The rise of the extra-inning playoff game

We're barely out of the divisional series, and we've already had four extra-inning games:

According to the Baseball-Reference Play Index, the MLB record for extra-inning games in a single postseason is eight, set in 1995. But we're just through a single round of the playoffs; percentage-wise, this year's postseason is a little behind 1980 for highest proportion of extra-inning games since divisional play began in 1969:

This follows a regular season featuring 232 extra-inning games, behind only the 2013 and 2011 seasons. What's behind the rise in extra-inning games?

Previous writing by Shane Tourtellotte at The Hardball Times and Andy at the Baseball-Reference blog shows that, as run frequency decreases, the likelihood of an extra-inning game increases. This is intuitive: In the extreme case, where no runs ever score, games stay tied forever and every game goes to extra innings.

But if we look at the graphs in those articles, we see that there is only a weak relationship at best between runs per game and the frequency of extra-inning games. And if we only look at playoff games, the relationship gets even worse: The 2013 regular season included a record 243 extra-inning games, but the 2013 postseason only featured one.

To get a better sense of this relationship, let's move into the realm of the theoretical, using Tom Tango's run expectancy generator. Put in a batting line, and this tool will give you (among other things) the average number of runs scored per inning*. As an illustration, we've plotted the expected runs per inning for two alternate-universe leagues below. In the first (graphed in red), every pitcher is 2000 Pedro Martinez. In the second (graphed in black), every batter is 2002 Barry Bonds.

* - This simulation isn't perfect because it assumes, among other things, that no outs are made on the basepaths, and that there are no stolen bases. So there will be some disagreement with the actual runs per inning numbers.

How do we get from here to the number of extra-inning games? For this, I pulled out one of my favorite tools: the Monte Carlo simulation. The basic strategy looks like this:

Using this method, we can find the theoretical probability that a game goes into extra innings, as well as the theoretical probability that a game already in extra innings extends at least one more frame. Here are the numbers for some illustrative real-world run environments...

...and our Bonds and Pedro alternate universes.

Now we can see that the lower the run environment, the better the likelihood of bonus baseball, and the more likely an extra-inning game continues. Making matters worse, there are a number of factors that could depress offense in October, from better pitchers to colder temperatures to more aggressive bullpen usage*. That would mean even fewer runs per inning, and a higher likelihood of extra innings. To get an idea of what that might look like, compare the 1968 runs per inning distribution (when the run environment was about half a run lower) with the 2014 distribution.

* - But, you know, I don't actually know if any of these statements are true, and there's probably too small a sample to draw any real conclusions. Yes, the pitchers are better on average, but so are the hitters. Yes, balls don't go as far in cold weather, but colder air is less humid, and that gives pitchers a harder time gripping the ball.

As the year of the pitcher turns into the decade of the pitcher, we are starting to see more and more extra inning games. Getting so much bonus baseball right at the outset of the postseason might be fluky, but the overall trend is not. With pitchers throwing harder every year, and relievers becoming increasingly specialized, future commissioner Rob Manfred might want to consider shrinking the strike zone a little to bring back some offense, and to make sure #weirdbaseball stays weird.

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All statistics courtesy of Baseball-Reference and the Baseball-Reference Play Index. Run expectancies courtesy of Tom Tango's Run Expectancy Generator.

Bryan Cole is a featured writer for Beyond the Box Score who regrets turning off the AL Wild Card game in the 7th. You can follow him on Twitter at @Doctor_Bryan.