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The Aging Curve for PGA Tour Golfers (Part III) – Using Bayesian Prior

Several weeks ago I posted a two studies on aging among PGA Tour golfers, the most recent of which compared sequential seasons, regressing both seasons to PGA Tour average based on the number of rounds a golfer had played in the seasons. DSMok1 suggested modifying the amount and degree of regression by including a better prior, which makes more sense than regressing every golfer to the same mean. Instead of simply adding 25.5 rounds of average play to each golfer’s season, I found a Bayesian prior based on play in the prior season and measured the change in performance from that prior in the following season.

Sample and Design:

I included every player with >20 PGA Tour rounds in a season for 2010, 2011, and 2012. This limited my sample to 703 seasons. I then gathered data for YR N-1, YR N, and YR N+1 (ie, 2009, 2010, and 2011 for golfers with >20 rounds in 2010) on all major Tours (PGA, European, Web.com, and Challenge).

Using the equation ((prior mean/prior variance)+(observed mean/observed variance))/((1/prior variance)+(1/observed variance)) I found my prior expectation on performance, inputting data from YR N-1 for prior mean and variance and from YR N for observed mean and variance. That equation adjusts the observed performance based on what we’ve observed in the prior season to generate a true-talent level (True YR N) for YR N+1. I used the same equation to find the true-talent level for YR N+1. I inputted the prior generated from YR N-1 and YR N as the prior mean and the data for YR N+1 as the observed mean. This produced True YR N+1. I then compared both True YR N and True YR N+1to find the change in true-talent for each age group.

I weighted the results using the harmonic mean rounds played in YR N and YR N+1. For example, there were 18 golfers for age 26, so I took the sum of each harmonic mean of rounds and divided each golfer’s change in true talent by their share of the total rounds. This produced my total change in true-talent due to age for each age-group.

If a golfer had no performance in YR N-1 I used +0.08 (slightly below PGA Tour average) as their YR N-1 prior. In most cases, these players qualified via Qualifying School and +0.08 is the observed true-talent for Q-School golfers for 2009-2013. Only 8 golfers had 0 rounds in YR N-1 however.

Results:

20    -0.05    2
21    -0.06    3
22    -0.01    6
23    -0.05    8
24    -0.07    9
25    -0.11    11
26    -0.13    18
27    -0.13    23
28    -0.14    29
29    -0.12    36
30    -0.13    34
31    -0.11    39
32    -0.12    36
33    -0.11    34
34    -0.13    34
35    -0.12    36
36    -0.11    37
37    -0.10    42
38    -0.08    26
39    -0.05    30
40    -0.01    21
41    0.03    35
42    0.07    28
43    0.12    19
44    0.13    17
45    0.15    13
46    0.21    17
47    0.25    19
48    0.31    13
49    0.36    12
50    0.35    9
51    0.45    4
52    0.47    2

bayesian aging

Discussion:

The curve generated is very similar to that of the prior study regressing to a mean of +0.00. The peak is slightly lower and the decline is deeper in the late 40s, but otherwise this study supports my prior conclusion of aging with a peak in the mid 30s and subsequent decline.

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4 responses to “The Aging Curve for PGA Tour Golfers (Part III) – Using Bayesian Prior

  1. Pingback: Thoughts on Patrick Reed (Without Using “Confident” or “Cocky”) | Golf Analytics

  2. Pingback: An Aging Curve for Putting | Golf Analytics

  3. Pingback: Aging Curves for Scrambling and Driving Distance | Golf Analytics

  4. Pingback: Golfers After 40: How Age Erodes Performance | Golf Analytics

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