Hey guys, data scientist here who was at the game yesterday. I was curious to see how truly rare what we saw yesterday was so I did the math:

218,400 games played in MLB history × roughly 9 innings (probably more considering extras but let's keep this simple).

That's 1,965,600 innings played in baseball history. There's now been 108 immaculate innings thrown in history. That's a 108 in 1,965,6000 chance or 0.0055% chance every inning (let's call this x).

So what's the probability this occurs in a game? That's a 0.0495% (9 by x) chance of happening in a game. And then, take the chance it will happen in one of the other innings 0.0439% (8 by x).

So take those two probabilities together you get 0.0000021% chance of happening in one game. That's a two in ten million chance of happening. But that's not all!

What are the chances this happened to the same the batters? Each inning has a one in nine chance of starting on the same batter. So you have to take 1/9 by 1/9 for likelihood that an inning will start on the same batter by our previous calculation.

That's a probability of 1/27 by the 0.0000021% chance of throwing two immaculate innings in one game.

That's a 0.00000026% chance or two in one billion chance of happening!