Advantages of Stealing Based on Expected Runs

In my last post, I showed how to use the probability of winning to evaluate the break-even probability for a base stealing attempt to be worthwhile. That is, if the probability of successfully stealing the base is greater than the break-even probability, then the player should attempt to steal the base because in this situation the expected probability of winning the game would be higher than if he did not attempt to steal the base. If not, then the player should not attempt to steal the base because the expected probability of winning the game would be lower.

The problem with using the probability of winning to find the break-even probability is that the probability of winning table is very large. It provides a unique probability of winning for every possible state of the game.  Therefore, there would be a unique break-even probability for each possible state of the game.

A simpler approach to evaluating the break-even probability is to use the expected runs table that I developed in an earlier post. This could be easily memorized for every possible state in an inning. In this case, if the estimated probability of successfully stealing the base is greater than the break-even probability, the player should attempt to steal the base because this would increase the expected runs that would be scored in the inning.

Below is the expected runs table for any situation in an innning with the break-even probability for attempting to steal a base.

Outs	IB	2B	3B	Expected Runs	Break-even Probability
0	0	0	0	0.4885
1	0	0	0	0.2884
2	0	0	0	0.1156
0	1	0	0	0.8729	0.76
1	1	0	0	0.5043	0.73
2	1	0	0	0.2011	0.72
0	0	1	0	1.0611	0.77
1	0	1	0	0.6461	0.68
2	0	1	0	0.2793	0.69
0	1	1	0	1.4657	0.66
1	1	1	0	0.9244	0.62
2	1	1	0	0.4046	0.67
0	0	0	1	1.2919	0.84
1	0	0	1	0.8993	0.67
2	0	0	1	0.4069	0.36
0	1	0	1	1.7092	0.81
1	1	0	1	1.1436	0.81
2	1	0	1	0.5224	0.41
0	0	1	1	1.8950	0.71
1	0	1	1	1.3165	0.61
2	0	1	1	0.6006	0.43
0	1	1	1	2.3333	0.64
1	1	1	1	1.8205	0.71
2	1	1	1	0.7774	0.49

Notice that the break-even probabilities, in this case, are quite high for most the situations. 

However, stealing home from third base with two outs has a relatively lower break-even probability than the other situations. For example, with two outs and a runner on third base, the break-even probability is only 36%. This shows the potential of being ready to attempt to score from third base on a wild pitch or a passed ball.

Although the break-even probabilities are higher, with two outs and runners on first and third base (41%), runners on second and third base (43%) and bases loaded (49%), it seems that the probability of successfully making it home on a passed ball or wild pitch does not need to be even 50-50 to make it worthwhile to attempt it based on the expected runs calculation.