Mean Reversion, Small Sample Size and the Mets

Mets1Nobody saw it coming before the season and even well into the season (see, e.g., here, here and here). But, as of tonight, the New York Mets will be playing in the World Series for the first time in 15 years. Sports is so entertaining in large part because the combination of luck, skill and variation involved creates an unpredictable stew of drama, intrigue, greatness and disappointment. Today, that stew smells a lot like the Mets and, so far, it smells pretty tasty.

While their pitching has been sublime this postseason and is the team’s overall key to success, Met second baseman Daniel Murphy’s bat is the big story.

Prior to this postseason, Murphy was a good-but-not-great player whose career highlight was being a reserve All-Star selection in 2014. But this postseason has been one for the ages and the record books to this point thanks to his having homered in six straight games and having hit .421. We’re talking about a player the owner of the American League champion Kansas City Royals recently called “the reincarnation of Babe Ruth” but who never previously hit five home runs in a month.

In just 39 plate appearances this postseason, Murphy has hit a total of seven home runs. A list of great players with more (usually many more) at bats and fewer postseason home runs than Murphy follows, and it’s a very impressive list.

  • Daniel Murphy: 39 plate appearances, 7 homers
  • Ken Griffey Jr: 79 plate appearances, 6 homers
  • Hank Aaron: 74 plate appearances, 6 homers
  • Paul Molitor: 132 plate appearances, 6 homers
  • Mike Piazza: 133 plate appearances, 6 homers
  • Kirby Puckett: 109 plate appearances, 5 homers
  • Prince Fielder: 185 plate appearances, 5 homers
  • Adrian Gonzalez: 96 plate appearances, 5 homers
  • Buster Posey: 210 plate appearances, 4 homers
  • Cal Ripken: 124 plate appearances, 1 homer
  • Joe Mauer: 39 plate appearances, 0 homers

Murphy’s recent success hasn’t come against batting practice fare either. He has victimized Cy Young candidates Zack Greinke, Clayton Kershaw (twice!) and Jake Arrieta, among others (including southpaw Jon Lester and his excellent cutter, marking the first time all season that a left-handed hitter has gone deep on that pitch). This hot streak was highly unlikely (advanced metrics project him to be a 4 percent above league average hitter with 11 home runs and a 1.7 WAR in 2016), but it has been great fun. As Grantland’s wonderful baseball writer Jonah Keri puts it, “through the wonders of small sample size and the kind of playoff weirdness we see every year, [Murphy is] making himself into an unlikely legend.” Mean regression may be coming, but as with Augustine’s wish re chastity, Murphy and Mets fans hope not yet.

The oddities in Murphy’s performance are downright astonishing too (also as pointed out by Keri). Mets manager Terry Collins bats him cleanup in Game 1 of the NLDS against the weight of the data and Murphy went yard off Kershaw. Murphy rates as an average baserunner for his career by advanced metrics yet pulled off one of the boldest and most influential baserunning moves in postseason history. Murphy ranks as one of the game’s worst fielders at second base yet he made a beautiful diving stop to seal a Mets win in Game 1 of the NLCS. It’s just the sort of craziness that makes baseball (and sports) wonderful to watch.

Issues of mean reversion, recency bias and sample size have ready applications to the investing world, obviously. According to Jason Zweig’s brilliant new book, The Devil’s Financial Dictionary, mean regression is “the most powerful force in financial physics.” It’s “[t]he tendency of above-average results to be followed by below-average results.” Because of effects of recency bias – our tendency to overvalue and overemphasize the recent past as compared to more distant events and then to extrapolate it into the future – we tend to deny the reality of mean regression. Accordingly, at the peak, “investors pay reckless prices to join the party” and, at the bottom, “investors conclude that the Apocalypse is upon us. The crowd thus gambles that extreme events will keep getting more extreme, rather than moving in the opposite direction.”

It is possible, of course, that near-term aberrations in performance reflect a major change in long-term norms that can be continued going forward. This postseason may vault Murphy to ongoing superstar status. But that’s not usually the case. As Dennis Green (then coach of the Arizona Cardinals) famously expressed it, nine years ago last week, “they are who we thought they were” most of the time and that doesn’t tend to change all that much.

Mean regression is the norm. Daniel Murphy is probably who we thought he was all along. Alternatively, per Robert Frost (much more lyrically), “Nothing gold can stay.” The market application to this discussion is that when prices are very high they will tend to decline and when they are very low they will tend to rise. Since our objective generally is to buy low and sell high, making good investment decisions in this regard should be pretty easy then, right? Sadly, the answer is a clear no.


Professionals are no less prone to its effects as anyone else. As reported by Bespoke, Bloomberg surveys market strategists on a weekly basis and asks for their recommended portfolio weightings of stocks, bonds and cash. The peak recommended stock weighting came just after the peak of the internet bubble in early 2001 while the lowest recommended weighting came just after the lows of the financial crisis. Obviously, following that advice would have been a big mistake and had an investor sold stocks at the peak stock weighting and bought at the rock-bottom weighting – doing the opposite of what the experts said – s/he would have done exceptionally well.

Emotionally, we get afraid when markets tank and euphoric (greedy) when markets are hot. No matter how quick we are to agree with Warren Buffet conceptually (“Be fearful when others are greedy, and greedy when others are fearful”), it’s really hard to do. The financial markets are the only places I know where people want to pay top dollar and resist buying anything on sale. Where else do people want to wait for prices to go up before they buy? That’s largely on account of recency bias and our emotions.

Recency bias frustratingly common. It’s why teenagers think the only songs worth listening to are current and why their parents and (especially) grandparents lament what’s going on with “kids these days.” If we were to get a fluke snowstorm in San Diego today, no doubt at least a few folks would race out to look at four-wheel drive SUVs. That’s all recency bias.

Finally, while we should be surprised at the specific craziness, we shouldn’t be surprised that there is craziness. Note (as Mike Pesca writes in Slate) that while it’s unlikely that you will win the lottery, it isn’t surprising when somebody wins. Murphy is that somebody right now and, since success often comes in streaks, his hot streak (despite multiple claims to the contrary, most famously here, “getting hot” is a real thing), is at least partially balanced by teammates going cold. For example, after a trade brought him to the Mets on July 31, Yoenis Cespedes had 42 RBI and, remarkably, hit a home run nearly every other game in his first 41 games. But in the playoffs Cespedes hasn’t hit nearly so well. Similarly, Lucas Duda, who led the Mets in home runs and RBI this year, was mired in a 3-for-24 slump up until Game 4 of the NLCS when he finally broke out. David Wright, the Mets’ best offensive player of all time, was just 1-for-16 in the divisional series against the Dodgers. The smaller the sample size, the more likely the craziness.

Murphy’s postseason performance and free agent status as soon as it’s over suggest that some team is going to pay Murphy as an emerging superstar even though his performance will likely revert to his mean, long-term performance over time. This mean reversion might start tonight, although Mets fans surely hope not, unless Cespedes, Duda and Wright get some mean reversion in the other direction. But baseball, like the markets, isn’t tame. Performance isn’t necessarily forthcoming just because we need or want it. Sometimes Mighty Casey strikes out and sometimes we see bear markets, even extended bear markets. And market performance is often streaky, just like player performance.


By some measures, it would take a best of 200 series or even more clearly to establish which team is really better in a World Series. The small sample size of seven games or even a postseason means that oddities, even wildly random oddities, are to be expected. And just like mean reversion got the Cubs versus the Mets — the Cubs had swept all seven regular season meetings with the Mets before getting bounced by them in the NLCS — mean reversion seems poised to strike Daniel Murphy. But the wonder is, in the same way that the market can stay irrational longer than you can stay solvent, we’ll have to watch the games to see. Indeed, as the great Yogi Berra (may have) pointed out, “There’s one word that describes baseball [and the markets]: you never know.”


6 thoughts on “Mean Reversion, Small Sample Size and the Mets

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  3. Brilliant analysis. Sadly, Murph only had base hits, not a Home Run. Promises to be a tought series between two excellent teams. Although a NY team fan, I think KC is the better all around team, especially in close games in late or extra innings.

    Nestor Olesnycky

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