## More fun with numbers - the value of a stolen base

A recent rumour about Toronto being interested in Jose Reyes got me thinking about the things he would bring to the Jays. In particular, the stolen bases. How much would they be worth?

Most people have seen the sabremetric run expectancy tables such as the one here. They show the expected (average) runs for each combination of men on base and outs.

For example, using the table referenced above, with a man on first and nobody out a team would score an average of .953 runs in the inning. With a man on second and nobody out, the expected runs would rise to 1.189. With one out and nobody on, the expected runs drop to .297.

It follows that a player on first with nobody out who steals second "creates" .236 runs for his team (on an expected average basis). Similarly, if the same player tries to steal second and is caught stealing, he costs his team .656 runs. The ratio of cost to benefit is 2.8.

To apply these figures to real-life base stealers, I took the list of the 50 players with the highest stolen base totals in 2011 and calculated the net runs generated by crediting them with .236 runs for a successful steal and charging them .656 for a CS.

The top 10 SB value-generators?

Coco Crisp - 5.66 runs

Michael Bourn - 5.21

Ichiro Suzuki - 4.85

Jose Reyes - 4.61

Ian Kinsler - 4.46

Tony Campana - 4.35

Cameron Maybin - 4.19

Will Venable - 4.17

Ryan Braun - 3.85

Eric Young - 3.75

Some surprises?

1. Bourn, with 61 steals, only generated about 5 expected runs. I would have expected more. Using the "rule of thumb" of 10 runs = 1 win, all his hard work would translate into one-half of a win
2. Players like Campana (24 steals) and Venable (26) generated more run value than players like Gardner (49 steals) and Kemp (40 steals). This was due to C & V's low CS (2 and 3, respectively)
3. Players like Jacoby Ellsbury (39 steals, 15 CS) and Curtis Granderson (25 S, 10 CS) actually generated negative value.

This calculation assumes that each steal was made with a runner on first and nobody out. This is a roughly average assumption, in terms of runs generated. For example, if we assumed that steals (and CS) all happened with a man on first and one out, Coco Crisp's expected runs generated would drop from 5.66 to 3.34. Or if we assumed that the steals were made with a man on second and nobody out, the 5.66 would increase to 6.33.

There are of course other implications to having a base stealer run: throwing the pitcher off his rhythm, possibly causing errors in attempted throws, fewer double plays, etc. But the value of the stolen base in and of itself - when weighed against the cost of the caught stealing - may be overrated.

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