Suppose that baseball had been integrated before 1947. The quality of the pitching would have been better since the talent pool would have been larger. But how much better would the pitching have been? I assume that the racial mix of pitchers would have been about what it was in the post 1947 era. I have one article on this on page 23 of recent issue of The Chicago Sports Weekly.
I estimate that about 15% of the IP then were by non-whites, blacks, dark-skinned Hispanics and Asians. Using the Lee Sinins Complete Baseball Encyclopedia, I found all the pitchers with 1,000+ IP in this period and then calculated what percent of the IP by these guys was by non-whites. You can see the list here. I checked the race of any pitcher I did not already know by looking at when they played and finding pictures of them in books or online. Any pitchers with Hispanic names were considered non-white. There were pitchers like Lefty Gomez before 1947, whose skin was light enough to play. But I did not want to have to judge who would have been able to play and who would not.
In that list, I have relative ERA listed. That is simply ERA divided by the league ERA. The relative ERA of all the whites combined was 105.75, meaning their ERA's were about 5.75% better than the league average. For the non-whites it was just a bit higher at 106.8. In the analysis below, I assume that the ERAs of whites and non-whites will be the same. The number of IP by the pitchers with 1,000+ IP since 1947 accounted for 58% of all the IP in this time period.
Now if you add in a bunch of new pitchers, who do you get rid of? The worst pitchers. Since the non-whites make up 15% of the IP, I assumed that the worst 15% of pitchers in Ruth's era would be replaced by non-whites. I did that by ranking pitchers in various years by ERA and eliminated the pitchers that made up the bottom 15% of the list. How good would the new mix of pitchers be? Since the non-whites and whites have basically the same ERAs, the new ERA in baseball would be the collective ERA of the top 85% of pitchers (actually the pitchers who made up the top 85% of IP on the ERA list). Again, since the non-whites have the same ERA as their white counterparts, I use the ERA of the best 85% of the pitchers (this lower ERA is about 8.7% lower below the league average).
After getting rid of the bottom 15% of the IP in each season from 1906 to 1934 in the AL, I recalculated the HRs, non-HR hits and walks per IP and found how much lower than the league average the new figures were. For example, as shown in the table below, the HRs per IP fell 14.2% in 1906. That is, the best 85% of the pitchers had a HR per IP rate that was 14.2% lower than the league average (which includes all pitchers). The table shows the percentage drop in each stat per IP for the AL in each of those years.
The average fall in HRs per IP for the years 1920-1934 was about 5%, when Ruth played with the Yankees and had all of his great seasons. So if you improve the pitching quality in a way that is consistent with integration, Ruth would hit 5% fewer HRs or hit about 678.
For Cobb, the relevant years are 1906-1928. The average decline in HRs would be 6.5% and non-HR hits would be 2.86%. Now Cobb did not hit many HRs, so that won't matter too much. But I reduced his HRs by 6.5% and the rest of his hits by 2.86%. I added those two totals together and that is his total drop in hits. But I have to drop his ABs by that amount too, since the drop was per IP. If a pitcher gives up one less hit in an inning, it is one less AB as well. Once that was done, Cobb's average was .361, not the .368 he had over the years 1906-28 (I did not use 1905 since he did not play much then).
What about Fielding?
Integration probably improved fielding. Some non-whites were above average fielders, some below average. But I think the quality would have been better overall. To try to quantify this, I found that of the top 300 players in games played by outfielders from 1947-2006, 63% were by non-whites. The putouts per game were about the same for the group of whites and non-whites. But we have to assume that some of the whites who got replaced were not as good as the new guys.
To see how much this might have improved fielding, I went to the top 300 players in games played by outfielders from 1901-46 and dropped the lowest 63% and found that the new putouts per game was about 15% higher than it was using all players. So if you drop the worst 63% of the fielders and the new crop of fielders coming in is just as good as the remaining guys, fielding improves 15%. I did something similar with assists per game for shortstops and second basemen. I looked at the top 100 players in games played and found that since 1947 about 45% of their games at both positions were played by non-whites. The assists per game for the best 55% of those fielders was about 5% better than average.
The improvements in fielding of 15%, 5% and 5% are close to the 8.7% drop I found in ERA (if you average those 3, it is about 8%). I did not look at 3B men since I don't think too many were non-white since 1947. 1B men are not too important and catchers don't take away too many hits (although they can have value). For Cobb, his AVG fell 7 points due to the better pitching. But in run prevention, pitching is more important (Bill James has it 2/3 pitching, 1/3 fielding). So my guess is that Cobb's average would fall no more than another 7 points due to better fielding. He would still have hit .354 over the years 1906-28. In other words, if fielding and pitching both improve by 8%, you would expect a bigger drop in hits due to pitching since pitching is more important in determining outcomes. If I go with an equal importance, the Cobb's AVG falls another 7 But if assume that 8% better fielding means 8% fewer hits, the drop in Cobb's average is going to be more than another 7 points from fielding.
Some OFers can rob batters of HRs. So maybe the Tori Hunters of the world would take a few HRs away from Ruth. But if each team had 2-3 good non-white hitters added to their teams, opposing pitchers might have to work harder and get tired sooner. That might help the existing white guys a little. But I don't know how much. Walks fall, too. Ruth and Cobb would both walk less, hurting their OBP. But I have not calculated the effect.
I also have no way to prove what the racial makeup of baseball would have been pre-1947. The percentage of non-whites might have been different. This analysis just asks what might have happened if Ruth and Cobb played in a league with a racial makeup like the one that we have had since 1947. Even the racial mix since 1947 has changed. The percentage of non-whites grew slowly. Aaron and Mays faced a different racial mix than Bonds and Sosa. The percentage of black players has fallen recently while the percentage of Hispanics has increased.
Maybe expansion would have occurred sooner if baseball had integrated sooner. Then pitching might have been diluted and that would change the equation. I also don't know what happens when HRs fall. Do those ABs become outs or does the batter get a lesser hit? I also have not taken into account any general improvement in quality of play due to better training or nutrition.