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Primate Studies — Where BTF's Members Investigate the Grand Old Game Tuesday, December 18, 2001Total Baseball’s Fielding Runs?A PrimerHow are Pete Palmer’s fielding runs calculated? This article is part of a broader series of articles, written for SABRL [The Society of Baseball Research’s Mailing list] and crossposted to STATLGL [Baseball (and Lesser Sports) Discussion List ], comparing the results generated by different defensive measurement systems. The players chosen for this comparison were two 1978 shortstops later traded for each other  San Diego’s Ozzie Smith and St. Louis’s Garry Templeton. I was intrigued by the similarities in their overall fielding stats prior to the trade and the separation that developed very quickly after they were swapped for each other. I’ve shortened the article from the original post but left the details of the method intact. In developing Total Player Rating (TPR), Pete Palmer devised a measurement of fielding skill in terms of runs. Fielding Runs (FR) is added to runs generated from batting skill and baserunning (stealing) skill (and pitching skill for pitchers) to come up with an overall total rating expressed in runs, later converted to wins. Palmer calculates FR for SS (see Note 1) by first calculating a league average for the position according to the following formula: AVG(POS,LG) = .20*(PO+2AE+DP)/(league PO  league K) where PO, A, E, and DP are the total putouts, assists, errors, and double plays for the league’s shortstops, and league PO  league K represents an estimate of the total number of outs made by the league’s fielders. Palmer multiplies assists by 2 because "more fielding skill is generally required to get one than to record a putout". Once Palmer has that average for the position and league, he compares what a SS actually did produce to what he estimates an average player would have roduced in the same number of outs: FR = .20*(PO+2AE+DP)  ((team PO  team K) * AVG(POS,LG) * %PT) where PO, A, E, and DP are the putouts, assists, errors, and double plays registered by the shortstop, team PO  team K is the number of outs made by that team’s fielders, and %PT is an estimate of the amount of playing time at the position by this shortstop, based upon the player’s complete fielding line and the number of plate appearances. Palmer doesn’t publish his formula for estimating playing time, making it impossible to reproduce his results. In my calculations below I use actual playing time calculated from Retrosheet data to demonstrate the method. NL SS, in 1978, had 3191 PO, 6199 A, 332 E, and 1105 DP. The league as a whole had 52,000 PO and 9905 K. The AVG(POS,LG) is therefore .20*(3191+2*6199332+1105)/(520009905) = 0.0777 Garry Templeton played 1353 2/3 of the 1437 2/3 innings played by the Cardinals (0.942 of the total). Templeton had 285 PO, 523 A, 40 E, and 108 DP. The Cardinals had 4313 putouts as a team and fanned 859 hitters. Templeton’s FR (see Note 2) are: .20*(285+2*52340+108)((4313859)*.0777*.942) = 27 Ozzie Smith played 1327 of the 1433 2/3 innings played by the Padres (0.926
of the total). Ozzie had 264 PO, 548 A, 25 E, .20*(264+2*54825+98)((4301744)*.0777*.926) = 31 TB7 has Templeton at 23, Ozzie at 26. The biggest flaw in FR is that Palmer makes no effort to derive event weights from the actual relationship between the defensive events and their impact on run scoring, as he does with his offensive measures. An assist is worth two times a putout based on Palmer’s subjective assessment of its value. Palmer also subtracts errors from plays made, even though not every error adds a baserunner, and adds DPs to the total even though DPs are also counted in PO and A. FR is flawed in three important ways:
The first flaw above, in my opinion, is the primary reason why most analysts discredit FR. It’s very natural for an analyst, when presented with a formula that looks like: R = AW1+BW2+CW3 to ask how the developer of the formula came up with the weights. If the developer of the formula doesn’t have satisfactory answers, as Palmer does not, the credibility of the entire formula is questioned, especially when the results aren’t always intuitive and the developer of the formula acts as though the results are just as accurate as the results from other, more rigorously developed formulae that measure other aspects of R. Notes:

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1. Charles Saeger Posted: December 18, 2001 at 12:18 AM (#604539)When evaluated as a team, each team is pretty much equal. There are a few differences, like errors and assist rates, but every team makes 27 putouts a game. FR for a team vary by only a few a year.
Palmer ignored the hits, the team failures. Were he to modify FR even just to make the denominator (POSO+HHR), he would greatly improve his accuracy, even without all the silly weights. That way, good defensive teams would have better FR totals than bad defensive teams.
The problem could also be fixed (somewhat) by removing some of the credit a pitcher gets for certain defensive events.
Speaking of responsibility for hits:
It is my opinion that there are only two ways that one can legitimately make this assignment without resorting to a guess:
1. The pitchers are 100% responsible for all hits;
2. The pitchers are only responsible for hits that leave the ballpark, and the fielders are 100% responsible for all other hits.
 MWE
1. The pitchers are 100% responsible for all hits; 2. The pitchers are only responsible for hits that leave the ballpark, and the fielders are 100% responsible for all other hits."
The trouble is, neither of those is true. The biggest problem in evaluating fielding, now that playbyplay, directionanddistance data is available, is to divvy up responsibility for all those events where the ball is put in play, but not out of the park.
Cheers,
Alan Shank
Certainly, the availability of "playbyplay, directionanddistance data" could make it possible to "divvy up the responsibility". But I don't think we need to do that. My belief  which I think is supported by a lot of evidence, including analysis of available playbyplay data, Voros's work, the tendency of pitchers to sustain success more readily when they restrict the number of balls put into play against them, the existence of what James called the "Tommy John" class of pitchers  is that the pitcher's level of control over the results of what happens when a ball is put into play within the ballpark is small enough so that we can effectively ignore it, and treat the fielders as being 100% responsible for the outcome when a ball is put into play within the ballpark.
I think we can gain a lot more by proceeding down that path than by expending a lot of energy trying to figure out something that we will find it extremely difficult to validate.
 MWE
1. the ballinplay outcomes are more random than the pitcheronly
2. they are obviously affected, to a considerable extent, by the quality of fielding
3. we would still see pitcher influence, in that the results for a given team would vary by pitcher by more than a random amount
We'd want to compare Boston's ballinplay data with different pitchers, inlcuding Pedro, etc.
Cheers,
Alan
Cheers,
Alan
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