Sunday, February 24, 2008

Revising the Rotation

Before going on to the minor league rosters, I went through and made a few modifications to the rotation optimizer. Some of the areas where I took shortcuts to make the math easier were likely to throw things off. Here are some of the modifications I made:

For a three game series, I estimated the likelihood of three games being played, two games being played, one game being played, and no games. I did the same for four and three game series. In the scenario of a game being rained out before the end of the series, I assume it to be made up as a doubleheader unless that doubleheader is rained out. This was pretty simple to do in Excel.

I went all the way out to the All Star break this time. I assumed that despite the fact that the rotation will be shaken up, this will be accounted for in the randomness after mid May. For example, the probability of the rotation spots pitching in the late June Colorado series is:

1. 86.3%
2. 67.2%
3. 42.3%
4. 35.8%
5. 67.2%

Rather than assume 10% of games being rained out, I went through and calculated the percentages of games rained out in a month in the ball parks since 2002. For Comerica in April, this is 8.2%, but just 1.2% in June. Fenway (14.3% in April) and Progressive Field (15.5% in April) are by far the highest postponement risks. In the event that no rainouts occured in an outdoor park since 2002 (Comerica in July plus all of the California parks in June), I assigned a low value <0.5% to the rain-out risk, since there is still some possibility.

The results this time were a bit different. Below I list the sum of the (LOPS-ROPS)*P, where P is the probability of pitching in a series against the team.

1. 0.287
2. 0.202
3. 0.188
4. 0.194
5. 0.245

It appears as if the best places to throw the right-handed pitchers are the #1 and #5 spots. This creates a bit of a problem because one of the constraints we had was the fact that Leyland rightfully likes to separate Bonderman and Verlander. Using purely this chart, Verlander would probably be the #1 starter with Bonderman at #5. I would throw Rogers #2, since he is more likely than the other two lefties to miss time and be replaced by a right-handed alternative. Now, where should we place Willis and Robertson? Because Dontrelle Willis is a strong hitting pitcher, it would make sense to place him in the rotation spot where he is most likely to get to bat in an NL Park. Here's the average games started in an NL Park by rotation spot:

1. 1.785
2. 1.618
3. 1.683
4. 1.984
5. 1.926

Using this model, it appears as if Willis would be best utilized as the #4 starter. So, the optimized rotation is now:

1. Justin Verlander
2. Kenny Rogers
3. Nate Robertson
4. Dontrelle Willis
5. Jeremy Bonderman

One big caveat with this analysis: one shift in the rotation can throw everything off. For example, if the #3 starter wakes up feeling sick and switches spots with the #4 starter in the middle of April, we get this rotation:

1. Justin Verlander
2. Kenny Rogers
3. Dontrelle Willis
4. Nate Robertson
5. Jeremy Bonderman

It makes sense that #3 and #4 would simply switch. Now, what happens if Jeremy Bonderman feels sick one day in mid April and is skipped, moving everybody in the rotation up one spot? I don't have a way to simply model this happening, but you have to imagine that the imperfections of a starting rotation perhaps make this exercise irrelevant.

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