"What are the odds?" The Athletics (MLB) and Sharks (NHL) Win By The Same Score of 8-1

WHAT ARE THE CHANCES?! pic.twitter.com/yoLoWrWg3F

— Brodie Brazil (@BrodieNBCS) April 17, 2018

Yesterday both the Oakland Athletics and San Jose Sharks won their respective games by a score of 8-1. This is impressive in both sports, but even more so in hockey (and in the playoffs no less). What are the odds that both Bay Area teams won by this exact amount, on the same night?

The last part of this question I'm taking as a given, since this occurrence wouldn't be notable if it didn't happen on the same night. Having home games at the same time is certainly extremely unlikely, since the NHL season doesn't overlap much with MLB, and the Sharks had to make the playoffs for this to be the case (or the Athletics would have to make the playoffs in October when the NHL season is starting). I'm starting from the assumption that this is already the case, since otherwise it wouldn't be notable (i.e. the teams had the same score at different points in the season).

That leaves two probabilities to be calculated: the odds the Sharks win a hockey game by exactly a score of 8-1, and then the odds the Athletics win a baseball game by exactly that score.

I don't have a very robust technique for predicting exact scores in the NHL, so I'm defaulting to the table found on Page 14 of "Poison Toolbox: a review of the application of the Poisson Probability Distribution in hockey" from Hockey Analytics. 

"Poison Toolbox: a review of the application of the Poisson Probability Distribution in hockey"

This estimates that there's a 0.1% chance that the Sharks would win by a score of 8-1. The Athletics I can determine directly by running my MLB play-by-play simulator. Over 10,000 simulations, the A's only win by a score of 8-1 0.59% of the time. 

Multiplying these together gives a likelihood of 0.00059%, or 1 in 169,492. While that's a very rare occurrence, that's nowhere near as unlikely as the time the San Francisco Giants and San Jose Giants had the exact same inning-by-inning run output on the same day.