1. Studying the Effects of Aging in Major League Baseball Phil Birnbaum www.philbirnbaum.com

2. Aging patterns in baseball How do players age? Is it different for hitters and pitchers? If you have a good player who's 31, how much do you expect him to decline over the next few years? Want a result like: "hitters decline X% between age 31 and 35"

3. Studies Bill James' classic aging study in the "1982 Baseball Abstract" Work by Tom Tango Academic studies: Jim Albert, Ray C. Fair, and others (This presentation is based mostly on Tango, with a bit of James)

4. Previous findings The best batters peak at 27 – that's when most of the major awards are won (James) Different skills peak at different times: speed early, HRs mid-career, BBs late (Tango)

5. A naive look What's the average performance of the various age cohorts? Fairly similar, it turns out, except at the extremes

6. Average Batting vs. Age

7. Average Pitching vs. Age

8. A naive look Statistical illusion Curve traces different groups of players Players at 25 are a cross-section of the league Players at 40 are former superstars The players at 40 were much better players when they were 25

9. Example Age 27 Player A: 6.00 … Player B: 5.00 … Player C: 4.00 Average: 5.00 Age 35 Player A: 5.50 … Player B: 4.50 … Player C: released Average: 5.00 Age 40 Player A: 5.00 … Player B: retired … Player C: released Average: 5.00 All players decline with age, but the mean is still 5.00

10. Paired seasons "Paired seasons" method Find all players who were 28 in season X See how they did in season X+1 (Weight the average by playing time) The average difference reflects the effects of aging from 28 to 29 Career path obtained by chaining (multiplying) single-year effects

11. Paired seasons: Batting

12. Paired seasons: Pitching

13. Paired seasons: results biased The paired-seasons method shows big declines as players age But it suffers from a bias – selective sampling Players who were "lucky" in season X (large positive error term) get more playing time in season X+1 Those "lucky" players will show bigger declines So big declines are over-represented

14. Example Three 37-year-olds, all of whom have skill of.250 this year,.240 next year This year, due to chance, they hit.200,.250,.300 respectively The.200 guy is forced to retire The.250 guy plays half time next year and loses 10 points (.250 .240) The.300 guy plays full time next year and loses 60 points (.300 .240) The weighted average loss is 43 points, not 10 points The decline is very much overestimated

15. How can we eliminate this bias? Can try to estimate the "true" talent of the three players Regressing to the mean The.200 guy is "probably".220 The.250 guy is "probably".250 The.300 guy is "probably".280 Now the third guy declines only 40 points, not 60 Average decline: 30 points More accurate than previous estimate of 43 points If we regressed "perfectly" – all players to their talent of.250 – we'd get the right answer (10 pts)

16. Regressing season X How much to regress? Need to do some research to figure that out Can probably get a theoretical lower bound from binomial (multinomial) distribution For now, consider 10% and 30%

17. Batting, regressed 10%

18. Batting, regressed 30%

19. Pitching, regressed 10%

20. Pitching, regressed 30%

21. Conclusions Results sensitive to how much we regress Getting correct estimates of aging using the paired- seasons method depends on solving the selective sampling problem and/or figuring out how much to regress Alternative: can fit curves to careers (Albert, Fair) But this method requires a long career, which means only the most successful players are analyzed Some selective sampling issues there too

22. References "Looking For the Prime," 1982 Bill James Baseball Abstract, p. 191 Tom Tango, http://tangotiger.net/agepatterns.txthttp://tangotiger.net/agepatterns.txt Tom Tango, "Forecasting Pitchers – Adjacent Seasons," http://www.tangotiger.net/adjacentPitching.html http://www.tangotiger.net/adjacentPitching.html Ray C. Fair, "Estimated Age Effects in Baseball," http://www.bepress.com/jqas/vol4/iss1/1/ http://www.bepress.com/jqas/vol4/iss1/1/