09 April 2008

Is a Starting Pitcher more valuable than a Cleanup Hitter?

Yesterday and today, there was a conversation over at the Sun's Oriole message board. The issue was whether it was better to have an ace pitcher or a cleanup hitter. On of the courses of argument led to whether a pitcher or a batter had more opportunity to effect a game. A pitcher averages roughly 25 batters a game and pitches every fifth day while a cleanup hitter typically average about 22.5 at bats every 5 days. To do a rough estimate as to the value each has, I chose to look at Jeremy Guthrie's April, 6, 2008 start and Millar's starts from March 31 to April 6, 2008. Guthrie threw to 27 batters and Millar had 21 at bats, so compared to the average . . . Guthrie has roughly 3 more at bats than he should over Millar. I will also compare the two, if Guthrie did not have that advantage.

At Bat Valuation
I am using an expected runs table. I will add up each at bat and come up with a total expected runs number, which will roughly relate to the opportunity inherent in each at bat for production. I will also calculate expected runs per at bat. These calculations will be done for the raw data and the adjusted data (which removes the expected runs attributed to three average at bats). The raw data for the games can be found here.

Guthrie's total expected runs are normal and not a product of his pitching success during the game in question.
Millar's opportunities are also normal.
Neither of these assumptions have been tested.

Raw Data
The raw data shows that Guthrie's 27 at bats resulted in 10.16 expected runs. Millar's 21 at bats resulted in 10.78 expected runs. Millar's numbers showed a 6.04% increase in value over Guthrie's. The average value of a Guthrie at bat was 0.376 expected runs, while our cleanup hitter's average at bat was worth 0.513 expected runs (36% greater in value).

Adjusted Data
If you remove three average at bats from Guthrie's totals, his total is reduced to 9.04 and Millar's value is now 19.3% more. If you shorten Guthrie's rest to four days and assume everything else stays the same . . . his adjusted four day production is 5% more valuable than Millar's opportunities over four days.

Based on the results of this study, the Orioles cleanup hitter had a greater effect on the team's success over five days than their ace pitcher. When the at bats were adjusted to league averages, the cleanup hitter's worth was 19.3% more than the starting pitcher's worth. This would agree with final VORP totals for hitters and pitchers in years past. For instance, in 2007 Arod had a VORP of 96.6 and Jake Peavy had a VORP of 77. Arod's number is 25% higher. Now VORP is not going to correlate with expected runs on a 1 to 1 basis as they do not exactly measure the same thing, but it definately gives credence to the idea that hitters have more opportunities to help a team than a fifth day starter. Simply put, it is in the ballpark.

A star pitcher seems to be less valuable than a star hitter if the pitcher is on a five man pitching staff. He seems to be slightly more valuable than a star hitter, if he pitches on three days rest instead of four. This suggests that hitting may win division pennants and wild cards, but pitching wins in the playoffs. This might explain why teams so well suited for the regular season may flounder in the post-season. Who knows? When teams face each other in the post-season you typically have clubs that differ in winning percentage less than 0.02. You cannot figure out who is better in a five or seven game series when the difference you are trying to discern is so slight.

Discussion over at the Sun Orioles message board.

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