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How long will that baseball game last?

"How long is that baseball game going to last?"

That is the question my wife asks when I say I'm planning to go a baseball game. This is one of life’s timing mysteries, like how long does it take to play a round of golf or how long does it take to have a beer with your buddies?

“I can’t say for sure. The game could be a pitchers' duel and last just over two hours. Or it could be a shootout with 10 pitching changes and last over four hours,” I say.

My wife then says, “It seems like baseball games are getting longer."

She is very intuitive, so I decide to check out the data. The graph below shows that MLB game lengths have indeed been increasing pretty consistently for the last 100 years.

Of course, I have not been attending games for that entire period, so let’s take a look at a more recent period. I have been regularly going to MLB games since I moved to Colorado in 2007.

Sure enough, the average baseball game this year is three hours and nine minutes long, which is 14 minutes longer than the average game in 2010. That is the overall average for the MLB, but does that trend hold up for each team? The graph below is the trend for each team from 2007-2017.

Every team has trended toward longer games since 2007. The length of New York Yankees games has remained the most constant, increasing by an average of only 3 seconds per year. The team with the biggest increase in average game length is the Pirates, whose games have been increasing by nearly 2 and a half minutes each year.

My wife is mostly interested in the Rockies as those are the games I attend. Sure enough, she is right. The average Rockies game has been increasing in length by 104 seconds each year.

Now to the original question of how long the game is going to take. The average Rockies game this year takes 3 hours and 10 minutes to complete, so that would be a decent guess for how long the game will go. I can make a better guess with a few factors that I know heading into the game: I know whether the game is a day game or night game; I know where the game is going to be played; and I know who the starting pitcher is for the game. If I take those factors into account, I may be able to get a better estimate of the time that the game will take. I set up my model looking at three main factors: home or away; the Rockies starting pitcher; day game or night game. Then I can look at all of the interaction effects as well.

After running the model, I find some of the effects have a high p-value and thus remove them from my model. The three effects that end up being significant to the model are the starting pitcher, day or night game, and the interaction between those two factors.

The Profiler in JMP is an excellent way to interpret the model. The Rockies game I am planning on attending has Jeff Hoffman pitching at night.

I tell my wife I now have a much better estimate of what time it will take for the game tomorrow night. The average night game that Jeff Hoffman pitches lasts 3:30 minutes. So I am 95% confident that the mean will fall between 3 hours and 13 minutes and 41.9 seconds (11621.9 seconds) and 3 hours 46 minutes and 35.2 seconds (13595.2 seconds).

“So, you are 95% confident that the game will last between 3 hours and 14 minutes and 3 hours and 47 minutes?” asks my wife.

“No, if I went to 10 games with Hoffman pitching at night, I am 95% confident the average time of those games would fall in that range,” I respond.

“OK, so how long do you think this game will be?” she asks, shaking her head.

“I can’t say for sure, but the night games Hoffman pitches on average last 20 minutes longer than the average Rockies game.”

“I guess that is useful information,” she concedes.

“As George Box says, 'All models are wrong, but some are useful,'" I tell her.

“Now can you make a model to figure out how long a round of golf will take?” she says, smiling.

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