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The Batter/Pitcher Match Up

by Dan Levitt

[ Webmaster's Note: The following article in the By the Numbers newsletter of Statistical Analysis Committee of SABR and appears here courtesy of the author. ]

One of the key questions facing baseball modelers revolves around determining of the outcome of the batter/pitcher match-up. When a .310 hitter faces a pitcher with a batting average against (OAV) of .290 what should the resulting batting average be? At first glance it may appear that the result should be the average of the two, i.e. .300. Upon reflection, however, this solution is flawed. Assuming a .260 league average, the .290 pitcher is worse than average. Therefore, the batter should hit for a higher average against this pitcher than his overall average.

Bill James in his 1983 Baseball Abstract introduces the log5 method for addressing this calculation. He credits the formula below for evaluating the batter/pitcher match-up to Dallas Adams.

Where PitAvg equals batting average against the pitcher.

In the above example this formula would be:

which evaluates to .343.

Does James' theoretical calculation hold true in actual play? The Stats Baseball Scoreboard 1996 contains a study that allows us to empirically test the validity of the above formula. Stats, in an essay titled "Who Hits Who?", looked at how batters hit in 1995 against three pitcher classes: Good (top third), Average (middle third), and Poor (bottom third). Stats' sample included all batters with at least 446 PA and pitchers who faced at least 100 batters.

The appendix to the Stats essay presented the batter data for all 136 batters with at least 446 PA. By breaking the batters into the same three groups (top, middle, and bottom third), we can create nine different comparisons in each league. That is, how do good hitters do against good pitchers, average hitters against poor pitchers, etc.

As an example of the batter calculation methodology, below I have listed the top 24 AL hitters by batting average (i.e. the top third) including how they did against the three classes of pitchers as reported by Stats. In total there were 72 AL hitters with 446 or more plate appearances and 64 in the NL.

Note that the above subtotals are simple averages; they are not weighted by at bats. 

In the next table below I calculated the opponents batting average for each of the three pitching categories. 

For example, the above tables indicate that when batters with an overall average of .315 face good pitchers (overall average against of .233), they will hit approximately .276. This ties out almost perfectly with James' formula which predicts a batting average of .275 when a .315 hitter faces a .233 pitcher given a league average of .269.

In fact, as the final table indicates, the actual batting averages in the eighteen situations (nine comparisons in each league) correlate extremely well with the formula. In other words, at least by this 1995 data, James' formula for predicting the outcome of the batter versus pitcher matchup holds up extremely well.

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This page updated November 4, 1999.

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