An Answer for the Sake of an Answer

Humans, as unique as we like like to portray ourselves, are remarkably easy to predict when we wonder. We notice something peculiar, intently observe the phenomenon, and try to come up with an explanation. Rarely, through the course of human history, has the conclusion been “we need to wait for more information.” This is why we homosapiens used to believe that the Earth was flat and that our planet was the center of the universe. In baseball, we act the same way, by and large. We notice peculiar early-season performances, assess them, and come up with a conclusion to satisfy our curiosity, often poorly-researched and made with impatience.

For example, a hitter will go 7-for-38 in his first 14 games. Fans and talking heads, who have watched most or all of those games, will offer something to the tune of “he’s just not seeing the ball well” or “his timing is off”, among any number of cliches. Hilariously, the better response to that 7-for-38 would have been a simple shrug of the shoulders. That is because 38 plate appearances tell us almost nothing about a hitter. As Brotherly Glove author Eric Seidman pointed out at FanGraphs several years ago, we need at least 150 PA for any of the truly meaningful stats to start to tell us anything useful about a player.

Why is that? One human comes from a group of other humans who generally share similar characteristics. This is as true for baseball players as it is for swimmers or biology students in a classroom. Given small samples, the mean of the population (all baseball players, all swimmers, all biology students, etc.) tells you more about any one player’s likely future performance than his current performance data. When the sample size grows large enough, we can make stronger inferences about a person’s skill level. In other words, we become more confident in what we know about the person in question.

For example, the world record for the 50 meter freestyle in swimming is 20.9 seconds held by Brazil’s César Cielo. I don’t know anything about swimming, but let’s say that the average time is 25 seconds. At the start of a new season, a team’s third-best swimmer (let’s call him Kwyjibo) puts up times of 28, 37, and 33 seconds. The fans start to panic. “Kwyjibo has lost it”, they say. “He’s putting too much pressure on himself!” Kwyjibo, however, is very much like his swimming peers, so he is more likely to put up times around 25 seconds than his current average of 33 seconds in three trials. You could completely ignore his current-season information, using only the population mean, and you will accurately predict Kwyjibo’s future performance more accurately than those who use his current-season information a vast majority of the time, until you have an appropriate number of trials.

If you weren’t able to decipher it above, the cited 7-for-38 player is John Mayberry, Jr. After a breakout 2011 season in which he posted a .369 weighted on-base average (wOBA; the league average was .316) in a shade under 300 PA, he sits with a paltry .173 mark as of this writing. His slow start has a lot of Phillies fans concerned as the offense collectively has been impotent and former top prospect Domonic Brown continues to wither away with Triple-A Lehigh Valley. Most of the explanations for Mayberry’s start — e.g. “he’s just not seeing the ball well” — tell us less about his likely future performance than the National League averages. Hitting coach Greg Gross says that Mayberry starts to put pressure on himself and changes his batting stance slightly. Via Matt Gelb:

Hitting coach Greg Gross has preached consistency and is happy that Mayberry has not attempted any drastic experiments to correct his problems.

But Gross sees a player who does everything correctly behind the scenes only to press once he’s at the plate. The sign is when Mayberry crouches more than usual. It’s his way of “grinding through it,” Gross said.

April 5, 2012 @ Pittsburgh

April 20, 2012 @ San Diego

Now, I don’t know about you, but in these .gifs, I don’t see much of a difference. The first is from the first game of the season in which Mayberry had two hits and, ostensibly, was not pressing. The second is from last night’s game in San Diego when, ostensibly, Mayberry was pressing.

Below are stills. The point of comparison is directly after Mayberry’s front foot comes back down. (Please make a slight mental adjustment for the difference in camera angles.)

The reason why I am stressing this point is because human beings are programmed to satisfy their curiosity with an answer. Gross will repeat his incorrect conclusion about Mayberry because that sounds better than “small sample size”, the general public will accept it and repeat it verbatim because that satiates them better than “small sample size”, when all along, the better response was a shoulder-shrug and “small sample size.” You can replace “small sample size” with any number of non-sequiturs as well, such as Base Ba’al, luck dragons, or chaos.

It very well could be true that Mayberry will be worse in 2012 than he was last year. In fact, that will likely be the case when all is said and done —  PECOTA did project a .740 OPS for him this year, a 110-point decline from last year. However, his first 40 trips to the plate have almost no impact on that conclusion whatsoever. When he starts to approach 150 plate appearances, then we can start to worry if he still hasn’t drawn a walk and one out of every four fly balls end up in the gloves of infielders. Until then, accept the randomness and regress his remaining plate appearances towards the MLB average.

In closing, the following chart shows the ten qualified players who had the lowest OPS in baseball at the end of April last year, along with their OPS from the next game through the end of the season. Each player improved, and improved substantially. (click to enlarge)

I would bet that the claims you’re hearing about Mayberry — that he’s pressing, not seeing the ball well, etc. — were the same things being said of the players depicted in the chart, especially those who are more well-known and thus more likely to cause worry. The lesson is to be indifferent to the early part of the season.

Leave a Reply



  1. LTG

    April 21, 2012 08:34 AM

    Was it not on this very site that someone pointed out that Mayberry’s O-Swing% is quite elevated (>40%) and that this stat stabilizes rather quickly? Is this not reason to worry about Mayberry going forward, especially since his plate discipline was particularly notable last season? If his elevated swing rates both outside the strike and within it persist, what kind of effect can we expect that to have on his performance for the rest of the season?

  2. Moose

    April 21, 2012 11:33 AM

    I was thinking of the exact same thing LTG

  3. LTG

    April 21, 2012 12:13 PM

    Yeah, but I sound like a bit of a snot saying it. So, I’ll rephrase in a less snotty way.

    While BB is right that many of the significant offensive categories require larger sample sizes than Mayberry has this year for their results to stabilize, one category where this is not the case is swing rates. (I could be wrong about this, in which case everything that follows should be disregarded.) If Mayberry’s increased tendency to swing at balls has stabilized, then we can expect it to persist unless an underlying factor in the increase is changed. If the swinging-at-balls tendency persists, we can expect Mayberry’s production to remain below last year’s, probably below the projections (since they either explicitly or implicitly relied on his previous swing rates), and maybe not much better than his current. It is hard to know just what to expect because it is hard to judge how swing rates influence production for any given player. Of course, he cannot remain as bad as he is now because he just won’t sustain a 25% infield fly rate, which ululates SSS. Nevertheless, it seems to me that there is good reason for pessimism about Mayberry’s production this year, even if you were already expecting him to regress. And, it seems to me, this is a disagreement with BB’s post.

    There. Not snotty.

  4. HBP

    April 21, 2012 01:08 PM

    You really know how to take the fun out of sports Bill. I kid….kind of.

    Part of the fun of sports includes the meaningless arguments about things we could in no way speak on with any authority.

    Despite that, I still appreciate your articles that often bring down my anxiety level due to overreacting.

  5. MD

    April 21, 2012 03:23 PM

    This was a great article. Seldom do you see this type of analysis on a blog. Great work. Human beings generally suffer from the phenomenon of “recency”. In other words, what has recently happened will continue to happen. Therefore, Mayberry’s struggles will continue without end.

    The good news is that is simply not true statistically. His struggles now actually make it more likely that he will do very well in the future if we believe he has the basic, necessary skills to be a success. I believe he does. The same thing could be said about Galvis. There were actually people suggesting that he be replaced after a total of 3 games in which he struggled to get on base.

    Now, he has reverted to the “mean” and is a hero to the same people. Actually, if you look at his minor league stats, comparable players who have come to the bigs at his age and with similar minor league stats, it isn’t really that hard to predict that he will hit between 240 and 260 with 5 to 7 HR’s over the course of a full year. The real wildcard has been his incredible defense. Since we had such a small sample of work at second, it was an unknown. He has outperformed if we expected the norm from him which would have been to struggle at a new position.

    The good news for the Phils as a whole is that while the team clearly doesn’t have the power it had in the past, the lineup has the capability to generate runs. I expect other guys to revert to their long term means and for that to improve. I also expect Hamels to finally get run support (let’s hope we can sign him!) and have a big year.

    This will be another very good year. Probably not 102 victories but I see no reason why we can’t expect 92 to 95 quite easily.

  6. LTG

    April 21, 2012 04:02 PM

    BB, you have a new admirer.

  7. MD

    April 21, 2012 05:02 PM

    I also think we will see Poly revert more to his long term mean but with some subtraction for age. Of course, injury with him is a big concern and that could change everything.

    Assuming mostly good health, there is no reason to believe that he won’t hit 270 to 280.

  8. Ben

    April 22, 2012 04:10 AM

    His front side flies open, trying to pull the ball, in gif #2. He stays nicely closed off in gif #1, going with the pitch instead of forcing a pull stroke.

    He also has a much more balanced finish in gif #1.

  9. LTG

    April 22, 2012 10:10 AM

    Ben seems to be right. JMJ’s left shoulder opens up in 2 but not 1. However, the pitches are in different parts of the strike zone. So, this could be the difference between trying to go the other way with a pitch away and trying to pull a pitch inside.

  10. Stephen

    April 23, 2012 08:55 AM

    A small sample (2) of swings, are they not, Ben?

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