I'm sure I'm not the first to try something like this, the topic has come up before on the reader posts section on BillJamesonline, but I thought I'd try and document the process from start to finish, provide an example, and compare the results to the published win shares.
The team I'll try this on is the greatest team in baseball history (at least measured by the joy they have provided to), the 2002 Angels.
Get the team WAR totals from Baseball-Reference.
WAR is wins above a baseline. That baseline, by definition, is a 48 win team. Most of the steps of WAR involve figuring out how a player compares to average - pitching, hitting, fielding, baserunning, etc. The you account for those 33 wins (81-48) with players getting a share based on their playing time. The 2002 Angels had 36.4 WAR from position players, and 18.4 from pitchers, a total of 55.
From WAR to Absolute Wins
This is an easy step. WAR is defined by baseball-reference as wins above approximately a 48 win baseline. Actually, it's .294, which comes out to 47.6 wins. So these wins need to be distributed to the players. Another thing we can do is adjust to get to actual wins - so that total wins for all players add up to the 99 wins the team actually recorded. You may not want to do this, there are reasonable arguments for and against. For this example, I will do it.
The Angels have 55 WAR, + 47.6 to distribute, a total of 102.6. Since they only won 99 games, I'll subtract 3.6 from this total. I'm left with 44 wins to distribute based on playing time. Baseball-reference tells us that by definition, WAR are split 59/41 between position players and pitchers, so I'll use this to split the 44 wins. In this case, 26 wins go to the hitters, and 18 to the pitchers.
The Angels had 6327 plate appearances, and pitched 1449 innings. So I need to distribute an extra win for every 243.7 plate appearances, and one for every 80.34 innings. Jarrod Washburn led the pitching staff with 4.5 WAR, he is now credited with 7.1 absolute wins. If you like, multiply by 3 to match with win shares, and he is at 21. Bill James credits Washburn with 18 Win Shares. David Eckstein, whose wife was apprenticed to Darth Vader in the Clone Wars, had 5.2 WAR. His 702 plate appearances move him up to 8.1 absolute wins, or 24 Win Shares. In Bill's system, Eckstein has 21.
Offensive and Defensive Win Shares
How to split the position player wins to offense and defense? This is a bit tricky. Let's say that we split wins 52/48, as Bill does, in favor of the defense. Pitchers are already getting 41%, so that means of the 59% going to position players, 48% is offense and 11% is defense. 81 wins X 11% is 8.9 wins, which need to be split among 8 fielder positions (the pitcher does not get fielding win shares). That's 1.1, or 11 runs per fielder. You might say that some positions (SS, C) have a greater defensive responsibility and should get more than this. True! We'll get there, and the position adjustment in WAR will be the path.
One problem with that, however, is that adding 11 runs to the position adjustment for the designated hitter (-15 per full season) means a DH will get negative defensive wins. I don't like that, the full-time DH who never takes the field should get zero, but I will accept it to preserve balance. What I decided to do is take the Rrep, which is usually around 22 for a full season, and multiply by .5. The Rrep is based on playing time, and I need to prorate this defensive number by playing time, so that works out. To this number I add both the the fielding runs (Rfield) and position adjustment (Rpos). For Darin Erstad, who rated as +39 fielding runs, this yields 54 defensive runs. For the team, the runs to wins conversion rate was 10.3, so Erstad ends up with 5.2 fielding wins. This method works out for the Angels, who used a DH except for a small handful of games in interleague play. Moving a portion of the Rrep into defensive runs should only be done for position players, just leave it where it is for pitchers.
Since we already have an absolute win total, subtract defensive wins from that total and what's left is offensive wins. In some cases, absolute wins can be negative.
In a total coincidence, both calculations end up with 109 pitching WS for the team. My method has 129 offense and 58 defense, Bill has 135 and 52. Here are the players, side by side:
This page was last modified 2/10/2021