Thinking Probabilistically About Sonny Gray, Stephen Piscotty, Kris Bryant, and Kyle Hendricks

In the last 10 days, I’ve run a pair of Twitter polls. In the first, which I ran on May 22, I asked followers who they would rather have, Kris Bryant or Stephen Piscotty.

My follower sample will totally skew the results, but: Who would you rather have?

— Matthew Trueblood (@MATrueblood) May 22, 2016

The poll received 462 votes, and of those, 89 percent (or something that rounds to that number, anyway) were cast in favor of Bryant. As I noted in the tweet, I expected Bryant to win, and I even expected it to be lopsided. I think, though, that the degree of lopsidedness probably points toward a problem with the way users of Baseball Twitter influence each other. We’ll get into the specific problem in just a few minutes.

For now, let’s switch gears. I ran another poll, on Tuesday morning, asking followers to state another preference.

All things considered, who would you rather have in your rotation?

— Matthew Trueblood (@MATrueblood) May 31, 2016

I was careful to couch this one a little differently, not demanding that respondents remove their fan orientation from the equation, but encouraging it by making them the hypothetical builders of a rotation. This poll was less popular, and closer, but Gray won fairly easily. The gap isn’t as extreme, but I find it just as eyebrow-raising.

Hendricks was an eighth-round pick by the Texas Rangers in 2011, and threw over 450 innings in the minor leagues before reaching the Majors with the Cubs. He was only half of the return for Ryan Dempster, a mid-rotation starter who had blocked the first trade in which the Cubs front office had tried to include him, and who would be a free agent two months after Texas acquired him. He went to Dartmouth, and between that fact, his lack of velocity, and his unremarkable physicality, he’s been viewed as an overachiever, if not a downright impostor, for much of his first two years in the big leagues. Bryant, of course, is Hendricks’s polar opposite. He went some 250 picks earlier in the 2013 Draft than Hendricks two years before, made $6.7 million as a signing bonus before playing a single pro game. He has loud tools, stands six-foot-five, weighs 230 pounds of pure fluidity, and is handsome enough to be a model—is one, in fact.

Piscotty has a lot of Hendricks in him. He was a first-round pick, but a much later one than Bryant, and he got less than a quarter of the money Bryant got. He went to Stanford, and between that fact, his lack of power early in his pro career, and a lack of standout speed or defensive ability, he’s been cast as a ‘tweener, not the middle-of-the-order threat teams want from a corner outfield spot, not a good enough fielder to man center, unlikely to sustain his early offensive success. Gray, meanwhile, is a former first-round pick with the velocity and the breaking ball scouts look for. He went to a major college baseball power, and ascended to the Majors within two years of signing. He’s short, but explosive, and has been an occasionally dominant workhorse in his two-plus full seasons.

So let’s talk about Bryant and Piscotty. Here are the essential data, the tale of the tape on this matchup so far in their respective careers.

• Bryant: 200 G, 873 PA, .320 TAv, -2.8 FRAA, 4.1 BRR, 1.4 POS_ADJ, 8.3 WARP
• Piscotty: 113 G, 476 PA, .324 TAv, -10.5 FRAA, -2.4 BRR, -4.1 POS_ADJ, 2.7 WARP

Bryant has been better; there’s no disputing that. Some trend lines favor Piscotty, though. For instance, he’s been the better hitter, which is by far the aspect of a player’s value on which we have the best handle at this point in the unfurling of a career. Bryant’s positional advantage (he’s played the majority of the time at third base so far in the big leagues, while Piscotty has been a corner outfielder almost exclusively) might be eroding: Javier Baez and Tommy La Stella have taken an increasing number of starts and pushed Bryant mostly into the outfield this year. Piscotty also won’t be eligible for arbitration until after 2018; Bryant will be eligible a year earlier as a Super Two player.

I believe Bryant was the right answer to this question, but more importantly, I believe this was a bad question. I should not have asked people to state a simple, binary preference. I should have asked for a probabilistic answer, because whether we admit it or not, any attempt to forecast the future is an exercise in probability. Given the information I have right now, I’m inclined toward Bryant’s future over Piscotty’s, but would peg the probability of Bryant being better no higher than about 65 percent (for example). I’d even err a little lower, because Piscotty has only begun to tap into his power over the last year and a half, and I wouldn’t be surprised if he showcases more of that power over the next two years or so—and that might put his offensive edge over Bryant on ice. So give me 62 percent Bryant shares, and 38 percent Piscotty.

Obviously, we can’t know for sure how people would have answered if they had been allowed to consider the question that way. We can guess, though. We know that 11 percent of respondents chose Piscotty. We also know (really, we just lack a reason to suspect otherwise, but let’s say we know) that whatever the average probabilistic expression of preference for Bryant would have been, answers would have clustered around it in a pretty normal distribution. Given those data, and the fact that those who answered Piscotty were implicitly stating less than 50-percent confidence that Bryant would be better than Piscotty, we can create a few hypothetical models to tell us what average probability score this poll’s results imply. It’s intimidating math, perhaps, but the Internet makes it easy.

For instance:

• If my 62-percent confidence in Bryant’s superiority were representative of the widest-held view, the implied standard deviation of answers on our hypothetical probability survey would have been roughly 9.8. In other words, over two-thirds of respondents would have answered something between 52.2 percent and 71.8 percent if asked the likelihood that Bryant will be more valuable than Piscotty.
• If the real average of answers would have been 70 percent confidence in Bryant, the standard deviation would be about 16.3, so over two-thirds would have pegged their confidence between 53.7 percent and 86.3 percent.
• If the average of answers would actually have been 75 percent, the implication would be that nearly a quarter of respondents were 90 percent or more certain of Bryant being better.

I suspect the second scenario there is the closest to reality. I doubt that many fans would say that Bryant is 90-percent likely to be better than Piscotty. Yet, I don’t think the first scenario, which would leave fewer than 20 percent of respondents stating a 70-percent confidence level in Bryant, is realistic. I wish it were. I think the fact that a majority of fans discount the marginal cost concerns, Piscotty’s offensive skills, and Bryant’s vulnerability to strikeouts so much that they remain quite certain of Bryant as the better player reflects insufficient appreciation for the unpredictability of baseball.

The lesson here: think probabilistically. Weigh choices carefully, even when it seems to be a simple choice between two or three options. When looking to the future, make a special effort to ratchet down your initial estimates of confidence. Most importantly, never, ever give just two choices on a Twitter poll.

If I’d learned quickly from the difficulty of disentangling the Bryant-Piscotty poll, I might have structured the Hendricks-Gray poll differently. Instead, we have to do a similar exercise with these two. I think this one is a little more straightforward. Using the results I got and the standard deviation I guessed to be closest to the hypothetical reality in the Bryant-Piscotty poll (16.3), I project that the average preference for Gray over Hendricks would have only been 55 percent to 45 percent. That’s not bad; it’s fair to have a preference that strong for one or another pitcher.

In this case, my objection is to the pitcher the crowd chose. Here’s the critical data on Hendricks and Gray:

• Hendricks: 54 starts, 315 2/3 innings, 20.3 K%, 5.5 BB%, 54 GB%, 89 cFIP, 3.86 DRA, 4.3 WARP
• Gray: 85 games (83 starts), 539 innings, 20.8 K%, 8.0 BB%, 55 GB%, 91 cFIP, 3.92 DRA, 6.5 WARP

Hendricks is a month younger than Gray, and a year further from free agency. He’s never been hurt as a professional pitcher, at least not badly enough to miss any time or draw a news report. Gray is on the DL right now, with a right trapezius issue. Hendricks has made 88 pitches per start, and just nine of his starts have seen him reach or exceed 100 pitches. He’s never thrown more than 108 in one game. Hendricks has also started on long rest (at least five days) 31 times in 54 starts. Gray, by contrast, has made 98 pitches per start, and 40 of his 83 outings have included at least 100 pitches. He’s thrown at least 108 pitches 12 times in his career. Fewer than half of his starts have been on long rest.

While Gray might be more interesting and kinder to the imaginations of scouts, Hendricks is the better pitcher of these two. Not only is he better—he has much better command, has a more reliable bat-missing pitch, fields his position better—but he’s safer, cheaper, and under control for one more season. That Gray is capable of facing more batters per start (to whatever extent he can do so without increasing his injury risk or becoming vulnerable to the times-through-the-order penalty, and that extent is not clear) is not, for my money, enough of a difference to offset Hendricks’s advantage. I think those who prefer Gray are committing the crime of evaluating the two, instead of valuating them. They’re both lavishing projected improvement on Gray, which flies in the face of what we know about aging curves and in the face of what we know about his career right now, and isolating what they see on the field in choosing between these two, instead of thinking about how they fit into an organization’s plans.

In the old days, before players had the ability to reach free agency, before revenue sharing and the draft and all kinds of other mechanisms that make allocation of resources a vital part of how modern teams make decisions, that might have been okay. In 2016, it’s okay not to simply cling to marginal WAR analyses, but it’s not okay to ignore considerations like service time, injury risk, and league-wide trends in gameplay. Taking all of those things into account, Hendricks is (by whatever small margin, I might buy 53 percent Hendricks shares and 47 percent Gray shares) the more valuable pitcher. The crowd likes Sonny Gray’s upside too much, and Hendricks’s quiet success too little. I promise to do better Twitter polls from now on. You can respond in kind, by widening the scope of your thought process about some players, and by never feeling too sure of yourself where baseball is concerned.

Lead photo courtesy Kim Klement—USA Today Sports.