I promised an example of how to work out Defensive Winning Percentage, so let's use Eddie Brinkman, Washington Senators shortstop for 1970, his last season before the Detroit Tigers got him in a trade.
The first part of the process is derived from Charlie Saeger's system of Context-Adjusted Defense. This allocates outs and hits to the infield and the outfield.
The first step is to estimate how many groundball and flyball outs the team allowed for the season.
Groundball Outs = Team Assists - Catcher Assists - 1b DPs - OF Assists.
Flyball Outs = Team Putouts - Team Strikeouts - Team Assists.
For 1970 Washington, we get the following
GB outs = 1942 - 80 - 145 - 28 = 1689
FB outs = 4369 - 823 - 1942 = 1604
Then, you need to estimate the number of hits held against infielders, and then those against the outfielders.
IF Hits = Subtract from the total Team Hits Allowed the total of (home runs + doubles + triples). Take 70 percent of the difference. Divide this by the ratio of GB outs to (outs-strikeouts).
OF Hits = Subtract from the total Team Hits Allowed the number of home runs and the total of IF hits. Take 70 percent of this number.
For 1970 Washington, we get:
IF Hits = ((1375-(139-232-47))*0.7)/(1689/3339) = 344
OF Hits = (1375-139-348)*0.7 = 625
Now you are ready to estimate the Zone Rating.
Subtract from the number of GB outs the number of Team pitcher assists. Add the number IF hits. Take 30 percent of this number (this is a positional adjustment, like the one used in Win Shares) and add it to the number of errors made by Senators' shortstops.Take the result and use it to divide the number of shortstop assists.The result is your estimated Zone Rating for all Washington shortstops in 1970.
((1689-220)+344)*0.3 = 543
543 + 23 = 566
593/566 = 1.05
Multiply the estimated Zone Rating by the average number of plays made at the shortstop position, as calculated by Chris Dial in his Dr Strangeglove piece on Baseball Think Factory, and then by the Run Value he has calculated for plays made at each position.This is the Runs Saved by all Senators' shortstops in 1970.
1.05 * 532 *.753 = 420.63
Following the same procedures, we get a total for the American League in 1970 of 394.39 Runs Saved by all AL shortstops. Subtract the league runs saved from the Washington runs saved.This gives you how much better a Washington shortstop was than an average AL shortstop at saving runs.
420.63-394.39 = 24.7
Brinkman started 157 games at shortstop for Washington in 1970, so at worst we can credit a substantial portion of that quality to him.It's worth noting that in 1968, when Brinkman only appeared in 77 games at short, Washington shortstops managed to save 0.7 runs, so it seems likely that Brinkman is worth even more than 24.7.
You're now ready to calculate the Defensive Winning Percentage.