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Saturday, August 28, 2004

The Effect of Pitchers

In an earlier post I introduced the MLB Pocket Manager that used play-by-play data from 1999-2002 in order to calculate probabilities for various offensive strategies including sacrificing and stealing. I wrote the application using the .NET Compact Framework and it can be downloaded here.

One of the immediate questions that come up when looking at how the application is works is how do the odds change when a pitcher is at the plate? This is an issue since the data used in the tables is an aggregate of all hitters and everyone knows that decisions about sacrificing, for example, are impacted greatly by whether or not a pitcher is hitting.

In order to answer that question I calculated the probability of various offensive events for all pitchers in the period 1999-2002 using the Lahman database. They were:

Out = .798
Single = .120
Double = .027
Triple = .002
Homerun = .008
Walk = .047

These calculate to a .164 batting average, .221 slug, and .203 on base percentage.

Next, I used a little algebra as described by Albert and Bennet in their excellent book Curveball. For example, the probability of scoring with a runner on first and nobody out is 43.7%. The same situation with a pitcher up yields a probability of 36.7%. This is calculated by multiplying the probability of each offensive event with the probability of scoring after the event takes place and summing the values. For example, a pitcher makes an out 79.8% of the time. This is then multiplied by probability of scoring after the out, 28.3% which equals .226. The same is done with each offensive event shown below and the values added:

.798 * .283 = .226
.120 * .641 = .077
.027 * .876 = .024
.002 * 1 = .002
.008 * 1 = .008
.047 * .641 = .030

The sum of these numbers is, accounting for rounding, .367. This number is then used in the break-even equation by substituting the present value (Pv) for either run potential or scoring probability with a value calculated explicitly for pitchers. You'll recall that to calculate the break even percentage you use the following equation:

P = (Pv - Fv) / (Sv - Fv)

where Fv is failure value and Sv is success value.

Finally, I added a checkbox to the user interface that can be checked in order to calculate the break-even percentages with the pitcher up. I also added an entry to the tables list that shows the pitcher stats that were used in the calculation.

Enough of the math, so what are the results? Here are some examples:

With a runner on first and nobody out the Pocket Manager says that an average hitter should never bunt. With the pitcher up the strategy makes sense if the goal is to score one run and if the pitcher's odds of laying down the bunt are 83.1% or better. In another example, with runners on first and second and nobody out an average hitter should not sacrifice if the goal is maximize runs and must be succesful 79.9% of the time if the goal is to score a single run. With the pitcher up these odds change dramatically as it makes sense to sacrifice with a break-even percentage of just 35.9% to score one run and 62.1% to maximize runs. In a third example a baserunner needs to be successful stealing second base 73.5% of the time with nobody out and an average hitter up in order to maximize the number of runs scored in the inning. With the pitcher up the stolen base percentage needed goes down to just 56%.

Of course, the lesson here is that the weaker the hitter, the more risks a manager can take with one-run type strategies like the bunt and stolen base.

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