Applying Park Factors
October 28, 2003
After calculating the marginal runs for each team, the Win Shares methodology calls for a park adjustment to marginal runs. This makes sense. It’s a lot easier to score runs in Coors Park than Dodger Stadium, and Win Shares takes this into account. However, the manner in which park factors are applied to marginal runs differs from typical park factor calculations, and it undermines the validity of the relationship between marginal runs and Win Shares.
Well, that got your attention, didn’t it? I love these opening headlines.
As a reminder, here’s a graph of American League Marginal Runs vs. pythagorean wins before the park adjustment.
Now, here’s a graph of Marginal Runs vs. pythagorean wins after the park adjustment.
See the difference? The park adjustment reduces the correlation coefficient from .996 to .926. This doesn’t pass our Win Shares validity test, because the park adjustment has actually weakened the relationship between the two key measures of the system.
Here’s why:
Most Park Factor calculations involve dividing the performance metric by the Park Factor. If Todd Helton creates 140 runs in Coors Park, you divide that by a park factor, say 120%, to get 117 runs created on a park-adjusted basis. I’m talking hypothetical numbers here.
James did something different for teams and individuals. He multiplied the Marginal Runs floor or ceiling by the Park Factor, and then compared the raw Runs and Runs Allowed to that floor or ceiling. This different methodology changes the inherent relationship between Marginal Runs and Wins, as shown above.
I was involved in a recent online discussion that can serve as an example. When comparing two Rookie of the Year candidates, it was noted that Hideki Matsui had created 52 Marginal Runs to Angel Berroa’s 35—a 49% difference.
Yet Matsui was credited with 70% more Win Shares than Berroa (16.4 to 9.6), even though the Royals had the pythagorean differential in their favor. Why? Because of the way the park adjustment was applied to marginal runs.
Well, this is pretty easy to fix. I went through the spreadsheets and recalculated team marginal runs by dividing runs scored and allowed by the park factor, and then applying the average ceiling and floor to calculate Marginal Runs. And here’s a graph of what I got:
And the correlation coefficient is restored to .995.
As a next step, I then applied the home park adjustment methodology to all individual player stats. Let me try and show the difference between the two methodologies, using some imagined stats:
Current New
RC 100 100
Floor 25 25
Park Fact 1.1 1.1
Floor* 27.5
RC* 91
Marg Runs 72.5 66
See? One approach changes the floor, the other changes the Runs Created, and the result is not the same.
The good news is that this didn’t change the individual Win Share totals of any individual player more than one share, because it tended to have a proportionately even impact on all players. But it did impact a fair number of players.
Regarding Matsui and Berroa, their offensive Win Share totals didn’t change, but their Marginal Runs did. With this new system, Matsui wound up with 54 Marginal Runs, and Berroa got 31—an 80% difference that Berroa closed thanks to the Royals’ pythagorean performance.
Here’s a list of all the AL players whose Win Share totals changed:
Player Team Orig WS New WS Diff
L Bigbie BAL 9 10 1
M Tucker KC 9 10 1
B Davis SEA 7 8 1
D Wilson SEA 7 8 1
L Rivas MIN 6 7 1
R Dickey TEX 6 7 1
J Peralta CLE 4 5 1
K Mench TEX 4 5 1
Hendrcksn TOR 4 5 1
D Turnbow ANA 2 3 1
Eknstahlr DET 1 2 1
G White NYY 1 2 1
A Piatt OAK 1 2 1
R Quinlan ANA 0 1 1
F Sanchez BOS 0 1 1
D DeJesus KC 0 1 1
B Boone SEA 30 29 -1
M Ramirez BOS 28 27 -1
J Giambi NYY 28 27 -1
E Martinz SEA 20 19 -1
O Hudson TOR 18 17 -1
E Byrnes OAK 16 15 -1
Guardado MIN 15 14 -1
A Guiel KC 12 11 -1
C Everett TEX 12 11 -1
Eckstein ANA 11 10 -1
Broussard CLE 9 8 -1
B Fordyce BAL 5 4 -1
R Mahay TEX 5 4 -1
S Wooten ANA 2 1 -1
Kingsale DET 1 0 -1
B Berger KC 1 0 -1
And here’s the same list for the National League:
Player Team Orig WS New WS Diff
P Polanco PHI 18 19 1
Schneider MON 13 14 1
T Worrell SF 13 14 1
Hampton ATL 11 12 1
J Wilson PIT 11 12 1
D Jimenez CIN 10 11 1
J Burnitz NYM 9 10 1
VanderWal MIL 8 9 1
E Perez STL 7 8 1
R Johnson ARI 6 7 1
K Ishii LA 6 7 1
A Nunez PIT 4 5 1
G Lloyd NYM 2 3 1
G Zaun COL 1 2 1
N Punto PHI 1 2 1
M Romero COL 0 1 1
T Womack COL 0 1 1
R Coomer LA 0 1 1
E Knott MON 0 1 1
C Rivera PIT 0 1 1
Sheffield ATL 35 34 -1
J Vazquez MON 21 20 -1
J Vidro MON 19 18 -1
R Sanders PIT 18 17 -1
A Beltre LA 15 14 -1
M Batista ARI 14 13 -1
M Stairs PIT 13 12 -1
A Ramirez PIT 10 9 -1
R Cedeno NYM 8 7 -1
B Clark MIL 7 6 -1
R Alomar NYM 7 6 -1
R Branyan CIN 6 5 -1
O Perez LA 6 5 -1
Michaels PHI 5 4 -1
F Vina STL 5 4 -1
Hernandez COL 3 2 -1
C Zerbe SF 2 1 -1
M Miller COL 1 0 -1
P Ozuna COL 1 0 -1
Stinnett PHI 1 0 -1
With such a small change in absolute Win Shares, does this change in methodology really matter? I would argue strongly that it does. This is not a matter of opinion or approach, like “Loss Shares” or DER splits. It’s mathematical logic that is necessary for Win Shares to be internally consistent.
For a complex system like Win Shares to be credible, it has to be valid every step of the way.
Okay, I thought I understood what you did, so I tried it out on my WS spreadsheets and I get absolutely no change on the Offense WS at all. So I want to express the formulas to see if I really do understand you.
Old Marginal Offense: RS - 0.52*ERS*PRunAdj
New Marginal Offense: RS/PRunAdj - 0.52*ERS
Old Marginal Defence: 1.52*ERA*PRunAdj - RA
New Marginal Defence: 1.52*ERA - RA/PRunAdj
where ERS and ERA are the non-park-adjusted expected runs.
Then for batters:
Old Claim Points = XR -0.52*Outs*LgR/Out*PRunAdj
New Claim Points = XR/PRunAdj - 0.52*Outs*LgR/Out
(I use XR rather than RC because I don’t like RC).
Is that what you meant? If so, then I wonder it resulted in no change in OffWS at all—not even to the smallest decimal point. I’ll have to go run some algebra to see why.
If not, do you think you could present some formulas like I did so I can understand you?
Posted by on 12/17 at 11:22 PM
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