The Crazy Probabilities in the Nationals Five-Homer Inning

The Nationals just exploded offensively against the Brewers, winning 15-2. It might be hard to believe, but it could have been worse as all 15 Nationals runs were scored in the first four innings. One inning in particular stands out as the Nationals hit five home runs in the third inning on their way to a seven-run inning. It might be hard to believe, but the inning didn’t appear to be a particularly promising one from the beginning as Max Scherzer and his .185/.215/.200 slash line led off. Here’s how the inning went down, per the FanGraphs play log.

Before we get to these probabilities, lets talk some other odds. Let’s say I told you four Washington Nationals hitters in a row hit homers, and you had to name the four hitters, how many guesses would it take. Bryce Harper would certainly be a good guess. So it would Ryan Zimmerman, but how many names would you have to cycle through before you named both Wilmer Difo and Brian Goodwin. I can understand Goodwin, as he’s popped ten in just over 200 plate appearances, but Difo had hit two homers this season and just 14 at any level since leaving low-A at the end of the 2014 campaign.

Jon Tayler took a rough stab at the probability here:

The odds of all of those happening in the same inning have to be roughly .000000000000000000001%, right?

— Jon Tayler (@JATayler) July 27, 2017

There are a lot of wild probabilities to cover, but let’s start with the four homers in a row.

Four homers in a row

Odds:

• 0.00000115744
• Roughly one in 864,000

According to our projections, Goodwin is likely to hit a home run in 2.9%, Difo in 1.5%, Harper in 5.5%, and Zimmerman in 4.6% of plate appearances. The odds of them going back to back to back to back is about one in 864,000. If you divide by 18 chances per game, 81 games per home team and 30 teams in baseball, we are talking about a one in 20-year occurrence. For four good home run hitters, say 4% chance of a homer, that number is once in nine years.

If you want to play the what-if game, Daniel Murphy had a shot to make it five homers in a row. The odds of those five players each hitting homers in a row is one in 26 million, or once in 604 seasons. It’s possible that’s why it hasn’t ever happened before.

That’s not the only homer probability from the inning though, as after Daniel Murphy flied out, Anthony Rendon hit a homer.

Five homers in six batters

Odds:

• .0000002914
• Roughly one in 3.4 million

I got a little bit lazy here and instead of taking the individual players’ homer percentages, I averaged out the six players and used 3.6% chances of each getting a homer to determine the chances of six players getting five homers. This is a once in 78 seasons occurrence. Of course, just getting five homers in an innings is slightly easier as you have three outs to work with and other players can get hits in between. For example, in 2006 the Milwaukee Brewers hit five home runs in an inning when Bill Hall, Damian Miller, Brady Clark, J.J. Hardy, and Prince Fielder all teed off, they hit four homers among six batters and five homers among nine batters, which is a one-in-two year and one-in-six year phenomenon at the Nationals’ homer rates.

Max Scherzer

Odds:

• .0000124305
• Roughly one in 80,000

In the third inning, Max Scherzer did three things that do not normally happen to Max Scherzer. First, he drew a walk, which happens about once in 30 plate appearances. Then he batted again, which required eight teammates not to make three outs, which at a .330 OBP clip, which is about a one in 70 shot, and then he got an infield single, which is about one in 40 tries. Put it all together and that thing would happen about once in 80,000 tries. Scherzer has come to the plate 304 times.

Adam Lind steals a base

Odds:

• .0011892857
• Roughly one in 840

Adam Lind gets on base via the walk or single about one in three times and according to Baseball-Reference, Lind has stolen six bases in 1,680 opportunities. Put it together and the odds aren’t high of seeing this, and it is possible I am understating things quite a bit as Lind hasn’t stolen a base since 2013 and has only attempted two in the last six seasons. It’s probably a bit more rare than I’m making it out to be.

As for Tayler’s question in the tweet above, I plugged all the information into my calculator and it told me to get outside more. Feel free to question my math or challenge any assumptions I made. I promise I won’t mind.