Yesterday I introduced a method to estimate the number of Runs Saved by a shortstop, as opposed to a zero-value defensive player. I believe there is merit in the method. I believe that it reliably identifies the best defensive players, not 100% of the time, and it creates a context in which to compare and contrast offensive and defensive values. I think it is worth having.
However, there were choices to be made in constructing that system, and it’s not absolutely clear that all of the choices I made were the right ones. The number of runs that we are estimating a defender to save seems unrealistically low. It is low compared to other types of defensive analysis, and it is low compared to intuitive observation. Anyone can look at a good defensive shortstop, playing short, and realize that the difference between him and a complete oaf at shortstop must be more than 30 or 40 runs a year.
What we are calling the zero-point in this analysis is not truly the zero point. This is true for two reasons. First, one cannot score fewer runs in a ballgame or in a season than zero. If my wife and sons and I were to play against a major league baseball team, we might score zero runs in a season, but we could not score fewer than zero—thus, could not miss the league average by more than 750 runs, assuming that 750 runs is the average.
We could and would, however, allow more than 1500 runs, or 750 more than average. 1500 runs allowed (2Lg, or twice the league norm) is not a true zero-point; it is merely a point which is equidistant from true zero on the opposite end of the scale.
Also, if a team scored zero runs in a season and allowed 750, their winning percentage would be zero, but if they scored 750 and allowed 1500, it would not be zero. It would be about .200. In order to have no expectation of ever winning a game, you would have to allow an infinite number of runs.
Of course one cannot work very well with infinite numbers, but one could make the system more realistic by moving the theoretical zero-point further away from the league norm. Let us suppose that the theoretical zero point was not 2Lg, but 3Lg (three times the league norm.) That would be treating a .100 winning percentage as .000, rather than treating .200 as .000, a smaller distortion. That system would portray the defenders on a team as preventing 1500 runs, if the league norm was 750 runs scored, rather than preventing 750 runs (including those prevented by the pitcher.)
In the system as I outlined it, if one pitcher allows 80 runs and a teammate pitches the same number of innings and allows 60 runs, this system doesn’t show a 20-run difference between them, since it will credit part of the separation to the fielders. If we changed the zero point to 3Lg, then we could restore the pitchers to full credit for runs saved, and still greatly increase the percentage of success that was credited to the defensive players. This would increase the runs saved against zero estimate for Ozzie Smith in a typical season from about 35-40 to something more than 100.
This would imply that the runs saved were much greater than the runs allowed, but we can still make offense equal defense by assigning less Win Value to one run saved than to one run scored. This is realistic. If a team is average defensively, if they allow 750 runs, then to go from 400 runs scored to 500 increases their expected wins by 14. But if a team is average offensively—that is, if the team scores 750 runs--then to go from 1100 runs allowed down to 1000, although it is a parallel step on the other side of the spectrum, increases their expected wins by less than 7. One run scored is more valuable than one run saved, since runs scored rise from zero and runs saved fall from an infinite sky.
But there are problems with that theory, too, among those that that theory reduces the Win Value of pitchers so low that teams appear to be behaving very irrationally in terms of the resources that they devote to pitching—resources being roster space, salary costs, and player development costs.
We could solve these problems by going back to a primitive assertion: baseball is 75% pitching. The argument isn’t as irrational as I once argued that it is. What is meant by saying that baseball is 75% pitching is this.
Offense is bounded by zero; a team cannot score fewer than zero runs, therefore wins result from scoring more runs than zero.
Defense, on the other hand, is unbounded; a team can allow any number of runs—let us say four times the league average. From a defensive standpoint, wins result from allowing fewer runs than four times the league average. Therefore, the number of runs that must be prevented to win the pennant is much larger than the number of runs that must be scored.
But there are problems with that theory, too. If this theory were meaningfully true in major league baseball, then the standard deviation of runs allowed would have to be higher than the standard deviation of runs scored, which is not true. The theory could be true in a theoretical universe involving players at widely different skill levels, but irrelevant in a real universe in which only players comparable in skill level are competing with one another.
All mathematical models represent the baseball universe as being more simple than it actually is. This is a limitation that we live with. Because the mathematical models are always simplifications, they are always untrue if looked at from one angle or another.