Baseball ProGUESTus: Investigating the “Best Shape” Phenomenon

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Rob Pettapiece, a recent Mathematics graduate from the University of Waterloo, wrote for Batter's Box for two years, currently edits the CIS Blog, and provides statistical analysis and consulting to coaches and journalists in several sports.

"One thing [Jerry] Coleman felt sure of was that he was in the best shape of his life."—David Halberstam in Summer of '49

If you're reading this, chances are you not only know all about the "best shape of my life" stories that resurface every spring, you've also mocked those stories (and maybe even joked about the stories written about those stories). This isn't new; we've snarked about it for years.

Since I was never any good at writing jokes, I originally figured that my contribution to this fine baseball tradition could be to compile a long list of all the BSOML players, just for the absurdity of it all. I undertook that effort four years ago with no grander goal than to have a few laughs with some friends. But one thing led to another, lists turned into spreadsheets, and before I could lift one off-season weight, I had a multi-year study on how BSOMLers perform while being in—you guessed it—the best shape of their lives. Now, this meant that I was, at least on some level, studying the effects of chicken-finger consumption on run production, but I soldiered on nonetheless, curious to see how it would turn out.

I'm not the first one to have had this idea, so to make this exercise worth your while, I'll go back a few years and try to take a more extensive look at whether it actually means anything (from a performance perspective) to be in great shape entering Spring Training. You may already have an idea where this is headed, but this is baseball in March…since when does the outcome matter? Grab a beer, take a seat in the fourth row, and enjoy.

Shaping the methodology

First we have to establish what "best shape" means. You have your obvious cases (Andres Torres makes it so easy, it's not even sporting) and similar, "I-feel-great-this-year" stories, but what about players coming back from injury?

"My wrist has healed" doesn't necessarily equate to "my fitness level has improved." But all I want to measure is whether a given player outdoes his established level of performance. Ill health of all kinds is distributed along a continuum; we tend to separate physical complaints into distinct buckets (injured, out of shape, etc.), but a player laying claim to BSOML status is, I would argue, talking about how healthy he feels. Injuries play a role in his physical self-evaluation; when a player says, "I feel great,” perhaps he’s really thinking, “I feel great because my wrist has healed."

Consequently, on the one hand I cast a wide net for best-shape players, including anyone who clearly stated that he was in better health than usual. One key requirement is that the player must self-select: he (or someone speaking directly on his behalf) has to declare BSOML status. I didn't count cases of, say, a manager talking up (and protecting) his players, so Miguel Cabrera is out, but Roger Bernadina is in.

The other key here is that the player in question be "established.” My lead-in quote about Jerry Coleman aside, I'd argue that rookies are not generally the players we think of as BSOML cases. Ideally, I want to look only at veterans, or at least players with a few lines on their baseball cards, because the history they have makes projecting their performance a bit easier.

A natural example

Let's take a quick look at Jeff Francoeur. On Feb. 3, 2007, he said, "Mentally and physically, I'm in the best shape of my life." And, hey, a player in the best shape of his life should outperform his projection, right? In '07, PECOTA projected Francoeur to have a .275 TAv in 523 plate appearances. He finished with a .274 TAv in 696 PA.

Okay, so that doesn't seem like much of a best-shape effect. (He had more PA, but projecting playing time can be tricky.) However, anything can happen with a sample size of one. Let’s get to the larger-scale results.

What BSOML really means

When I originally did this study on my own, I included every BSOML hitter who had a Marcel reliability score of .70 or higher entering the 2007, 2008, 2009, or 2010 season. Even though this piece uses contemporary PECOTAs instead of Marcels, I've kept the same list of players. (Note that you could do the same for pitchers, but I didn't have enough of them in the BSOML group to make the exercise worthwhile.)

There were 15 qualifying best-shape hitters in 2007, 11 in 2008, 16 in 2009, and 13 in 2010, for a total of 55, roughly half of whom were Brian McCann. Those 55 players produced these results:

(“Runs per season” is simply EqR per 4,200 outs.)

At first glance, four points of TAv doesn't seem like such a big deal, but once converted into runs and expressed on the same scale as a team's season totals, that difference translates to 24 runs per season. So, if we believe these results, a team full of hitters in the best shape of their lives would increase their offensive output by about 3%. A three-percent increase is nothing to sneeze at. Still, there's always going to be some uncertainty in players' projections, so how do we know that what we're seeing is a real effect, best-shape or otherwise?

(For the sake of completeness, I’ll observe that the TAv difference of .004 remains even if you weight each player by the minimum of his projected and actual PA or outs—that is, giving each player the same weight in each group, instead of according a greater weight in the “actual” group to those who played more than PECOTA anticipated.)

Let's try to reduce the unpredictability. We'll remove all the BSOMLers whose PECOTA projections yielded Beta values above 1.00; in other words, we’ll keep only the forecasts that were determined to be less risky than that of the average major leaguer. What do the results look like for the 24 remaining players?

Now we see a mere six-run difference. In other words, these hitters, who claimed to be in the best shape of their lives and had forecasts which were generally less volatile than average, wound up outperforming their projected run production by a majestic 0.7%. Does that mean that being in the best shape of one’s life is meaningless, at least from a performance projection standpoint? Probably. But not so fast…

The non-BSOML invitees

In one sense, we have already compared the best-shapers to a control group: their own projections. But what if we construct a parallel set of players who did not claim to best in the best shape of their lives and treat their over- or under-performance as another control?

For each player, we'll go through and choose someone else from the same year who was the same age (or close to it), played the same position, and had a Beta below 1.00, but did not claim to be in the best shape of his life. This group of players turns out not to be as good as the best-shapers, but that shouldn't matter too much: we are only interested in how each group performed as compared to its collective projection, not in terms of true talent level. Let's add these 24 non-BSOMLers to the above table and see what we get:

It appears that BSOMLers may, in fact, outperform their projections more than non-BSOMLers outperform theirs. More accurately, the best-shapers held steady (as indicated by the +6 runs we noted earlier) and the non-best-shapers failed to meet expectations (-27). Of course, the non-BSOMLers who had poor seasons and received less playing time as a result don't affect the actual numbers as much as they would have had they kept putting up poor numbers, so the true drop-off by the control group should actually be larger.

For whatever reason, playing time was also much lower relative to the projection for the control than for the BSOMLers. (This may be a form of newspaper bias: BSOML stories might be devoted to a disproportionate degree to players expected to stick all year with the local nine, as opposed to players inevitably headed for the minors.) Given the results in the last table, perhaps the "best-shape effect" is instead a "seal of approval" effect, meaning that a player is not necessarily going to have the best year of his career when declaring BSOML, but that he might stay healthy and effective enough to play close to expectations for most of the season.

Then again, there are several other factors that could explain what we're seeing. We're working with just two dozen players in each group, and a different control group could yield different results. What’s more, we made a binary distinction at the beginning—best-shape or not—and the reality probably isn’t that simple. When 2011's results come in, they may provide quite a bit of evidence either way: there are at least 20 players who claimed BSOML this year, more than any other single year in our study.

Closing things out

What we might be able to conclude is that, all else being equal, a player who went into "beast mode" in the offseason (or whose name is an anagram of Dani Rogerberna) could be more likely to put up numbers in line with his recent history, and that one who previously had issues with staying fit or healthy and didn’t address them over the offseason could be at greater risk of losing a step in his game. That's only intuitive, but again, it's not necessarily going to be the case—which probably means that the most likely effect of a player declaring "I'm in the best shape of my life" will be nothing but a few more cookie-cutter news stories and some additional jokes from Craig Calcaterra.

Note: I have provided a list of all hitters used in this article here. I also included the 20 best-shape players for this year who were mentioned above, as well as six others for 2011 whose Marcel reliability is below 0.70, but who still declared BSOML.