First Basemen

For first basemen, as you see above, we have three inputs into their defensive rating—from Double Plays, Range, and Fielding Percentage.  For first basemen, we are going to do something that we didn’t do or didn’t have to do at any other position.   First, we’re going to figure team totals at the position for Double Play Runs Saved and Range Runs Saved, add those two together, and then allocate them to individual fielders by one formula.  We do this, frankly, because defensive stats at catcher are so inarticulate, so. . . .difficult.   We’re doing the best we can with the data we have, but first base defensive stats do a poorer job of describing what the fielder has done than at any other position, so you wind with a radically different process. 

Formula 54:  1B-Tm-RS-DP  (First Basemen’s Runs Saved on Double Plays, team)

            This one is dead simple.  First basemen are assigned credit for 10% of the Double Play Runs Saved by their team.  It is done this way because:

1)     First basemen have to be given some credit for their role in this, and

2)     It is virtually impossible to determine, based on traditional fielding statistics, what the individual contribution of each first baseman is to double plays. 

Team Runs Saved on Double Plays were calculated much earlier in the series, as a result of Formula 16.  It was tagged as DP-RS-TM (Double Play Runs Saved, Team.)   I alerted the readers at that time to make a mental note of the number, because we would use it again.  The credit for first basemen is simply 10% of that number:

1B-Tm-RS-DP  = (DP – RS -TM) * .10

These were the Runs Saved by DP for these 15 teams, presented earlier:

Formula 55:  RS-1B-Range-Tm  (Runs Saved by First Basemen, Range, Team)

The manner in which all players including first basemen are credited with Runs Saved by range has already been explained in detail in formulas 26 to 31 and Formulas 36 to 38.   Formulas 26 to 29 created a stat called 1BQA, First Base Quasi-Assists.   Formulas 30 and 31 Translated 1BQA into 1B-En-Range, First Base Enhanced Range.   Formula 36 created a stat called Tm-Adj-Rg-Outs (Team Adjusted Range Outs.)  Formulas 37 and 38 created a value called Tm-RS-Range (Team Runs Saved by Range).  

First Base Runs Saved by Range is simply First Base Enhanced Range, divided by Team Adjusted Range Outs, times Team Runs Saved by Range, times .9. 

            RS-1B-Rg-Tm = 1B-En-Range / Tm-Adj-Rg-Outs  * TM-RS-Range * .90

That is, Formula 54 is Formula 31, divided by Formula 36, times Formula 38, times .90.  The "times .90" is in there because 10% of the Runs Saved by Range were diverted to give pitchers credit for a better-than-team-average batting average on balls in play (BABIP).     This chart summarizes the relevant data for the 15 teams in our study.  All of this data has been presented before; this chart merely brings the relevant material together into one:

And this chart gives the First Base Runs Saved by Range for each of the 15 teams:

Formula 56:  1B-Ind-Share (Individual First Baseman’s Share of Team Credits)

In Formula 57, we will add together the results of Formulas 54 and 55, First Base Runs Saved by Double Plays, Team and First Base Runs Saved by Range, Team.  Then we will split them between the Individual First Basemen on the team.   This formula, Formula 56, will be used to split them.  Formula 56 is:

1B-Ind-Share = (PO+2*Ast +DP – 7*Err) Ind-1B / (PO+2*Ast+DP – 7*Err)  Team-1B

            In other words, we add together a first baseman’s putouts, 2 times his assists, and his double plays, and subtract 7 times his errors.  We do that for all of the first basemen on the team, and each first baseman’s share of the team’s credits for double plays and for range depends on this formula.

            I know that people will argue with me about the decision to include Errors in the formula which is intended to represent Range and Double Play contribution, and.  . .go ahead and argue.   My goal is not to observe all of the proper and approved protocols of statistical attribution; my goal is to get the answers right.  I think that including errors in that formula gets us closer to the right evaluations of individual fielders than not including them.  So I’m doing it; when you do ratings, you can do them your way. 

Formula 57:  1B-Ind-1  (First Value for Individual First Basemen)

So the formula is:

1B-Ind-1 = [(1B-Tm-RS-DP) + (RS-1B-Range-Tm)] * (1B-Ind-Share)

We’ll outline the data for individual first basemen within our study after we explain how Fielding Percentages are dealt with. 

Formula 58:  Errors Avoided, First Base

The process for giving credit for errors avoided is the same at every position.  The process for pitchers was explained in this series under the headings Formula 20 through Formula 25.   The process for catchers was repeated briefly in Formula 53.   It is the same process here; you:

1)     Figure how many errors the player would have committed, if his error rate had been three times the league error rate at the position,

2)     Subtract the number of errors actually committed by the player,

3)     The result is errors avoided,

4)     Do the same for every player on the team,

5)     Find the team total,

6)     Find the player’s share of the team total,

7)     Apply that to the team’s total of Runs Saved by Error Avoidance, which was Formula 21 in this series.