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Thursday, August 12, 2004

MLB Pocket Manager

When should a major league manager attempt to steal? When should he attempt to bunt? How does that change in the late innings of a close game?

These are all questions that baseball fans have long thought and argued about. As Alan Schwarz shows in his excellent book The Numbers Game, the first real attempt at answering that question came in the late 1950s when father and son Charles and George Lindsey manually scored and tabulated over 1,000 games. From this data George went on to publish a 24-page article called "An Investigation of Strategies in Baseball" in the journal Operations Research.

In that article Lindsey included tables that show the number of expected runs and the probability of scoring in the remainder of a half-inning given the 24 base-out combinations and used them to answer the questions posed above. John Thorn and Pete Palmer produced an updated version of the table looking at data from 1961-1977 in their 1984 book The Hidden Game of Baseball and importantly also included a similar table of the probabilities of the home team winning in the bottom of the 7th down by a run. With the availability of play by play data starting in the mid 1980s other tables that show the probability of scoring one or more runs have been developed from play by play data a number of times and discussed, for example, in Curve Ball by Albert and Bennett show a table for 2002 data. One such set of tables calculated for 1999-2002 is provided by Tangotiger on his site. Another great computer-ready Win Expectancy table using data from 1979-1990 can be found here.

It always amazes me that this information is not more widely distributed and used in telecasts that regularly pack the screen with useless stats based on ridiculously small sample sizes (Matt Stairs is 3 for 11 when leading off an inning on Tuesdays) or that are simply meaningless (Corey Patterson has a hit in 24 of his last 30 games). So that I could watch a game and evaluate the odds of scoring and wining using various strategies I wrote a small .NET Compact Framework application for the Pocket PC called MLB Pocket Manager. This app uses the run potential, scoring probability, and win expectancy tables from Tangotiger. Using these tables it's simple to evaluate, for example, whether a manager should steal second with 1 out. The calculation goes like this:

Run Potential Before the Attempt = .573
Scoring Probability Before the Attempt = 28.3%

Run Potential If Successful = .725
Scoring Probability If Successful = 40.6%

Run Potential If Caught = .117
Scoring Probability If Caught = 7.7%

So the break-even percentage, the stolen base percentage that the runner needs to exceed, to increase the run potential and the scoring probability can be calculated as:

BErp = (.573 - .117) / (.725 - .117)
BEsp = (.283 - .077) / (.406 - .077)

The results: the break even percentage for increasing the run potential (BErp) is 75% while for increasing the probability of scoring (BEsp) it is 62.6%.

The same calculation can be made using the Win Expectancy table. For example, in the bottom of 7th with 1 out the win probability for the home team is 59%. The break-even can then be calculated as 65.7%.

In MLB Pocket Manager the strategies included are Steal 2nd, Steal 3rd, Double Steal, Sacrifice, Attempt an Advance on a Fielder's Choice, and Tag up to advance.

Here is the simple user interface for the situation described above.

The second tab includes the tables for quick reference.

The third tab describes the methodology.

You can download the CAB files for the various processor types here. Use at your own risk and you'll need the .NET Compact Framework v1.0 installed on your device first which you can get here.

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