I came across a stat I forgot about today, Gross Production Average, published by the Hard Ball Times. GPA is an improved version of OPS that weights On Base Percentage more heavily than slugging percentage, plus, puts the stat in a scale similar to batting average.
The underlying metric prior to any conversion is very similar to the clunky AOPSAP that I have been using. AOPSAP uses (OBP*1.4+SLG) whereas GPA uses (OBP*1.8 + SLG). It also takes it a step further and converts to runs and this is where AOPSAP got the clunkiness. Instead of just taking the raw rate stat and multiplying it by total plate appearances (cringe!) GPA uses linear weights to encompass playing time. The formula: PA*1.356*(GPA^1.77). I don't pretend to understand why, but it works wonderfully.
Now we have the raw ATB Value calculation. Currently, here are the leaders among qualified batters:
.344 - Lou Gehrig (PR)
.342 - Tip O'Neill (DCC)
.319 - Barry Bonds (SBD)
.317 - Joe DiMaggio (EPL)
.315 - Jimmy Foxx (DB)
Taking into times at the plate, the leaders are:
83.3 - Lou Gehrig (PR)
73.3 - Tip O'Neill (DCC)
72.1 - Ted Williams (LDS)
71.6 - Bobby Murcer (PR)
70.5 - Joe DiMaggio (EPL)
The raw GPA is the starting point for ATB Value. From there, we need to account for defense, park factor, and positional scarcity.
Defense
Through the miracle of VLOOKUP I can readily scan hundreds of players, interpret their defensive range, assign a value, and include it in a metric. We've seen how important defense is to the DMB Engine, and I assigned defensive values based upon ranges accordingly. From that linked report, we found that infielder range was the most critical, outfield range was almost as critical, and pitcher and catcher ranges were basically irrelevant. As such, I assigned the following "rating values" to each possible range of defense by position.
These values are simply multiplied by the GPA score. A great infielder improves the score by 4%, a great outfielder by 3%. Conversely, the worst infielder reduces the score by 4% and the worst outfielder by 3%. These percentages came from the defensive study referenced above.
The omissions on the defensive side include outfield arms and fielding percentage. Compared with range, this are minimal. Perhaps another day or another season.
Park Factor
This was the hurdle I could not overcome. As you know, Diamond Mind uses individual park factors for Lefties and Righties, for Singles, Doubles, Triples, and Home Runs. To fairly incorporate this into a metric was impossible to do so on a repeatable basis. For each player, the calculation would have needed to include game by game data to see how many games a Lefty or Righty played in each park with each park factor. Possible, but insurmountable for a fun simulation league.
Instead of worrying about the individual park factors, I tried to create my own "High Level Park Factor" based upon the individual split park factors. But, then again - how much weight do HR's get versus Singles? And how much less does a lefty HR factor get weighted vs a Righty HR factor. I could not figure these problems out mathematically.
Then the light bulb went off. Sean Foreman has already done this with the Baseball Reference Ball Park Factors. And I have even been publishing them for years in the draft day batting files. Doh!
So, now ATB Value also uses Baseball-Reference.com's ball park factors.
Positional Scarcity
Any all in one metric worth its salt adjusts for positional scarcity. A great hitting second basemen is more valuable that a right fielder that hits at the same level. This is because there are very few great hitting infielders and plenty of great hitting outfielders. Taking a page out of the AOPSAP book, I adjust GPA in the same manner - by comparing each players GPA against the average GPA of their main position.
Tying it All Together
Simply stated, ATB Value is Gross Production Average adjust for park factor, defensive range, and positional scarcity. The formula:
ATB Value = (OBP*1.8+SLG)/4) * BPF * Def Rating * (Best Pos GPA / Avg Pos GPA)
The Results
ATB Value
0.364 - Tip O'Neill, DCC
0.340 - Lou Gehrig*, PR
0.337 - Jimmie Foxx, DB
0.335 - Duke Snider*, DCC
0.332 - King Kelly, LDS
0.332 - Larry Walker*, P10
0.325 - Nap Lajoie, PGB
0.322 - Ted Williams*, LDS
0.319 - Arky Vaughan*, DCC
0.319 - Eddie Collins*, HH
ATB Value Runs
81.9 - Tip O'Neill, DCC
81.8 - Lou Gehrig*, PR
77.9 - Ted Williams*, LDS
77.8 - Eddie Collins*, HH
77.7 - Arky Vaughan*, DCC
76.7 - Larry Walker*, P10
76.5 - Jimmie Foxx, DB
70.4 - Bobby Murcer*, PR
70.1 - Mickey Mantle#, HH
69.9 - King Kelly, LDS
The entire list of players can be accessed here and linked on the top right. Moving forward, ATB Value will replace AOPSAP permanently.
In the linked file, the Overall Tab players are sorted first by ATB Value among qualified batters, and the lower section is sorted by ATB Value Runs for non qualified batters. There are also separate tabs for each position.
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