I had a post about this a couple of weeks ago called Ted Williams 1941: May 16th, .333; June 6, .436. This post will go into more detail. It looks like his performance at the ages of 22-23 (1941-2) might be much greater than anyone else in history.
The table below shows that he had the biggest gain in offensive winning percentage (OWP) from ages 21-22 (he was 22 in 1941 when he batted .406). (OWP) is the Bill James stat that says if all 9 hitters were identical, what would the team's winning percentage be if it gave up an average number of runs. The lists I show below are from the Lee Sinins Complete Baseball Encyclopedia, so the OWP they are based on is park adjusted.
But OWP cannot go above 1.00. So Williams could only increase by .236. Other players had alot more room to improve. So I ranked everyone by what percentage of the possible increase they attained. Williams jumped from .764 to .908, a jump of .144. That is 61% of of the possible .236 (shown as .610 in the table). This is by far the greatest increase (I only looked at hitters who had at least 400+ plate appearances (PAs) at each age.
Here are the leaders in the simple gain in OWP.
I also did something similar for the gain in OPS or on-base percentage (OBP) plus slugging percentage (SLG). But I looked for the biggest gainers relative to the league average, assuming a league average OPS of .750. For example, if a player had 1.000 OPS when the league average was .800, his relative OPS was 1.25 (1/.8). Multiplying that by 1.25 leaves .938. With this adjustment having been done, Williams has by far the biggest gain from 21 to 22. The next table shows this.
The next table shows how he had the biggest improvement in OWP (relative to what was possible, like the first table) for all players who had 800+ PAs at both ages 20-21 & 22-23.
The next table shows the leaders simply based on the absolute gain in OWP.
Now the gain in relative OPS from ages 20-21 to 22-23.