Michael Frain takes a look at the correlation between “consistently high hitting streaks and consistently high batting averages”.
My simulator of choice is Diamond Mind Baseball, using the 1941 season disk with the factory settings. For this initial look, I ran the season 10 times on autoplay, and found some interesting trends. In nine of the ten season runs, Williams led the AL in batting average, each time surpassing the .400 mark (and one time surpassing the .500 mark, which would seem to qualify as an outlier statistic). In only one run did Williams finish second in hitting, and in that run he finished with a .388 mark (second to Cecil Travis’ .396 mark in that run).
In the long run, it appears that a batting average would seem to be fairly repeatable achievement - over the course of a 150+ game season, the batting average is a pretty good indication of expected performance.
The hitting streak, on the other hand, was a far livelier statistic. In each of the 10 season runs, the longest season streak ran from 22 (set by Williams himself) to 59 (a surprising mark set by the Tigers’ Rip Radcliff). Discounting that outlier statistic, the high marks ranged from 22 to 33 consecutive games with a hit.