THE BOOK--Playing The Percentages In Baseball

Monday, February 01, 2010

Bill James turns Win Shares into Wins above replacement (WAR)

He doesn’t come right out and say it, but his explicit rankings shows this implicit acceptance.  Follow me for the proof.

The first thing to note is that he ranks 15 semi-random firstbasemen in… some order.  What order is that?  He didn’t say.  This is the Win Shares and Loss Shares of the 15 guys, in his order:
BJ WS LS
1 319 152
2 289 120
3 269 99
4 257 90
5 265 118
6 291 199
7 181 106
8 218 202
9 143 67
10 150 93
11 146 118
12 162 166
13 144 147
14 109 116
15 79 61

As you can see, it’s not in Win Shares order.  How about if I rank them in Win Shares minus Loss Shares order?
BJ WS-LS
1 167
2 169
3 170
4 167
5 147
6 92
7 75
8 16
9 76
10 57
11 28
12 -4
13 -3
14 -7
15 18

Nope, that’s not it either, though it’s getting closer.  Then I thought “Oh no he di’int.” Yes, he did.  If you do Wins above .333, here’s the list you get:

BJ wsWAR
1 54
2 51
3 49
4 47
5 46
6 43
7 28
8 26
9 24
10 23
11 19
12 18
13 16
14 11
15 11

Fref McGriff, his number one guy in this sample, has 319 win shares and 152 loss shares.  You can just do 2*WS - LS, or WS - LS/2, or WS*.667 - LS*.333, or whatever, as long as you weight the wins twice as much as the losses, and you get the same rankings.

To convert Win Shares to Wins Above Replacement, you do:
WS/3 - .333 * (WS+LS)/3

That “/3” is to convert win shares into wins.  And the “.333” is the win percentage replacement level.  So, the final simple equation is (2*WS-LS)/9.  For McGriff, that’s 319*2 - 152 or 486.  And divide by 9 to get to 54.  This is how you convert Win Shares and Loss Shares into Wins Above Replacement (WAR).  And Bill James has ranked his firstbasemen by (his version) of WAR.

Here is the comparison of Bill James’s WAR and Rally’s WAR, ranked in Bill James’ order:

rWAR bjWAR
51 54 McGriff Fred
61 51 Hernandez Keith
53 49 Cash Norm
52 47 Giambi Jason
44 46 Delgado Carlos
36 43 Garvey Steve
26 28 Vaughn Mo
23 26 May Lee
27 24 Teixeira Mark
22 23 Parker Wes
14 19 Sexson Richie
14 18 Power Vic
9 16 Pepitone Joe
6 11 Stuart Dick
6 11 Aikens Willie

Every player is within 5 wins, except for:
- Keith Hernandez, 10 more wins for Rally than Bill James
- Steve Garvey, 7 more wins for Bill James than Rally
- Joe Pepitone, 7 more wins for Bill than Rally

That’s it. 

It seems to me therefore that Bill has accepted that some sort of wins above baseline is needed.  And he is using a level that pretty much match what we’re using for wins above replacement, since the results are consistent.  I wouldn’t worry about the implication of the “.333 win percentage”, since that number is specific for the way his system is constructed.

This really brings Bill James back to where he always was 25 years ago, when he first wrote about replacment level in the context of Rice v Guidry and Clemens v Mattingly.  And when he ranked players as “chance of being better than a .400 player”.  Bill took a detour along the way in terms of ranking players by Win Shares (without considering Loss Shares).  Him bring Loss Shares into the mix really resets his position back along the Wins above replacement track that the rest of us are on.

Welcome back Bill.

Now, let me ask: if Bill is going to rank players by 2*WS-LS anyway, then why not show that single number as well?  Why show the WS and LS numbers separately (which is fine), but not show the actual single number he’s ranking the players by?  And, to give that number meaning, why not just divide it by 9, so you get the wins above replacement scale that the rest of us use?