This is a first step toward measuring defensive in terms of offense. The question to answer is: how much good hitting makes up for poor fielding? Or, to look at it from the other side, to what extent does superior glove work compensate for light hitting?
There are two components to defense: error and range. Let’s consider error rating only for the moment. And let’s hope my logic is correct.
For one PA of his own, a player will be in the field for approximately nine PAs by the opponent. For one opponent PA, the chance of rolling a possible error is 6.3%, which is 60 rolls on 11-70 plus about 20% of the 16 rolls on 81-96 (Park Effects). A possible error will fall on our guy’s position 10% of the time. So, over 9 opponent PAs, the average number of possible errors for our guy will be 9 * 6.3% * 10% = 0.057, which is equivalent to 57 rolls.
Now we have to consider specific positions. Let’s look at 3B/SS, where errors occur the most, and let’s consider the most extreme difference in error ratings. On a possible error, an error-20 thirdbaseman (Jeff Cirillo) will make an error 24% of the time, while an error-1 (Ryan Braun) will boot it 99% of the time. Let’s ignore the more complex outcomes (E(2), 1B+E(1), RG+) and just say that an error is equivalent to a single. In other words, an error made on defense neutralizes a single hit by the same guy on offense. The 57 rolls calculated above will work out to 14 rolls for a Cirillo error/single and 56 rolls for a Braun error/single, a difference of 42 rolls.
One could use these results to adjust a player’s offensive rating. 14 of Cirillo’s average 25 1B range are neutralized by his errors. Via linear weights, Braun’s 56 neutralized singles are equivalent to 18 neutralized HR rolls. (Braun has a 95 HR range vs. L, 35 vs. R.) You could also do a comparison and say that Braun would have to have 42 more 1B rolls (or 14 more HR rolls, or equivalent) than Cirillo to make him equal value, all other things (range, power, etc.) being equal.
These “neutralized rolls” can be similarly calculated for other positions and all the error ratings. The results are plotted in the graph below. I didn’t count E(0)s (dropped fouls) as errors on the catcher.
The numbers in the chart are just approximations, and each position’s accuracy is different. For example, all the catcher errors counted are of the two-base variety. Anyway, it’s a start.
It’s interesting that, with the exception of the catcher & outfielders, all the lines are nearly parallel. So the difference between an error-20 & an error-1 at a given position is pretty much the same for either 1B, 2B, SS, 3B, or P.