Mariners have their work cut out for them

In 2009, the leaguewide on-base percentage was $0.333$. That figure has fallen over the past decade, and this year, it’s all the way down to $0.313$, which helps explain the surge in no-hitters.

Assume that all batters have the same chances of reaching base, that at-bats are independent from each other, that there are 30 MLB teams, and each club plays 162 games, and that no games go into extra innings.How low would a batter’s chances of reaching base have to be for you to expect one perfect game per season?

Let's assume that the leaguewide on-base percentage (OBP) is $a$ with all of the other simplifying assumptions above, then the expected probability of a perfect game is $(1-a)^{27}$ with an expected number of perfect games being $P(a) = 4860(1-a)^{27}$. So solving for $P(a)=1$ gives a league-average OBP of $$a = 1 - 4860^{-1/27} = 0.26977295.$$

Having obscurely avoided a perfect game against the Orioles earlier this year based on Sam Hagerty reaching first base on a dropped third strike, my Seattle Mariners are leading the charge towards this abysmal on-base percentage with only $0.281$ so far this year (through Sunday, May 30). That level of futility would blow past the previous Wild Card Era (since 1995) full 162-game record held by the 2014 Padres and (ugh, . . . of course) 2011 Mariners of $0.292,$ and even eke under the Pirates' COVID shortened 2020 mini-season low of $0.284$. (The soon-to-be-known-as Cleveland Baseball Team is also in the hunt for new Wild Card Era lows in OBP this season sitting at $0.290$.)

Los Marineros are simultaneously chasing the record for most no hitters thrown against them, just one behind the 1906 Brooklyn Superbas record of 3 no hitters against. (Here, again, the M's will need to shake off some competition as both the Cleveland Baseball Team and the Texas Rangers are also vying for most no hitters against record this year.)

All this to say, at least they are no where near the $0.171$ OBP that any individual team would have to average a perfect game against per year. Sometimes, you have to just throw out the glass and claim that you weren't ever interested in how much water there may or may not have been in there in the first place. Wait, what were we talking about?

P.S. Go M's!