This is an article at espn.com by Christina Kahrl. Here is the link

She
points out that Gehrig did not have to face the good pitchers on the
Yankees, and, of course, no black or Latin pitchers. But although those
things are true, I wonder how much they would or should change our
estimate of Gehrig. My guess is not much.

Yesterday I pointed out that Hank Aaron only faced black/latin pitchers about 13% of the time and that Gehrig not facing his own pitchers would lower his OPS+ by just 3 points, leaving him still 4th best all-time.

But, as you many of you may know, the Yankee pitchers were not quite as good as they
look since they did not face the great Yankee hitters. So that decline for
Gehrig is probably not that big.

I calculated Gehrig's OPS+ using the formula they have at Baseball
Reference. Then I assumed that the Yankees staff is 1/8th of the league
and took them out and got a slightly higher league average OBP & SLG
and then recalculated Gehrig's OPS+ (I did all this without park
effects). His OPS+ fell from 183 to 180. As far as I can tell, BR does not account for not facing your own pitchers.

Now to the question of not black/latin pitchers. This math may get gory. About 10 years ago I estimated that from 1947 to 2006 or so about 15% of innings were pitched by black/latin guys. I also determined that collectively those guys were about as good as the remaining white guys (white guys who did not get replaced).

So, I tried to figure out how many HRs this cost Ruth. I removed the bottom 15% of pitchers (by innings or batters face, not sure which). Then I calculated the HR rate for the remaining pitchers. It was, collectively, about 5% lower than for all pitchers. So I declared that if Ruth had faced black/latin pitchers 15% of the time, his HR rate would fall by 5%. I assumed that the HR rate for those black/latin guys who were now in baseball would have been the same as the best 85% of white guys.

I did something similar with Gehrig. I tried to estimate how much to decrease his OBP and SLG to recalculate his OPS+. The first thing I did was rank all AL pitchers over the years 1925-38 by runs per game (per 9 IP). Then I removed the bottom 15% (by batters faced).

The top 85% allowed 4.92 runs per game while the whole group allowed 5.20. So we have runs per game falling by about 5.6%. That means OBP & SLG would be lower. But by how much?

Using all MLB teams from 1925-38 (this was easiest using the Baseball Reference Play Index since there was no option just to get AL teams, you have to use all MLB teams), I ran a regression with team runs per game as a function of OBP & SLG. Here is the equation

R/G = 11.82*SLG + 18.37*OBP - 6.12

Using that formula, to get runs per game to go down 5.6%, both OBP & SLG would have to go down about 2.545% each (assuming they each go down by the same %).

That is what Gehrig would face with the better pitching in the league from black/latin guys (remember, as a group they are about as good as the remaining white guys). Runs go down 5.6% so we have a corresponding drop in the league in OBP and SLG.

The formula for OPS+ at BR is 100*[OBP/lg OBP + SLG/lg SLG - 1]

Gehrig had a career OBP & SLG of .447 & .632. Lowering those by 2.545% each gets us .436 & .616. The league averages (taking out Yankee pitchers) were .353 & .411. That gets me a 173 OPS+. I started with 183 (recall I am not doing park effects here-also recall that maybe the Yankee pitchers were not that good since they never faced the great Yankee pitchers). So Gehrig falls 10 points in OPS+ (maybe less).

At BR's leader list

http://www.baseball-reference.com/leaders/onbase_plus_slugging_plus_career.shtml

Gehrig would fall from 179 to 169, and be in a tie with Trout for 9th best ever (but probably a bit higher).

But, if these good black/latin pitchers are added to the league, the league OBP & SLG go down, then Gehrig's OPS+ is calculated with a lower league average and it would come back up. In fact, it would all cancel out. He goes down 2.545% and the league average goes down 2.545% .

But (yes, another one), there is one potentially big factor left out so far. If blacks/latins are added to the league, many of them, as we know, will be position players and that should raise the league average for things like OBP and SLG (think of it as a 2 stage process-first black/latin pitchers come in and league OBP & SLG go down a bit-then black/latin hitters are added to the league and that would bring the league OBP & SLG back up).

Maybe we end up an even higher league OBP & SLG than we started with (I think this likely since black/latin position players have been a bigger % of the total than in pitching) and that would lower Gehrig's OPS+. That means we need some estimate of how much league OBP & SLG would be affected if you added in all the good black/latin hitters, who would generally replace the worst white hitters (not entirely since some weak hitting guys who were good fielders would stay).

So I need to come up with that estimate to adjust Gehrig's numbers again.