Great Debates: Do Hot Streaks Exist?

Twitter is good for many different things. Perhaps the most important is for my friends to show me pictures of what they ate for lunch. A close second, however, is that Twitter also happens to be an incredible format for public discourse, and three nights ago we saw a very interesting debate unfold between two very smart men in the baseball industry: former A's starter (and perhaps my favorite Oakland Athletic of the past decade) Brandon McCarthy and respected analyst and scout Keith Law.

Often times in modern baseball debates, we hear about the split between the "stats nerds" and the traditionalists. This dichotomy suits the media members who take sides, dividing themselves into camps. Depending on which side of the aisle they choose, they rip advanced statistics for "attempting to reduce baseball to binary code" (a direct quote from Mitch Albom), or lambast traditional scouting for focusing on things like "grit" and "heart".

However, this specific disagreement is not one of grit vs. numbers. Brandon McCarthy is well known as a player who embraces the sabermetric movement with open arms. His refusal to buy into Law's argument clearly does not come from a place of steadfast refusal to see the light of statistics.

Keith Law is describing a phenomenon that is known commonly as the Hot-Hand Fallacy, and its more well-known converse the Gambler's Fallacy. If you flip a coin, it has a fifty percent chance of landing on heads, but over a short period it will rarely come up 50/50. You will often get a "hot streak" of multiple heads in a row. This is just due to random variation- the coin isn't "getting hot"- each successive flip still has a 50% chance of landing heads.

Law's argument is that this applies to baseball as well. A hitter (or a pitcher) has an absolute skill level- and over a short period, you can get random variation. A hitter like Miguel Cabrera might have a 6% chance of getting a home-run in any given at-bat (last year he hit 44 in 697 plate appearances, or 6.3%). In the game Keith Law and Brandon McCarthy were debating, Cabrera hit 3 home runs in 5 plate appearances. Assuming that Cabrera hits a home run 6% of the time in any given plate appearance, Cabrera would by random chance hit 3 home-runs in 5 PA's 0.2% of the time. This would mean that over a 162 game season, Miguel Cabrera has an approximately 32% chance of having a single three-homer game.

Keith Law argues that the notion of being "locked-in" has nothing to do with the hitter gaining confidence or getting hot; rather it's random fluctuations in the distribution, much like flipping a coin 5 times in a row and getting all heads. It doesn't happen often, but if you flip enough coins it will happen from time to time. Law even linked to an interesting article from a joint study at Cornell and Stanford to support his case, which can be found in its entirety HERE.

McCarthy's response?

McCarthy may seem to be dismissing Law out of hand, but he's actually making a very succinct, if blunt, counterargument. Law's hypothesis is predicated entirely on the assumption that a player's talent level is like a coin or a pair of dice: the chances of getting heads, tails, a 7, or a home run does not change no matter the circumstance. McCarthy, on the other hand, is arguing that a player's talent level and his mindset cannot be separated. Here's more McCarthy on the effects of being "in the zone":

A player who has gone 0 for his last 7 might be pressing and losing confidence, while a player like Miguel Cabrera who has already hit two homers on the evening might just have the ability to play loose and fluid. How many commenters right here on AN have noted Josh Reddick's struggles when he comes up with men on base in a crucial situation? Of course, according to McCarthy, these things are nearly entirely unquantifiable, but that does not mean they do not exist.

Personally, I'm still not quite sure where I stand on this issue. I tend to be a volume consumer of advanced statistics, and for statistics to have predictive value they have to assume a true talent level. But everyone agrees that talent level fluctuates- players improve as they reach their prime, and decline with injuries and age. So why is it so crazy to assume that things in the short term can affect a player's current talent level?

What do you guys think?

EDIT: Tom Tango, the principal author of The Book and one of the foremost thinkers in sabermetrics, linked to this article and proposed a simple method for determining whether "locked-in" exists. I highly advise checking it out HERE.

UPDATE: MGL ran the numbers for Tango's proposed study, and the results can be found HERE.

EDIT AGAIN:

@tangotiger a hit isn't the only positive outcome. Again, when you devalue the mental side of the game, you miss the big picture.

— Brandon McCarthy (@BMcCarthy32) May 22, 2013

@tangotiger since you know I exist on twitter- next time you "teach me science" you can tag me too

— Brandon McCarthy (@BMcCarthy32) May 22, 2013