How Unlikely Have Daniel Murphy’s Clutch 2015 Playoffs Been?

By Will Ezekowitz

If you’ve been following the MLB Playoffs—or maybe even if you haven’t—you will know that Daniel Murphy has been hitting some home runs lately. In fact, he has hit a home run in five games in a row, leading the Mets first past the Dodgers and now one win away from the World Series. Hitting a home run in five consecutive games is not altogether unheard of (Barry Bonds, who had two separate 6 home run streaks in 2001, is not impressed), but the fact that it’s being done now, in the Playoffs, by a second baseman not known for his power, makes it noteworthy. So I decided to look into exactly how unlikely Murphy’s feats have been, and whether or not we can conclude that his performance has been “clutch”.

Murphy played 130 games this season, 121 of which he completed, and hit 14 home runs. He never hit two home runs in the same game, which means he was hitting a home run about once in every nine games.

Put another way, the chance that Murphy would hit a home run in a given game in the 2015 season is 0.116. If we raise this number to the fifth power, we get the chances that Murphy would hit a home run in five consecutive games, which is what has done. The result of this is 0.0000207. In percentage terms, we could expect Murphy to hit accomplish this feat about 0.002% of the time.

This is an incredible unlikelihood, and it is has caused many to pose the idea that Murphy has been clutch. “Clutch” is a scary word in analytical circles, as it is usually over-emphasized and applied to high-leverage situations with sample sizes that are too small to properly analyze. But saying “clutchness” doesn’t exist is a bit of a cop out. Everyone who has watched or played sports has a feeling that it does; it’s just hard to quantify. Perhaps, though, we could conclude that Murphy’s play this past week has been “clutch” if we prove that it is a statistical outlier compared to his regular season play.

To do this, we can look at his power in the context of his at bats. In the regular season he hit 14 home runs in 499 at bats, and in the last five games he has hit 5 in 20 at bats. If we run a difference of proportions hypothesis test for those two sets, we find a P value that rounds to 0, and is significant at the .05 level, and indeed the .01 level. Even if we extend the population to include Murphy’s total playoff performance, 6 homers in 33 at bats, it is still significant.

This means that, put in context with his regular season performance, Murphy’s power this year has been a statistical outlier. The statistics conclude that 2015 Playoffs Daniel Murphy is a significantly different player (or at least home run hitter) than 2015 Regular Season Daniel Murphy.

We can quibble about whether or not this is “clutch”, but at the very least his newfound power stroke is convenient for the Mets, who will look for him to continue his unlikely power trip later tonight as they try to clinch the NLCS.

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  • Nice analysis. By it understates his achievement. Being the playoffs he is naturally facing much better pitchers than he did during the regular season. However, when you look at the specific pitchers he faced they are amongst the best pitchers in the playoffs as well.

    Quite amazing.

  • I used his career numbers: ~900 games and 62 homeruns. I got .0000001 or 1 out of 10,000,000 that he would hit a homerun in 6 consecutive games. Somebody argued that the postseason is different, so it should actually be higher, but it was more of an assertion than mathematically founded. I think .0000001 is a fair probability, however, I would like to see if someone could show that it’s more likely to occur in the postseason or what factors actually made it more or less likely.

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