OK, it will take us nine formulas to formalize all of that stuff that I just explained (yesterday.)  All nine formulas are pretty simple.  We will get to Runs Saved by Fielding Range in Formula 38. 

Formula 30:  Inf-Ast-Sum

            We need the SUM of the infield assists in order evaluate the assists number for each fielder.  What we will treat as the sum of the assists is:

            Inf-Ast-Sum = 1BQA + Ast(2b) + Ast(3b) + Ast(ss)

That is, the team’s First Base Quasi-Assists, plus the assists by all of the team’s second basemen, third basemen, and shortstops.

Formula 31:  1B-En-Range  (First Base Enhanced Range)

The first basemen’s enhanced range is twice the First Base Quasi-Assists, minus .20 * the Infield Assists Sum:

1B-En-Range = 2 * 1BQA – (.20 * Inf-Ast-Sum)

This refers to the team totals, not to any individual first baseman. 

Formula 32:  2B-En-Range  (Second Base Enhanced Range)

The second basemen’s Enhanced Range is figured in the same way, but with the standard for second basemen being 30%, rather than 20%: 

2B-En-Range = 2 * Ast(2b) – (.30 * Inf-Ast-Sum)

Formula 33:  3B-En-Range  (Third Base Enhanced Range)

The third basemen’s Enhanced Range is figured in the same way.

3B-En-Range = 2 * Ast(3b) – (.20 * Inf-Ast-Sum)

Formula 34:  SS-En-Range  (Shortstop Enhanced Range)

The shortstops’ Enhanced Range is figured in the same way.

SS-En-Range = 2 * Ast(ss) – (.30 * Inf-Ast-Sum)

The sum of the enhanced range for the four infielders is the same as the sum before they were enhanced, which was defined as Inf-Ast-Sum. 

Formula 35:  OF-En-Range  (Outfield Enhanced Range)

The outfield’s enhanced range is 1.14 times the putouts made by all of the team’s outfielders:

OF-En-Range = 1.14 * PO(of)

Formula 36:  Tm-Adj-Rg-Outs   (Team Adjusted Range Outs)

The team’s "Adjusted Outs" are the sum of the Infield Assists (Inf-Ast-Sum), the pitchers’ Assists, and the Outfield Enhanced Range:

Tm-Adj-Rg-Outs = Inf-Ast-Sum + Ast(p) + OF-En-Range

Formula 37:   Tm-H-Av  (Team Hits Prevented, or Avoided)

We assume that a completely incompetent defense would allow base hits on 36% (.360) of balls in play.  Any play made beyond that is a Hit Prevented (or Hit Avoided):

Tm-H-Av = (BFP – SO – BB – HBP – HR) * .360 – (H – HR)

Formula 38:  Tm-RS-Range  (Runs Saved by Range)

Each Hit Avoided on a ball in play is assumed to have a Run Prevention value of .373 Runs:

Tm-RS-Range = Tm-H-Av * .373

As mentioned before, 90% of this value will be assigned to fielders based on fielding stats.   The other 10% will be assigned directly to pitchers based on their Batting Average on Balls in Play (BABIP). 

Turning our attention now to the task of giving you the data for the 15 test teams that we are following, we will start with the range numbers for the four infield positions on each team

And from that, we can move to Enhanced Range.  Enhanced Range gives us the Range Plays Made by each team (Team Adjusted Range Outs):

As you seem, team Adjusted Range Outs is not highly variable from team to team, since each team makes 27 outs per game.   Range Outs go down when strikeouts go up; otherwise they don’t change very much.   What really matters is not the plays they DO make, but the plays that they DON’T make, the balls that fall in for hits.   We chart those by looking at the elements of Tm-H-Av (Team Hits Avoided), which was formula 37:

Tm-H-Av = (BFP – SO – BB – HBP – HR) * .360 – (H – HR)

            And, since each Hit Saved prevents .373 runs (Formula 38), we can now figure the Runs Saved by Range for each of these 15 teams:

The number of Runs Prevented by Defensive Range is quite large compared to most other categories.  It is larger than any other category except strikeouts. 

Formula 39:  RS-Pit-Ast-P9  (Runs Saved-Pitcher’s Assists—9^th pitcher’s value)

We are now ready to assign Runs Saved value to pitchers based on their defensive assists.  For any other position, we would have to make another adjustment, the adjustment of crediting each fielder with superior range (or limiting value based on limited range.  But since pitcher’s assist totals are not enhanced by range considerations, we can skip that step in their case.  In this formula, Ast(p) refers to the fielding assists by the individual pitcher, rather than by all of the team’s pitchers:

RS-Pit-Ast-P9 = Ast(p) / Tm-Adj-R-Outs * .9

Team Adjusted R Outs is the result of Formula 36. 

The only pitcher credited with saving 2.00 runs or more by his assists was Denny McLain in 1968, who was just over 2.00.   These are the updated standings for pitchers saving the most runs:

We’ve got one category of Run Prevention left on the pitcher’s account.   When we get to the end of the pitchers, I’ll do a couple of things like outlining the records of the pitchers with the most runs saved, and looking at Runs Saved/Innings Pitched. 

Your reader comments on my last article in this series were good and helpful, and thank you all for your interest.