Adjusting the best WPA games for opposing pitcher quality

See List of all games with a WPA of 1 or higher from Stathead.

This has links to the box scores to each of the 98 games. That is where I found the opposing pitchers. The measure of quality I used was a weighted average of the ERA+ of all the pitchers each batter faced from that year (most of the batters faced more than one pitcher in their game). 

That weighted average was divided by 100 and then multiplied by each batter's WPA. For example, if the weighted average of ERA+ was 120, the batter's WPA was multiplied by 1.20. The idea is that the level of difficulty was 20% above average.

The reason why I did this study is that Bobby Grich's game (which is 9th highest, unadjusted), was against Ron Guidry (all 5 PAs). His ERA+ in 1979 was 146. So a pretty tough opponent for Grich. Everyone knows "The Sandberg" game when he hit 2 HRs off of Bruce Sutter (the Sandberg game is the 48th best unadjusted game). But no one talks about "The Grich Game."

Here are the top 10 WPA games adjusted for pitcher quality:

Player	WPA	Date	ERA+/100	Adj WPA
Brandon Crawford	1.448	8/8/2016	1.34	1.939
Art Shamsky	1.503	8/12/1966	1.27	1.914
Bobby Grich	1.211	7/15/1979	1.46	1.768
George Burns	1.170	6/9/1916	1.50	1.750
Dolph Camilli	1.398	9/1/1941	1.22	1.702
Joc Pederson	1.112	5/24/2022	1.52	1.692
Jimmie Foxx	1.307	7/10/1932	1.26	1.644
Raúl Mondesi	1.056	4/5/1999	1.55	1.633
Fred McGriff	1.084	8/24/1996	1.42	1.539
Brandon Inge	1.113	8/24/2003	1.38	1.538

So Grich jumps to number 3. Shamsky was number 1. Crawford had been number 2. But he had 8 PAs as did Camilli. Foxx had 10. Maybe it is easier to get a high WPA with more PAs (and a really low one, too). 

The next table has the top 10 adjusted WPA games divided by the number of PAs each player had:

Player	Date	Adj WPA	PA	Adj WPA/PA
Midre Cummings	5/10/2000	1.418	2	0.709
Art Shamsky	8/12/1966	1.914	3	0.638
Randy Hundley	7/1/1973	1.038	2	0.519
Bobby Grich	7/15/1979	1.768	5	0.354
George Burns	6/9/1916	1.750	5	0.350
Earl Averill	5/3/1961	1.365	4	0.341
Al Spohrer	7/4/1929	1.324	4	0.331
Joe Dugan	8/10/1918	1.316	4	0.329
Fred McGriff	8/24/1996	1.539	5	0.308
Brandon Inge	8/24/2003	1.538	5	0.308

Brandon Crawford fell to number 38 with .242.

Some issues:

I wonder if it is easier to get a high WPA in a high scoring environment. But the 1960s had 15 games while the high scoring period of 1996-2010 (with more teams) had 15 as well.

Maybe I should have used the WPA for pitchers instead of ERA+. But I was not sure if I would need to turn it into a rate stat, like divided by batters faced or innings. It seems like relievers would be in high leverage situations so they would have more chances to increase (or decrease) their WPA. Of course, relievers also generally have lower ERAs and, therefore, will have better ERA+s. So that is a problem either way.

Speaking of relievers, it might be easier to get a high WPA if you don't have to face them (like Grich). Batters generally do better the more times they see a pitcher during a game. There were only 5 games where the hitter only faced one pitcher. Just two of them were in the top 33 of the unadjusted WPA.

I did not take park effects into account. Maybe being in a higher scoring park gives you more chances to increase your WPA. But like I showed above in comparing the 1960s to the 1996-2010 period, higher scoring did not necessarily mean more high WPA games. In fact, the highest WPA game from the 1920s was number 28, George Kelly.

I did not take into account platoon advantage. Grich (a righty) faced Guidry all 5 times in his game and Guidry is a lefty. Maybe the batters who faced 2, 3, even 4 relievers did not get the platoon advantage very much.