Runs Saved on Home Runs

And One-Base Advancements

            Formula 4:  Home Runs Avoided (HR-Av)

            The formula for Home Runs Avoided by a pitcher is:

            HR-Av = (BFP * .054183 – HR)/2

            The standard .054 183 Home Runs per batter faced is four standard deviations worse than the historic average, on the team level.  However, we cut that number in half, for this reason.  Let’s take, say, Pete Alexander in 1917.  Alexander was a great pitcher, 30-13 with a 1.83 ERA, his third straight thirty-win season.   But Alexander allowed only 4 home runs that season, while facing 1,529 batters.  .054 183 times that number is 83, so at four standard deviations worse than the historic norm, he would have allowed 83 Home Runs.   Allowing only 4, he thus "prevented" 79 home runs.  

            But that’s a totally unrealistic number.   Given the game he was playing—the ball that he was playing with, the parks he was playing in, the hitters he is facing—there is no conceivable way that he could have allowed 83 Home Runs.  His entire team only allowed 25 home runs.   Alexander DOES deserve a lot of credit for keeping the ball in the playing field; in that era, that was basically what the pitcher did:  keep the ball in the playing field and don’t walk anybody.  

            But if you say that he prevented 79 Home Runs, the effect of this, in the portion of the study in which we derive the value of each event by forcing the event numbers to try to predict the team’s Runs Saved, is to force the value of preventing a home run to an absurdly low level.  You wind up concluding that each home run prevented has a run prevention value of barely over half a run.  

And the reason for that is, it’s not really the pitcher who is preventing the home runs; it’s the conditions of the game at that time and place.   So we figure the number in that way, but then divide the home runs prevented by two, so that we wind up with a more reasonable value for each home run prevented. 

            Formula 5:  Pit-HR-Av-P3 (Pitcher, Home Runs Avoided, 3^rd pitcher value.)

            We credit the pitcher with 1.076 Runs Saved for each Home Run Avoided:

            Pit-HR-Av-P3 = HR-Av * 1.076

            Bob Friend in 1960 allowed only 18 home runs in 276 innings, thus is credited with NOT allowing 21 home runs, the largest number of any pitcher in the study.   But this doesn’t get Friend out of the third place in the updated standings.   I’ll stretch the list to 15 pitchers this time:

              Formula 6:   Team-OBAE (Team--One Base Advancement Events)

            One Base Advancement Events are Balks, Passed Balls, Wild Pitches and Stolen Bases Allowed.  Each pitcher and catcher will eventually be credited with Runs Saved based on the space between the number of these things that can be traced to their hands, and the number that a totally incompetent defense would allow. 

            OBAE = BK + PB + WP + SBA

            One Base Advancement Events will sometimes be referred to here as bases advanced.    We won’t actually USE this exact formula in figuring Runs Saved.  We’ll use a "pitcher’s variation" of it and a "catcher’s variation" of it.

            Formula 7:   OBAE-Budget (Budget for One Base Advancement Events)

            A pitcher’s "Budget" for One Base Advancement Events is  .037123 times his Batter’s Faced. 

            OBAE-Budget = .037123 * BFP

            The TEAM Budget for one base advancement events is .074246 times batter’s faced; however, one-half of that budget is allocated to pitchers, and the other half to catchers, since pitchers and catchers bear essentially equal responsibility for the base-advance events that are included here. 

              Formula 8:  BaSv-Pit  (Bases Saved by the Pitcher)

            A pitcher’s Bases Saved are his Budget for Bases Saved, minus his Balks, minus .70 times his Wild Pitches, minus .40 times the stolen bases allowed while he is on the mound, minus .35 times the Passed Balls that occur while he is on the mound, divided by two.

            We hold the CATCHER to be 30% responsible for Wild Pitches, 60% responsible for Stolen Bases Allowed, and 65% responsible for Passed Balls.   This is the formula for Bases Saved by the Pitcher:

            BaSv-Pit = [(OBAE-Budget) – Bk - .70 * WP - .40 * OSB - .35 PB] / 2

It is divided by two because the One Base Advancement Events Saved are not based on Formula 7, but on ONE-HALF the difference between the result of Formula 7 and the pitcher’s base advancements allowed.  If the difference is 50 bases, we don’t credit the pitcher with saving 50 bases; we credit him with saving 25 bases.   This is done because by far the largest element of one base advancement events is Opposition Stolen Bases, and stolen bases, like Home Runs, vary widely over time.   In 1950 native Kansan Willie Ramsdell, pitching for Cincinnati, allowed 15 stolen bases with only 4 caught stealing while facing 672 batters.  This is absolutely horrible data for 1950, when the league average was one stolen base allowed for each 130 batter’s faced.   Ramsdell was allowing about three times the league norm in stolen bases.  

            However, compared to the HISTORICAL average, he actually looks pretty good, or, at least, pretty average.   15 stolen bases allowed with 672 batters, by historical standards, is not a bad average.   The stolen bases that he did NOT allow were not being prevented by Ramsdell; they were being prevented by the nature of the game that he was playing.   So we use the standard of five standard deviations worse than the norm, so that we have space within the measured boundaries to accommodate everybody, but then cut the distance from the upper boundary in half, so that the numbers for pitchers in low-stolen base eras are kept within range.

Formula 9:  BaSv-RV-P4  (Bases Saved Run Value, 4^th Pitcher’s Value) 

            Each Base Saved by the Pitcher has a Run Value of .373 Runs.

            BaSv-RV-P4 = BaSv-Pit * .373

            Updating the chart that of the 15 top-rated pitchers on the 15 "test teams" the top seven pitchers remain in the same order as they were.   Dan Petry, 1984, moves up from 10^th to 8^th, and Jon Lester moves down from 8^th to 10^th:

            The number of runs involved in this category is relatively small, and it doesn’t ordinarily have a big impact on the total.   No one in this group is credited with saving more than 7 runs by limiting the number of one-base advancements.  They are small, but not meaningless.  Jake Arrieta (2016) was previously in 15^th place among these pitchers, but has dropped to 19^th because he threw 16 wild pitches and allowed 23 opposing stolen bases, both pretty high numbers.   Jack Fisher, a 24-game loser with the 1964 Mets, was not on the list before, but is now because, in 228 innings, he threw only 5 Wild Pitches and allowed only 11 stolen bases.  (2016 was not Arrieta’s great year.  That was 2015.) 

            Denny McLain, 1968, is now credited with saving 100 runs.   Let’s put that number in context.   The system generically expects that each team would allow one run per inning—thus, for McLain, 336 runs in 336 innings.  He allowed only 86 runs, so that’s a difference of 250 runs.   We have only credited him with saving 100.   Where are the other 150 runs?

            They’re in three different places.   First, 1968 was very much a pitcher’s year, as you know, so the run expectation in that season would be lower than 1.00 runs per inning.   That might knock McLain’s expectation down to 250, 280 runs, something like that.    Second, many of the runs that didn’t score while McLain was on the mound were not prevented by McLain; they were prevented by the fielders behind him.  That would explain another 50 to 80 runs.  And third, we’re not done yet with the Runs Saved  by McLain.  We are transitioning now to his Runs Saved as a fielder, rather than his runs saved as a pitcher, but his Runs Saved total will still go higher.

            One can also figure, with this data, the success of each pitcher at preventing one-base advancements by baserunners.   The best pitcher in this data at preventing advancement was Vinegar Bend Mizell, with the 1960 Pirates.   Mizell faced 631 batters, thus had a budget of 23 bases.  He threw 1 Wild Pitch (cost to the pitcher:  .7 bases) and allowed 4 stolen bases (cost to pitcher:  1.6 bases), thus he is charged with 2.3 base advancements, out of a budget of 23 bases.   He "saved" 90% of the bases that he might have allowed, the best percentage of any pitcher facing 400 or more batters on any of these 15 teams:

            I think those are mostly left-handers, I don’t know.  Be something to study after I have this all worked out.   Anyway, there are 92 pitchers in this study who faced 400 or more batters, and one of the 92 actually busted his budget, giving up more one-base advancements than the zero-value pitcher.  That was Richie Lewis with Detroit in 1996.   Facing 412 batters, he balked twice (cost to pitcher:  2 bases), threw 14 wild pitches (cost to pitcher:  9.8 bases), had one passed ball while he was on the mound (cost to pitcher:  .35 bases), and allowed 12 stolen bases (cost to pitcher:  4.8 bases.)   That wasn’t actually his worst year; just glancing at the data, in 1994 with Florida he would have been even worse.  These are the ten pitchers who were least successful at preventing baserunner advancement.