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(You can also read a fuller discussion of this Table.)
(Please see the page of this site that deals with fielding for background summaries.)
What we want to see is the effect of fielding on runs allowed and thus games won. The easiest way to do this is to see how the team is actually doing, then see how it would be doing with an all-MLB-average level of fielding. There is no 100% exact way of doing that, but we can make a pretty good approximation.
We make a few assumptions to begin with. First, we assume that the number of outs made is invariant—that is, the team would have played the same number of defensive innings with average fielding as it actually did. While theoretically better or worse fielding could change the number of extra-inning games, or games with no bottom-9 half, the assumption is by and large a good one, so we make it (because without it, we can't really get anywhere).
Next, we assume that the rates of things that pitchers control would remain the same no matter the fielding. Those things include the so-called "three true outcomes" (walks, strikeouts, home runs) plus hit batsmen. Those also are perfectly reasonable assumptions.
We will further assume that the rates (per plate appearance) of sacrifice bunts and sacrifice flies are invariant with changes in fielding. That is less likely to be exactly so, but the total numbers of sacrifices are quite small compared to the big-ticket out-making items like strikeouts and ordinary fielding putouts, so any difference that better or worse fielding might introduce would be trivial.
We know, of course, that the number of plate appearances depends on the on-base percentage: the higher the OBP, the more men will, on average, get to come to the plate before the third out of the average inning. The converse of OBP is the outs rate: if the team has an opposing-batters OBP of .333, then the team has an outs rate of .667. Changes in fielding obviously change the outs rate, and thus the total plate appearances (here more rightly called "BFP", Batters Facing Pitchers) of the opponents. If we can reckon the change in the defensive outs rate, we can calculate the change in the BFP and thus in all the team defensive stats.
The outs rate has two components: strikeouts and fielders' outs. Fielders' outs are simply all non-strikeout outs, which is innings pitched times three minus strikeouts. Note that the fielders' outs rate is not simply the number of batters put out by the fielders: it also includes an especially important aspect of fielding, outs made on runners who have already safely reached base (a class that includes double and triple plays, caught stealings, pickoffs, and outs on runners trying to advance).
The strikeout rate is simply K/BFP taken from the actual team stats. To get a useful FO (Fielders' Outs) rate, we need to relate actual FO not to PA but to BIP (Balls In Play). As we said above, the BIP rate (BIP/PA) we assume to be invariant; its components are At-Bats, Strikeouts, Home Runs, and Sacrifices. The equation is just:
BIP = AB - K - HR + SF + SH
What we here call FE ("Fielding Efficiency") is just FO/BIP. We can readily calculate the all-MLB average FE, and use that to do our projecting.
What we do is, for each team, calculate its actual FE and its actual BIP rate, using actual data. We then apply that all-MLB FE to the BIP rate (which rate, remember, we are reasonably assuming to be invariant); that gives us the projected FO rate if the team had a perfectly average defense.
Finally, we add that projected FO rate to the known (and invariant) Strikeout rate to get a projected total Outs rate; from that, using the invariant total Outs number, we get the new, projected BFP total for the team, if it had average defense.
We can now take the ratio of those BFPs to the actual BFPs and use that ratio to pro-rate all the actual stats into projected average-defense stats. (Naturally, we round all those pro-ratings off to whole integers.)
Now we have two team-defense stat lines: the actual one, and the one they would have with perfectly average defense. For each, we then calculate, using the established runs- produced equation, the normally expected runs for each, which allows us to see how many runs the team's fielding has saved or cost it so far this season.
(We use calculated runs even for the actual-data line, rather than actual runs, because we want to compare apples with apples: the actual team runs allowed will almost always differ somewhat (usually but not always a small somewhat) from the calculated value from sheer luck, and we are interested in the effects of fielding, not the outcomes of luck.)
To look at the impact of those runs lost or saved, we use a quick-and-dirty approximation, simply dividing the runs difference by the average number of runs per game in the appropriate league (which is typically the number of runs needed to change the win total by one game). That isn't exact, but it gives a reasonable engineering approximation.
You can see the results of all this, right up to date, in the Table below.
Listed in ascending order (worst first) of fielding quality based on Fielding Efficiency.
For each team, the first line is actual data and the second projected stats with all-MLB average defense. FE is "Fielding Efficiency". The ΔW is the current difference in team wins attributable to fielding; ΔWyr is that difference pro-rated to a full season.
|— Team Stats —||— Calculations —|
From the data tabulated above, we can draw conclusions about the relative significances of fielding and of pitching to total defense.
We first reckon the average difference in runs that fielding alone contributes; for each team, we take that difference and divide it by games played, to get a "fielding-runs per game" number, which we then divide by 30 to get a team-average fielding effect. Next, we reckon the all-MLB average runs allowed and reckon, for each team, the difference between that and the fielding-neutralized runs allowed by that team (and again divide by games played); that gives us the difference from average for that team attributable solely to actual pitching, because fielding has already been neutralized to average. When we divided that sum by 30, we have the average difference in runs that pitching alone contributes. If we then sum those two figures—fielding effects and pitching effects—we get the total average difference from team to team on defense. We can then see what fraction of that total came from fielding alone and what fraction from pitching alone.
The results so far this season are these:
Average Fielding ΔR per Game: 0.119
Average Pitching ΔR per Game: 0.313
So: Pitching is 72% of defense; fielding is 28% of defense.
And, total defense being 50% of the game, fielding is thus 14% of the total game of baseball. Is that figure perfectly exact? No. But it's probably within a couple of percent either way. Certainly it is quite indicative of relative significance.
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