Formula 20:  Tm-Err-Av (Team Errors Avoided)

            We come now to the one category by which fielders have traditionally been measured, the one category which was designed in baseball’s primordial soup to evaluate fielders, and which served that function, however badly, for 100 years. 

            I’ve been avoiding writing essays here to explain the logic behind the system; I’m trying to reach the end of the long process of explaining how the process works, and essays about why it works that way just hold us up.  But sometimes it is necessary to explain.

            As you all know, fielding percentages have been going up steadily since organized baseball began.   Eventually, fielding percentages went up so much that they became largely irrelevant, no longer central to the task of evaluating fielders. 

            Errors are awkward to deal with because, more than any other statistical category, there is an inconsistency in their consequences.    An "error" can be a one-base error, a two-base error, a three-base error, even, in theory, a four-base error, although I have never seen a four-base error in the major leagues.  (The last time it happened was ten years ago.)   An error can put a runner or base, or it sometimes (often) does not result in an out/no out distinction, but merely advances a runner who is already on base.  It might advance him one base, or two bases, or three bases.   Some errors occur on foul balls, and have no base or out consequence; they merely extend the at bat.

            No other statistical event has this range of outcomes.  Also, fielding statistics including fielding percentages are extremely different from one position to another, much more so than batting statistics.   These things can make it difficult to place a run value on errors, but we haven’t reached that problem yet.   At this time, we’re just dealing with the question, "How many errors did this team NOT commit, that they might have committed?", not the question of "what was the run benefit of those errors not committed?"

            The New York Giants of 1900, a last-place team, committed 439 errors, which seems like a lot, but you had to be there.   439 errors was .0721 of their fielding opportunities; they had a fielding percentage of .928, but I focused on the error percentage. 

            The error percentage of all teams in the data (1900-2019) is .0246 with a standard deviation .0092, so five standard deviations worse than the norm would be an error percentage of .0708, or a fielding percentage of .929.

            To this point in our process we have encountered only one team which is five standard deviations worse than the norm in any category, that being the 1915 Philadelphia Athletics, who were five standard deviations worse than the norm in Walks + Hit Batsmen.   We have, however, not one but two teams which had fielding percentages more than five standard deviations worse than the norm—the 1900 Giants, and the 1901 Baltimore Orioles.

            As I have explained before, we have to create SOME room to say that INDIVIDUALS on the team can be given credit for run prevention in this area, even if the TEAM deserves none.   On the 1900 Giants, for example, Hall of Fame shortstop George Davis had a fielding percentage of .944, which was much better than the league average at the position, .922, and certainly better than five standard deviations below the norm.  We have to do something to create space to acknowledge the few players on those teams who did make a contribution to run prevention in this area. 

            I will make a "carve out" rule that every team in baseball history must be credited with at least 100 errors not made, regardless of how many errors they DID make.   That rule would affect 32 teams in the 1900-1911 era, which otherwise would be credited with less than 100 errors not made.   All teams since 1911 would already be above that standard.

            Second, I will award claim points, for those errors not made, based on the player being above the standard of three times the error percentage at his position, in his season.  In other words, let’s say that the fielding percentage at Catcher in a given season is .950; then catchers in that season would be given Claim Points for the runs prevented by not making errors based on how far their fielding percentage was above .850.  If the fielding percentage was .970, they’d get claim points for fielding above .910. 

            The lowest error percentage for a team was .0090 (fielding percentage .9910) by the 2013 Baltimore Orioles.   The most Errors NOT MADE, however, was by the 2006 Boston Red Sox.  That star-crossed team fielded .989 (error percentage .0107) but had several hundred more fielding chances than the 2013 Orioles.   That team is crediting with not making 389 errors. 

            Is it reasonable to say that a team’s fielders should be credited with not making 389 errors, in a season?

            In my opinion, yes, it is very reasonable.  I mean, we’ll see, down the line, whether the numbers work out so that that works within the structure I am trying to create, but "just doing your job", as a fielder, is really, really important in preventing runs.   A baseball team prevents a lot of runs, over the course of a season, by people just doing their job.   One of the basic questions we have to ask, in an analytical system designed to measure the defensive contribution of every player, is "how do we assign each player credit for just doing his job at a major league level?"   I think this is how we do that.   We’ll have to check the proportions later on. 

            Anyway, first we assign "errors not made" to the TEAM, and then we assign "claim points" to individual fielders based on their individual fielding records and fielding percentages.   It’s a two-stage process, like flying from Kansas City to Los Angeles but you have to go through Atlanta or Denver.   This is the first flight. 

            The Errors Avoided by a Team are figured as follows.  Team Error Percentage is the complement of the fielding percentage, 1 minus the fielding percentage:

Tm-Err-Av = (PO + Assists + Errors) * .0708 – Team Errors

But never less than 100.  

These are the errors "not made" by each of the 15 teams that we are following:

Formula 21:  RS-Tm-Err-Av (Runs Saved by Team Errors Avoided)

Each Error not made has a run-saving value of .293 runs. 

            Rs-Tm-Err-Av = (Tm-Err-Av) * .293.

            These are the Runs Saved by Error Avoidance for the 15 teams:

            Formula 22:  Pos-BL  (Positional Base Line for fielding percentage)

            Credit for these Runs Prevented is transferred from the team to the individual player by the way of "Claim Points".   The more claim points each player has—that is, the more errors he doesn’t make—the more Runs he will be credited with saving. 

            The positional baseline for each position is one minus three times the error percentage for that position in that league in that season. 

            Pos-BL = 1 – ((1- LgFPct) * 3)

            These all being pitchers, the baseline is established by the league fielding percentage for pitchers.   For the pitchers on the 15 teams we are following, these are the baselines:

            Formula 23:   Claim-Ind-Err-Av   (Individual Player Claim Points for Errors Avoided)

            Each player’s Claim Points for Errors are avoided are established by subtracting his errors from the number of errors that would be made by a player with the same number of fielding chances, fielding at the level of the positional base line:

Claim-Err-Av  = ((PO + Ast + Err) * (1 - Pos-BL)) - Errors

            Formula 24:  Claim-Team-Err-Av  (Team Claim Points for Errors Avoided)

            The Claim points for each team is the sum of the Claim Points for the Individual fielders on the team.  Not sure how to write that as a formula:

            Claim-Team-Err-Av  =  Sum all (Claim-Err-Av)

            Formula 25:   RS-Err-Av-P8  (Runs Saved by Error Avoidance, 8^th pitcher’s value) 

            The Team Runs Saved by Error Avoidance (RS-Tm-Err-Av, formula 23) are distributed to the individual players in the same proportions as their Individual Claim Points  (Claim-Err-Av, Formula 25):

            RS-Err-Av-P8 = (Claim-Err-Av) / (Claim-Team-Err-Av) * RS-Tm-Err-Av

            The process for Runs Saved by Error Avoidance will be the same at the other 8 defensive positions as it is for pitchers.  I just had to run through the entire process at pitcher to establish how it works for pitchers.  It works the same at the other positions. 

            I need to explain why the system works this way.  Why can’t we just figure the number of errors that each fielder avoided, compared to a fielder making twice the league norm for errors, and credit the fielder with .293 Runs Saved for each error that he did not commit?

            In a relative runs saved analysis, in which each fielder was compared to the other fielders in his league and season, that is the way you would do that.  But this is not a relative measurement; this is an absolute measurement.   Think about two fielders, one from 1900, who fields .940  in a league in which the fielding percentage at the position is .915, and one from 2010, who fields .980 in a league in which the fielding percentage at the position is .975.  

            In a relative analysis, the fielder who fields .940 in a .915 league has had a better season.  But in absolute terms, it is .980 against .940.  In absolute terms, the higher number is better. The player making fewer errors has avoided more errors—not a novel concept when you think about it. 

            IF you can measure the runs saved by each fielder accurately, THEN you can very easily make a relative comparison based on that.   But if you make the relative comparison first, then it is basically impossible to transition from that to an absolute number.  

            Because fielding percentages vary widely both over time and from position to position, any fielding percentage between .910 and .990 can be a completely normal fielding percentage, based on the era and the position.  I created this two-tiered system to interpret error rates both globally—that is, on a constant scale from 1900 to 2019—and locally—that is, in a manner specific to the position and the year.   I don’t know how else you could do it. 

            (Later note—This system has some issues.  To be honest, this part of the process is not working sensationally well.  What we are doing, really, is measuring two things which are a little bit different but mostly the same, and then treating them as if they were actually the same.   The result of this is that the value of an error avoided. .. the cost of an error.  . .can vary with the team in ways that may not be rational.  But I don’t know how to do this and avoid that problem, with the great multiplicity of standards in fielding percentage.)

            Anyway, this the updated list of the 15 pitchers on these 15 teams who are saving the most runs.  Bob Friend has moved ahead of Randy Johnson into second place on the list, and Dan Petry has now moved up to 5^th on the list, ahead of Whole Camels.   I’m glad that has happened, actually, because it shows that these "little" categories do matter, although the number of runs in each one is small compared to strikeouts and walks and homers, but there is a cumulative effect.  Dan Petry illustrates the point, as he was not even in the top 10 after strikeouts and walks, but has now moved up to 5^th place by posting consistently strong scores in the small-ball categories.  Andy Pettitte drops a slot because he made four errors in 2000:

            The new categories are Errors Avoided by the pitcher, Errors Avoided by the team, Runs Saved by Error Avoidance, and the pitcher’s runs saved, which are calculated based on the other three.  Lucas Harrell of Houston (2012) was the leader in this category, as he did not commit an error in 51 fielding chances, the most of any pitcher in the study who fielded 1.000.