Maybe somebody else already did this, but I wanted to get some context for how crazy Luis Arraez's start has been (he's hitting 52% better than the league average), so I calculated the "batting average above average" for every batting title winner for the last 100 years. Think of it as OPS+ but just for batting average and without any park adjustments.
Prior to this year, there have been only two seasons in MLB history where a player hit 50% better than the league average: Ted Williams in 1941 (.406 BA, 156 BA+) and Ted Williams in 1957 (.388 BA, 150 BA+). Arraez is currently at a 152 BA+. The closest modern comparison (not counting the Covid-shortened season in 2020) is George Brett in 1980 (.390 BA, 147 BA+).
When you consider that pitchers still hit during Williams's time (and Fenway Park was a crazy hitters' park in 1957), it's clear that Arraez is currently having the best season for pure batting average since Ted Williams became the last player to hit .400.
Now, the league average is likely to come up over the next four months and Arraez is unlikely to keep hitting .367, but for two months, this has been all-time great season for pure hitting.