Pitching WAR Aging Patterns

I decided, along with Sky Kalkman's Bad Contracts discussion, to look into finding a players aging multipliers for WAR and apply them to project a few contracts by selecting a pitcher and seeing what his numbers project to do one year to the next.

Note/Disclaimer/Venting Rant: I originally started this endeavor with wanting to look at pitchers (starters and relievers) considered to be regulars and what they did the next year. I decided on 40 innings as being my point of reference for a regular pitcher. I went to Fangraphs and download all the data of pitchers with 40 innings or more. As you can tell, when I went to match the pairs later, I wouldn't catch the pitchers that had less than 40 innings in the second year, but greater than 0. I didn't notice the problem until I was almost done and was looking at my beloved Royals and couldn't find the 2008 numbers on Jimmy Gobble. It was then I relized my error. I decided to go forward with the semi-biased data and might go back later and redo it when I am not so mad at myself.

I looked at all the pitchers between 2002 and 2008 that pitched 40 innings in consecutive years. Then I divided the first year by the second year for the Starting, Relief and Total War and also for Starting, Relief and Total innings pitched to get the multiplier factor for each of these factors. Here are the results:

Adjustment (going to age):	Staring War	Starting IP	Reilver War	Relief IP	Total WAR	Total Innings	Number of Paired Seasons
22	1.38	1.41	1.75	0.90	1.42	1.34	11
23	1.53	1.26	1.10	1.05	1.51	1.23	34
24	1.18	1.16	0.86	1.08	1.12	1.15	72
25	1.17	1.08	1.23	1.01	1.18	1.07	94
26	0.99	1.03	1.25	1.17	1.02	1.05	118
27	1.02	0.98	0.74	1.05	0.98	0.99	132
28	0.99	1.03	1.25	1.17	1.02	1.05	134
29	0.80	0.84	1.05	1.08	0.85	0.89	132
30	0.92	0.99	1.02	1.04	0.94	1.00	141
31	1.03	1.02	0.63	0.94	0.90	1.00	133
32	0.85	0.84	1.14	1.03	0.92	0.90	104
33	0.68	0.82	0.69	1.07	1.04	0.89	86
34	0.84	0.88	0.74	1.05	0.81	0.94	58
35	0.80	0.85	0.73	0.99	0.77	0.90	39
36	0.80	0.91	0.89	1.06	0.81	0.96	19
37	0.80	0.85	0.93	0.90	0.87	0.87	20
38	0.60	0.87	0.74	1.09	0.68	0.98	10

There is for sure a lack of data and the extremes, but significant number for reliable numbers from 24 to 34. Here is the graphs of starting and relief WAR for each year:

A few notes I have observed:

1. Pitchers add to their WAR to ~28 years old and stay fairly level until they begin to decline at age 32.

2. I averaged the Total WAR values of pitchers that did not reach 40 innings the next year their WAR averaged 0.46. Replacement level pitchers get replaced.

3. 70% of all pitchers did not reach the 40 innings from year to year.

With this information, I decided to look at the contracts signed this off season by C.C. Sabathia and A.J. Burnett by the Yankees. I just used there 2008 WAR numbers to base the next year on. What exact number is used is debatable, but I used 2008 for ease of discussion/calculation. I used the dollar value of the wins from Fangraphs of 4.5M to be paid for each WAR in 2008. I needed to calculate the inflation value for the future. The percent increase in the past was for baseball salaries was ~10%. I decided to go a little more conservative consider the economy and went with 7%. Here are the two pitchers:

Name	Amount of Contract (Millions)	Years of Contract	Amount per Year
C.C. Sabathia	$161.00	7	$23.00		Multiplier Used
					1.07
Age	Innings	Innings Multiplier	WAR	Starter Multiplier	Projected Value of 1WAR	Projected Amount of Value (millions)
28	353		7.7		4.5
29	296.37	0.84	6.19	0.8	4.82	$29.83
30	293.63	0.99	5.68	0.92	5.15	$29.24
31	299.3	1.02	5.85	1.03	5.51	$32.25
32	251.94	0.84	4.95	0.85	5.9	$29.18
33	205.83	0.82	3.38	0.68	6.31	$21.31
34	180.27	0.88	2.85	0.84	6.75	$19.26
35	152.53	0.85	2.27	0.8	7.23	$16.43
		Total War =	31.17		Estimate Value of contract =	$177.50
		Value with constant value for WAR (4.5M) =	$140.26

Name	Amount of Contract (Millions)	Contract Length (Years)	Amount per year
A.J. Burnett	$82.50	5	$16.50		Multiplier Used
					1.07
Age	Innings	Innings Multiplier	WAR	Starter Multiplier	Projected Value of 1WAR	Projected Amount of Value
32	220		5.7		4.5
33	196.51	0.89	3.89	0.68	4.82	$18.73
34	184.26	0.94	3.29	0.84	5.15	$16.93
35	166.68	0.9	2.62	0.8	5.51	$14.45
36	160.51	0.96	2.09	0.8	5.9	$12.34
37	139.83	0.87	1.68	0.8	6.31	$10.59
		Total War =	13.57		Estimate Value of contract =	$73.04
		Value with constant value for WAR (4.5M) =	$61.05

As you can see C.C.'s contract doesn't look like a good deal with today's prices ($140M vice $161M) , but when you take inflation into consideration, it doesn't look as bad ($177M vice $161M). A.J.'s on the other hand doesn't look like a good deal for the Yankees either way ($61M/$73M vice $82.5M).

Let me know if you have any questions/commnets and remember to double check your data.