Thursday, December 26, 2019
Weighted Enhanced Game Score
?You will feel you are walking in the middle of four conversations. That's because you will be walking in the middle of four conversations. Hopefully, by the end of this thread, you will have joined me to where I am.
The first conversation is Game Score. Bill James created a wonderful little tool that found a renaissance in the internet age. Unlike most of the things that Bill does, he has not (officially) tinkered with this metric. I have. A few years back I identified three holes, which I've addressed. If Bill wanted to, he would have done it himself. But as Bill said in the past "I can't do this all by myself". So, I did my little part. The three main issues were
- (a) making the starting point as 50, or average, which if you know Bill, is not really something that he would have subscribed to even at the outset. And in his unofficial tinkering, he has modified it down to around 35, but not officially. In my enhanced version, I made the starting point 40;
- (b) changing the valuing the walks v hits consistent with DIPS; DIPS of course was a Voros creation about 15 years after Game Score, though Bill himself was on the precipice with DER; in any case, I provided that fix;
- (c) actually including HR; when Bill first did this, HR were NOT part of the line score for a pitcher; but now they are; it seems clear we want to include HR, especially in light of DIPS.
The second conversation is WARcels. This was my method to creating a WAR forecast, using only WAR. No component data, no playing time, nothing but WAR. While the normal weighting for rate stats is about 5/4/3 or 4/3/2 for the last three seasons, the weighting for playing time is 5/1/0. Since WAR is a combination of rate stats and playing time, WARcel proposes a 60/30/10 scheme. And then to forecast the future, take 80% of that, or 48/24/8.
The third conversation is the ballast. The term I should use, and do use in The Book, is Regression Toward the Mean. But, let's be honest here: if I say "regression", most people think of it as a bad thing. Michael Lopez suggested Reversion, which is an excellent word. Bill James (him again) uses the word Ballast. And that is the winner; it's the winner because it better describes what we want, and it is less technical. Observations inherently have alot of good luck and bad luck associated with whatever real thing that drives that observation. When you strip away that luck, you are pulled back into that real thing. The ballast is what does that.
The fourth conversation is, again, from Bill, and his World's Starting Pitcher rankings. Bill weaves his magic into a simple looking equation of starting every pitcher at 300, then adding 30% of his Game Score to the total. And then for his next start, take 97% of the running total, and 30% of his current start. (It's actually 3% of his Game Score had he started each pitcher at 30.)
Ok, so those are the 4 conversations. Now I can talk about my riff off of Bill's idea.
The first thing I do is I apply a decay rate. This is typical for me, and it's far easier to code in SQL. I simply give a weight of 0.998^daysAgo. So, for a game today, daysAgo=0, that's a weight of 1. For a game 365 days ago, that's a weight of 48%. And for games 730 days ago, that's a weight of 23%. Those numbers look familiar? That's WARcels. So, for every game between today and 1000 days ago, I have a weight of each game. That's what I am doing here, a weighted running total for every pitcher. (That's conversation 2.)
And what metric do I use? My version of Game Score. (That's conversation 1.)
What starting point do I use? In my case, it's not so much a starting point, as a constant ballast. Every pitcher gets a presumed 5 starts of a Game Score of 30. Why 5? And why 30? I'm glad you asked. The 30 comes from the fact that virtually every pitcher who has faced 200 batters has a Game Score of at least 30. That is in essence the replacement level. The WARcels works on the basis of replacement level, not average. And while we'd normally use average as a ballast, it makes no sense in this context. You could argue for a ballast of 35, and maybe as high as 40. But I think it makes more sense to make sure not to give a pitcher too much of a running start. So, 30 is what I use.
As for the 5 start ballast: when I looked at all pitchers with an average Enhanced Game Score of at least 60 (average of 63.5), and then looked at their next start (average of 58.6), in order to estimate that value, I can get there by adding 5 starts of a 30 game score ballast. (That's conversation 3.)
And so, now that I have a metric, know how to weight each start, know how much ballast to apply, I simply add it all up, and I have a Weighted Enhanced Game Score metric. And this is how it has looked for a few pitchers.
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