Don’t worry, no one ever gets close. One person got to 40 a few years back and everyone lost their minds.
If a batter got a hit 70% of the time and you needed 56 in a row, your chances are ~0.0000002% of winning (or about 1 in 500 million). If they “only” hit .300 then your chances are astronomically small. Although that isn’t right is it, because they don’t need 56 hits in a row, just a hit in 56 games in a row. If you assume a league average hitter batting .250 and getting at least one hit in (say) each “set” of 4 at bats (representing a game)...
That said, I guess every gameday has at least a few dozen players getting a hit, so probably a better check on win probability is to define the number of possible batters that could be selected by a player each day (1 from any of the 9 players for each of the 30 teams plus pinch hitters = 1/~300 if just selecting randomly), the likelihood of each one being picked, and the probability of the more popular batters recording a hit...
I can’t think about this too much because I have work to do, but it would be an interesting exercise to figure out the odds of winning. Fuck all, is the take home message.