Having reached a total for Runs Saved Above Average for Washington Senators shortstops in 1970, we can use this to calculate a Defensive Winning Percentage.
Offensive Winning Percentage is a tried and tested sabermetric stat that uses a player's Runs Created to make an estimate of how many games a lineup of nine players with that Runs Created would win. You can find one set of Offensive Winning Percentages at each player's page on baseball-reference.com Ed Brinkman's page, under the Special Batting heading, shows his 1970 OWP was .394. That means a team of Ed Brinkmans would win about 63 games in a 162-game season. Let's look at whether his glove made up for that.
The first step is to calculate how many runs an average team in that league scores. In 1970, 12 teams scored 8109 runs, so that means the average team scored 675.7
Subtract the number of Runs Saved Above Average. That was 24.7 as we saw in the last post. (If it had been negative, as was the case with the Cleveland Indians' shortstops in 1970, we would add it.)
675.7 - 24.7 = 651
Now, with Offensive Winning Percentage, you'd take the runs created for a team of Ed Brinkmans, and divide it by the sum of Ed Brinkmans plus the league average, all raised to the exponent 0.83. That would represent the runs scored divided by the runs scored plus the runs allowed. We do the same thing, but in this case it is the runs allowed that is the variable. Eg,
Average Team's Runs Scored = 675.7
Team with Washington SS Runs Allowed = 651
675.7^0.83/(675.7^0.83 + 651^0.83) = .508
Therefore, the Washington shortstops, backing up a league average offense, would win about 82 games. If you added 82 and 63, and divided by two, you'd get a reasonable estimate that a team of 1970 Washington Senators' shortstops, batting like Ed Brinkman, would win about 72 games. No way is Ed Brinkman going to carry you to the pennant, but he was a better player than his team, which could only manage 70 wins.
However, when you compare the Senators' shortstops to the rest of the league, you can see that, starting from the mean point of DWP's, .501, Washington, with Minnesota, had the best fielding shortstops in the league. The Twins' Leo Cardenas was probably the proper Gold Glove winner that season, as his fielding percentage was slightly better, .978 to Brinkman's .974 .508 is excellent for DWP, but it isn't historically remarkable. You really need to push your DWP past .510 to get into remarkable territory.
Oh, who won the AL Gold Glove that year? It was Hall of Fame shortstop Luis Aparicio, then playing for the White Sox. Their shortstops managed a DWP of only .498, so Cardenas and Twins fans have a good case for feeling aggrieved.
I'm going to look next at a couple of problems with DWP, which I think is good, but with a couple flaws that always need to be borne in mind when using it.
EDIT: Edited to correct the omission of the Exponents!