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Tuesday, May 06, 2008
Pitchers WAR Aging Curves: 5 year forecast
I finally got around to doing an initial look. This is what I did:
1. Took all pitchers born since 1918 (since Bob Feller)
2. Figured out runs above replacement, runs per win converter, wins above replacement (WAR)
3. For any season where a pitcher had at least 50 IP, figured out how many WAR they had in the following 5 years
4. Create a function using age and WAR in year X, to figure out total WAR in years x+1 through to years x+5
And so, here it is:
WAR5 = 2*WAR + 10 - Age/4
where WAR5 is the WAR for the next 5 years, WAR is the WAR for the most recent season, and Age is season minus birth year
Let’s take an example. Someone is a .630 pitcher, with 225 IP, and is 28 years old. What’s our expectation for the next 5 years?
His WAR is (.630-.380) * 225/9 = 6.25
WAR5 = 2*6.25 + 10 - 28/4 = 15.5
So, we expect 15.5 WAR over the next 5 years. And this is a top-flight pitcher.
If you have a $ per wins over the next 5 years of 4.8, 5.3, 5.8, 6.4, 7.0, that gives us a rough average of 5.8, remembering though that we want to weight the earlier seasons more). That gives us a 90 million$ contract over 5 years. And that is for the prime meat of pitchers.
Take a more reasonable high quality pitcher, say one who is a .580 pitcher, 207 innings, and 30 years old, and we get: 11.7 WAR over the next 5 years. This gives us a 68MM$ deal over 5 years.
And what about a .500 pitcher who is 32 years old, with 180 IP? WAR5 = 7, or a 40MM deal over 5 years.
Gotta run…
One quick thing.
If you figure the average pitcher being 28 years old, the function becomes WAR5 = 2*WAR + 3
Remember also that my really quick rule of thumb would be to lop off 0.5 wins per year. So, if you have 2.5 WAR, then the next 5 years would be 2, 1.5, 1.0, 0.5, 0. The total would be 5.0.
If you have 4.0 WAR, then the next 4 years would be 3.5, 3.0, 2.5, 2.0, 1.5, for a total of 12.5.
You can see pretty quickly how the quick rule of thumb becomes:
WAR5 = 5 * (WAR - 1.5)
A WAR of 3.5 gives us a WAR5 = 10, using either of the two equations.
So, we can see how the rule of thumb of simply chopping off 0.5 wins per year had some basis.
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I’ll compare to my Rule of 10 (drop IP by 10% and win% by 10 basis points) to see how that looks too, next time.