Gary Sanchez and the Persistent Belief in Small Samples

Perhaps no player in Florida is the object of greater expectations this spring than Gary Sanchez.

Consider: in the fantasy baseball world, only Buster Posey is being drafted earlier at catcher. Generally conservative projection systems forecast that Sanchez will be a star this season. ZiPS pegs Sanchez for 27 homers a 112 wRC+ and a 3.4 WAR season. PECOTA’s 70th percentile outlook has Sanchez recording 33 homers, a .504 slugging mark, and 4.8 wins. And the Fans’ average crowdsourced projection for Sanchez is a .274/.344/.488 slash line and 5.4 WAR season. The Fans believe, in other words, that Sanchez and Bryce Harper are going to produce similar value this season.

Last week, ESPN ran a poll asking respondents to guess how many home runs Sanchez will hit in 2017. Fewer than 10 home runs? That option received 1% of votes. How about 10 to 20 homers — i.e. the range within which he’s resided over each of his first five professional seasons in the minors? That seems like a reasonable wager, right? Only 4% agreed.

The most popular range was 21-30 homers, receiving 44% of votes. Forty-one percent predicted he will slug between 31-40 homers, and 10% think he will hit more than 40.

There’s much to like about Sanchez. This is a player with pedigree, who was regraded as the top catcher in the 2009 international class, and perhaps the second-best bat in that class after Miguel Sano.

The raw power, the arm strength, those are loud tools. They are very real.

The receiving appears to be about league average, but that’s perhaps the biggest question mark based upon his 2016 work. For RotoGraphs, Andrew Perpetua employed Statcast data to get a sense of what to expect from Sanchez in 2017.

Wrote Perpetua:

“These are just a few guys who seem to be most closely related to Sanchez in terms of these batted ball stats. Cespedes and Cruz appear to be the closest matches, with similar vertical and horizontal angles along with similar exit velocities to Gary Sanchez.”

Anyone for a Cespedes- or Cruz-type bat at catcher? You can lower your hands.

Everyone, it seems, loves Sanchez in 2017. But let’s pause and take a deep breath. Have we learned nothing?

Despite years of warnings about the dangers of small sample sizes, it’s possible we’re still, and always will be as humans, susceptible to making judgment errors from too little data. Michael Lewis’ most recent book, The Undoing Project, has some potentially important implications for the industry. It details the friendship and work of Israeli psychologists Amos Tversky and Daniel Kahneman.

The first paper Tversky and Kahneman wrote together was titled “Belief in the Law of Small Numbers”. The paper refuted the idea that people are, by nature, Bayesians, or that we have some innate understanding of probability and statistical principles and act in such a manner.

From the book:

“The power of the belief could be seen in the way people thought of totally random patterns — like, say, those created by a flipped coin… People seemed to believe that if a flipped coin landed on heads a few times in a row it was more likely, on the next flip, to land on tails — as if the coin itself could even things out. ‘Even the fairest coin, however, given the limitations of its memory and moral sense, cannot be as fair as the gambler expects it to be,’ they wrote.

“They went on to show that trained scientists — experimental psychologists — were prone to the same mental error… Even people trained in statistics and probability theory failed to intuit how much more variable a small sample could be than the general population… This failure of human intuition had all sorts of implications for how people moved through the world, and render judgments and made decisions.”

Remember, Sanchez hit .225 in September after a torrid August, a month he might never repeat in any 31-day period of his career. Sanchez’s 2016 Triple-A slash line was good — .282/.339/.468 (and 10 homers in 313 plate appearances) — but it also mirrored the slash line of his seven-year minor league career: .275/.339/.460.

He’s not going to sustain a 40% home-run rate on fly balls, of course, and I don’t think anyone is expecting him to.

While projection systems have greatly aided in our understanding of performance, while they are designed to be unbiased, they can still struggle with small samples and the translation of minor-league statistics to major-league equivalencies. There’s no greater leap for professional players than from Triple-A to the majors.

When I think about reasons to pump the brakes, I think about Brett Lawrie’s 43-game close to the 2011 season, when he hit nine homers and slashed .293/.373/.580. Many were predicting stardom based in part upon that sample of performance. While Lawrie’s had a major-league career, he’s never developed into the dynamic player that many, including evaluators, thought he would become.

Even former Baseball Prospectus prospect analyst Kevin Goldstein, when suggesting that expectations be tempered regarding Lawrie, still predicted Lawrie would become “a star.” In ESPN’s franchise player draft in 2012, Lawrie was selected 15th overall, two spots behind Mike Trout and only three spots behind Harper. (Matt Kemp and Troy Tulowitzki went 1-2, reminding us how quickly fortunes can change in what can be a cruel game.) Jim Bowden predicted Lawrie he would win a batting title early in his career, and ZiPS projected a .275, 27-HR, 79-RBI, 24-steal season in 2012.

Lawrie and Sanchez are different people and players and they will follow different career arcs, mostly likely. But Lawrie is an example of a recent player to really enhance his perceived value through a small sample to close a season.

Sanchez seems to stand a good chance to become a quality major-league player, perhaps even a star. But expecting stardom right away might be too much. And perhaps the lesson from the “Belief in the Law of Small Numbers” is, as humans, we cannot help ourselves from getting caught up in small samples. As you prepare and conduct your fantasy drafts, this is just a reminder Yasmani Grandal will be available about 100 picks later according to these consensus rankings.

Sanchez might be great. But will he be in 2017? One scout with whom I spoke very much believes in Sanchez’s power and throwing arm and says his work behind the plate in receiving and handling a staff has come a long way, but suspects expectations have grown too large for 2017. The league will make adjustments to Sanchez. He will have to counterpunch.

Yankees general manager Brian Cashman is one of the few curbing expectations this spring.

“I don’t know if you can repeat that type of year,” said Cashman recently. “That kind of is impossible… I’ve been around the game long enough to know that you can never count on anything.”

Including a small sample of performance to be extrapolated out over the course of a full season or career.

A Cleveland native, FanGraphs writer Travis Sawchik is the author of the New York Times bestselling book, Big Data Baseball. He also contributes to The Athletic Cleveland, and has written for the Pittsburgh Tribune-Review, among other outlets. Follow him on Twitter @Travis_Sawchik.

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5 years ago

This is really important for people to remember. Thank you, Travis!