3 | 4.2% | 1.1% | 78.4% |

0 | 2-3 | 0.2% | 0.1% | 62.6% |

0 | 1-2-3 | 0.2% | 0.1% | 65.5% |

1 | 1 | 6.1% | 3.7% | 62.2% |

1 | 2 | 1.9% | 0.9% | 69.2% |

1 | 3 | 0.3% | 0.7% | 29.9% |

1 | 1-2 | 1.8% | 1.4% | 56.7% |

1 | 1-3 | 4.7% | 1.9% | 70.8% |

1 | 2-3 | 0.2% | 0.3% | 38.7% |

1 | 1-2-3 | 0.2% | 0.3% | 45.9% |

2 | 1 | 6.7% | 3.3% | 67.5% |

2 | 2 | 0.9% | 0.2% | 80.4% |

2 | 3 | 0.4% | 0.2% | 63.2% |

2 | 1-2 | 0.9% | 0.4% | 69.1% |

2 | 1-3 | 5.9% | 1.4% | 81.3% |

2 | 2-3 | 0.3% | 0.1% | 68.7% |

2 | 1-2-3 | 0.3% | 0.2% | 65.6% |

In addition to wins and losses for actually stealing bases, baserunners, pitchers, and catchers are also credited or debited with their failure to steal or be caught stealing. The win probability at the beginning of a play is calculated based on the probability of each possible event which could subsequently occur. This includes, of course, some possibility that a baserunner may steal one or more bases as well as the possibility that some baserunner may be picked off or caught stealing.

The net win probability in the absence of any stolen bases is calculated as follows. The overall win probability is equal to the weighted average of the win probability with and without base-stealing, i.e.,

The net win probability in the absence of any stolen bases is calculated as follows. The overall win probability is equal to the weighted average of the win probability with and without base-stealing, i.e.,

WinProb = Prob(SB)•WinProb_{SB} + (1-Prob(SB)) •WinProb_{noSB}

where Prob(SB) is the probability of a stolen base, which, as noted above, is base-out dependent. If no stolen base occurs, then the resulting Win Probability will be WinProb_{noSB} above, which can be calculated as follows:

where Prob(SB) is the probability of a stolen base, which, as noted above, is base-out dependent. If no stolen base occurs, then the resulting Win Probability will be WinProb

WinProb_{noSB} = [1/(1-Prob(SB))]•(WinProb – Prob(SB)•WinProb_{SB})

The net effect on Win Probability, then, of not stealing a base will simply be the difference: WinProb_{noSB} – WinProb.

Balks are included in Component 1 under the assumption that balks tend to be the result of pitchers worrying about possible stolen bases. Of course, balks are relatively rare, so it makes little difference whether they are lumped together with stolen bases or with wild pitches and passed balls in Component 2.

One way in which stolen bases are unique among the nine components of Player Decisions is that stolen base attempts are purely elective. That is, the offensive team chooses whether or not to attempt to steal a base, unlike, say, balls in play or wild pitches, which just happen. Because of this, the value of a stolen base is intrinsically dependent on the context in which it takes place. To acknowledge this, I do not calculate a “context-neutral” version of stolen base Player Decisions. All stolen base Player Decisions are tied to the context in which they occurred, so that “context-neutral” Component 1 Player Decisions are exactly equal to “context-dependent” Component 1 Player Decisions. An example of how context affects the value of a player’s stolen bases is discussed in a separate article, which compares Ichiro Suzuki’s and Mike Cameron’s Component 1 Player Games for the 2002 Seattle Mariners.

Offensively, stolen bases, caught stealings, and the lack thereof, are credited to baserunners. Defensively, the credit for these things is shared by pitchers and catchers. This is one of several cases where credit may be shared by different players. The basic process whereby this credit is divided is described elsewhere. The specific division of defensive Component 1 Player Decisions is presented next.

One measure of the extent to which a particular factor is a skill is the extent to which a player’s winning percentage persists over time. To evaluate the persistence of skills, I fit a simple persistence equation which modeled Component 1 winning percentage on even-numbered plays as a function of Component 1 winning percentage on odd-numbered plays:

The net effect on Win Probability, then, of not stealing a base will simply be the difference: WinProb

Balks are included in Component 1 under the assumption that balks tend to be the result of pitchers worrying about possible stolen bases. Of course, balks are relatively rare, so it makes little difference whether they are lumped together with stolen bases or with wild pitches and passed balls in Component 2.

One way in which stolen bases are unique among the nine components of Player Decisions is that stolen base attempts are purely elective. That is, the offensive team chooses whether or not to attempt to steal a base, unlike, say, balls in play or wild pitches, which just happen. Because of this, the value of a stolen base is intrinsically dependent on the context in which it takes place. To acknowledge this, I do not calculate a “context-neutral” version of stolen base Player Decisions. All stolen base Player Decisions are tied to the context in which they occurred, so that “context-neutral” Component 1 Player Decisions are exactly equal to “context-dependent” Component 1 Player Decisions. An example of how context affects the value of a player’s stolen bases is discussed in a separate article, which compares Ichiro Suzuki’s and Mike Cameron’s Component 1 Player Games for the 2002 Seattle Mariners.

Offensively, stolen bases, caught stealings, and the lack thereof, are credited to baserunners. Defensively, the credit for these things is shared by pitchers and catchers. This is one of several cases where credit may be shared by different players. The basic process whereby this credit is divided is described elsewhere. The specific division of defensive Component 1 Player Decisions is presented next.

2.As explained elsewhere, Component 1 Player Games are divided between pitchers and catchers based on the extent to which player winning percentages persist across different sample periods.Division of Component 1 Game Points Between Pitchers and Catchers

One measure of the extent to which a particular factor is a skill is the extent to which a player’s winning percentage persists over time. To evaluate the persistence of skills, I fit a simple persistence equation which modeled Component 1 winning percentage on even-numbered plays as a function of Component 1 winning percentage on odd-numbered plays:

(Component 1 Win Pct)_{Even} = b•(Component 1 Win Pct)_{Odd} + (1-b)•(WinPct)_{Baseline}

where (WinPct)_{Baseline} represents a baseline winning percentage toward which Component 1 winning percentages regress over time.

Equations of this type were fit for Component 1 Player Games for pitchers and catchers. Separate equations were estimated for each base. The results for these equations are shown below. A brief explanation of these variables follows.

The number n is the number of players over whom the equation was estimated, that is, who accumulated any Player wins and/or losses on both odd- and even-numbered plays. The value R^{2} measures the percentage of variation in the dependent variable (WinPct_{Even}) explained by the equation (i.e., explained by WinPct_{Odd}). The numbers in parentheses are t-statistics. T-statistics measure the significance of b, that is, the confidence we have that b is greater than zero. The greater the t-statistic, the more confident we are that the true value of b is greater than zero. Roughly speaking, if the t-statistic is greater than 2, then we can be at least 95% certain that the true value of b is greater than zero (assuming that certain statistical assumptions regarding our model hold). The value of (WinPct)_{Baseline}, the baseline winning percentage toward which winning percentages regress over time, is set equal to 0.500 by construction.

note: To be precise, I estimate unique Persistence Equations for every season, which use all of my data in all of these equations, but weight the data based on how close to the season of interest it is. The equations shown here weight each season equally.

where (WinPct)

Equations of this type were fit for Component 1 Player Games for pitchers and catchers. Separate equations were estimated for each base. The results for these equations are shown below. A brief explanation of these variables follows.

The number n is the number of players over whom the equation was estimated, that is, who accumulated any Player wins and/or losses on both odd- and even-numbered plays. The value R

note: To be precise, I estimate unique Persistence Equations for every season, which use all of my data in all of these equations, but weight the data based on how close to the season of interest it is. The equations shown here weight each season equally.

Persistence of Component 1 Winning Percentage: Baserunner on First Base

Pitchers: n = 32,398, R^{2}= 0.0582

WinPct_{Even}= (27.35%)•WinPct_{Odd}+ (72.65%)•0.5000 (51.88)

Catchers: n = 6,872, R^{2}= -0.0046

WinPct_{Even}= (23.35%)•WinPct_{Odd}+ (76.65%)•0.5000 (19.64)

For baserunners on first base, Component 1 win percentage is significantly persistent for both pitchers and catchers with t-statistics far greater than two for both sets of players. The persistence is somewhat stronger for catchers
(23.4%) than for pitchers
(27.4%). The percentage of Component 1 Player decisions with a runner on first base (Component 1.1) which are attributed to pitchers is set equal to the pitcher persistence coefficient
(27.4%) divided by the sum of the persistence coefficients for pitchers and catchers
(27.4% + 23.4%). This leads to
53.9% of Component 1.1 decisions being allocated to pitchers and
46.1% of Component 1.1 decisions allocated to catchers.

Persistence of Component 1 Winning Percentage: Baserunner on Second Base

Pitchers: n = 31,982, R^{2}= -0.0210

WinPct_{Even}= (15.24%)•WinPct_{Odd}+ (84.76%)•0.5000 (26.51)

Catchers: n = 6,791, R^{2}= -0.0389

WinPct_{Even}= (4.76%)•WinPct_{Odd}+ (95.24%)•0.5000 (4.122)

Based on these results, Component 1.2 decisions are split
76.2% to pitchers
(15.2% / (15.2% + 4.8%)) and
23.8% to catchers.

Persistence of Component 1 Winning Percentage: Baserunner on Third Base

Pitchers: n = 30,549, R^{2}= -0.0252

WinPct_{Even}= (11.58%)•WinPct_{Odd}+ (88.42%)•0.5000 (19.87)

Catchers: n = 6,604, R^{2}= -0.0570

WinPct_{Even}= (12.58%)•WinPct_{Odd}+ (87.42%)•0.5000 (9.912)

Finally, in this case, there is no positive persistence (in fact, there is significant negative persistence) for pitchers in preventing steals of home. There is, however, significant persistence for catchers. Because of this, Component 1.3 decisions are allocated 100% to catchers.

Regardless of whether a net positive or net negative, it is worth noting that very few Player Wins are actually earned by failing to attempt a stolen base. With a runner on first base and second base open, the failure to steal second base cost an average of 0.000292 losses per plate appearance in 2009, for example. Avoiding being caught stealing (or picked off), on the other hand, earned an average of 0.000266 wins per plate appearance.

An interesting contrast can be made between the most prolific basestealer in the Major Leagues from 2000 – 2006, Juan Pierre, who stole 325 bases and was caught stealing 116 times, and perhaps the least prolific basestealer during this time period, Tony Clark, who reached base approximately 580 times over this time period (excluding home runs) and was credited with no stolen bases and a single caught stealing over this time period.

Juan Pierre, from 2000 – 2006, earned a total of 6.43 stolen base wins, the most stolen base wins earned by any baserunner over this time period. He also led all players in stolen base losses, however, with 6.28, for a Component 1 winning percentage of 0.506 and 0.15 net wins.

Tony Clark, on the other hand, because he never ran, amassed a mere 0.24 stolen base wins, but, because he was only caught stealing once, he also amassed only 0.15 stolen base losses, for a Component 1 winning percentage of 0.614 and 0.09 net wins.

In other words, Juan Pierre’s 441 stolen base attempts generated 0.06 more net wins for his teams than Tony Clark’s one (unsuccessful) stolen base attempt did over these seven years.^{*}

^{*}To be fair, Juan Pierre has earned a total of
1.91 net Component 1 wins over his entire career.

Because of the perfect symmetry between offensive and defensive Player Game Points, basestealing accounted for a total of 2.2% of total offensive Player Decisions. The importance of basestealing varied considerably, however, across players. Returning to the above examples, Juan Pierre has accumulated 7.1% of his total Player decisions in Component 1 over the course of his career, while Tony Clark’s basestealing only accounted for 0.6% of his total Player decisions.

The highest percentage of total offensive Games within Component 1 for a single season for a player that played regularly^{*} was probably
Otis Nixon for the 1990 Montreal Expos who had 50 stolen bases and 13 caught stealing in 119 games (263 plate appearances and 26 pinch-running appearances), for a Component 1 Won-Lost record of
1.45 - 1.12. Basestealing accounted for a total of 20.7% of
Nixon’s total offensive Player Decisions and
16.0% of his total Player decisions that year.

^{*}min. 100 games played, 10 player decisions

In contrast, basestealing is a more minor aspect of overall pitching, with Component 1 Player Decisions accounting for only 1.8% of total pitching Player Decisions (not including fielding, batting, and baserunning decisions earned by pitchers). For catchers, on the other hand, Component 1 Player Decisions are a huge percentage of overall catcher fielding, accounting for 62.5% of total fielding value for catchers.

Component 1 leaders can be found here.

3.Player Decisions are awarded not only for stolen bases and caught stealing, but also for a lack of stolen bases and caught stealings when given the opportunity. For most of the seasons for which I have calculated Player won-lost records, the failure to attempt a stolen base was actually a net positive for a base runner. That is, the expected gain in win percentage to an offensive team from a stolen base times the number of actual stolen bases (defensive indifferences and balks) was less than the expected loss in win percentage to an offensive team from being caught stealing times the number of actual caught stealings (including pickoffs). This has not been true every season, and, in fact, this tendency has reversed itself for seasons since 2007.Level of Credit for Not Attempting Stolen Bases

Regardless of whether a net positive or net negative, it is worth noting that very few Player Wins are actually earned by failing to attempt a stolen base. With a runner on first base and second base open, the failure to steal second base cost an average of 0.000292 losses per plate appearance in 2009, for example. Avoiding being caught stealing (or picked off), on the other hand, earned an average of 0.000266 wins per plate appearance.

An interesting contrast can be made between the most prolific basestealer in the Major Leagues from 2000 – 2006, Juan Pierre, who stole 325 bases and was caught stealing 116 times, and perhaps the least prolific basestealer during this time period, Tony Clark, who reached base approximately 580 times over this time period (excluding home runs) and was credited with no stolen bases and a single caught stealing over this time period.

Juan Pierre, from 2000 – 2006, earned a total of 6.43 stolen base wins, the most stolen base wins earned by any baserunner over this time period. He also led all players in stolen base losses, however, with 6.28, for a Component 1 winning percentage of 0.506 and 0.15 net wins.

Tony Clark, on the other hand, because he never ran, amassed a mere 0.24 stolen base wins, but, because he was only caught stealing once, he also amassed only 0.15 stolen base losses, for a Component 1 winning percentage of 0.614 and 0.09 net wins.

In other words, Juan Pierre’s 441 stolen base attempts generated 0.06 more net wins for his teams than Tony Clark’s one (unsuccessful) stolen base attempt did over these seven years.

4.Overall, Component 1 Player Decisions account for 2.2% of total Player Decisions. The relative importance of basestealing as a component of total player value is quite different, however, for baserunners, pitchers, and catchers.Baserunners versus Pitchers versus Catchers

Because of the perfect symmetry between offensive and defensive Player Game Points, basestealing accounted for a total of 2.2% of total offensive Player Decisions. The importance of basestealing varied considerably, however, across players. Returning to the above examples, Juan Pierre has accumulated 7.1% of his total Player decisions in Component 1 over the course of his career, while Tony Clark’s basestealing only accounted for 0.6% of his total Player decisions.

The highest percentage of total offensive Games within Component 1 for a single season for a player that played regularly

In contrast, basestealing is a more minor aspect of overall pitching, with Component 1 Player Decisions accounting for only 1.8% of total pitching Player Decisions (not including fielding, batting, and baserunning decisions earned by pitchers). For catchers, on the other hand, Component 1 Player Decisions are a huge percentage of overall catcher fielding, accounting for 62.5% of total fielding value for catchers.

Component 1 leaders can be found here.