On the Value of Sprint Speed

Baseball players, you’ll be surprised to hear, are evaluated in part based on how fast they are. You know: speed is one of the five tools! To that end, what follows briefly examines player quickness and how it does or doesn’t relate to other appealing player qualities. First, the relationships between several statistics are visualized in scatterplots. Second, using the simplest model possible, outfield defense is estimated. Using that rudimentary model, I construct leaderboards for players whose performances were the most drastic exceptions to that model’s estimates.

Starting with the charts: below is a scatterplot juxtaposing the sprint speed and wOBA of all qualifying players from 2015-2019 where sprint speed data from Baseball Savant was recorded. In all, this chart features 708 player-seasons.

wOBA, created by Tom Tango, does a good job capturing overall offensive performance. For that reason I have included it here. However, sprint speed, despite being sought after, has essentially no relationship to offensive production based on this chart. Of course, that is a considerable oversimplification; a plethora of factors are omitted in a chart such as this, which conceivably influence the relationship between offensive output and speed. The chart above does not control for a player’s age, nor any number of other factors (SwStr%, launch angle, etc.) which might further capture their offensive approach. As one example, faster players very generally tend to hit the ball on the ground more often according to Baseball Savant (there is a weak positive correlation between GB% and Sprint Speed); GB%, in turn, is counterproductive to offensive production.

Meanwhile, another Statcast-created metric, average exit velocity, has a considerably stronger relationship with offensive production as given by wOBA. Again though, omitted variables loom large.

So how does sprint speed contribute to a player’s profile if not with the bat? Well, in the case of outfielders, sprint speed certainly appears to positively influence defensive value. To depict this relationship I have drawn upon yet another Statcast metric, Outs Above Average (OAA). Until recently, OAA was a metric exclusive to outfielders; given that, the chart below features 230 data points representing individual outfielders’ seasons.

So faster players tend to have higher Outs Above Average in the outfield. This isn’t much of a stretch, given OAA is a “range-based metric” and foot speed is, well, a range-based human trait. However, despite a present and positive relationship between sprint speed and OAA, sprint speed doesn’t explain much of a player’s OAA. To illustrate this point, I ran a simple linear regression, to see how well sprint speed predicts Outs Above Average. Results from R have been copied below.

While the single variable model indicates that sprint speed is a statistically significant variable for predicting OAA, the modest R-Squared figure (which, to put it too simply, measures the “goodness of fit” on a scale of 0-1) of 0.18 suggests that that model isn’t a particularly good fit. This isn’t too surprising, given the simple nature of this exercise and model, but it does beg the question: which players’ performances deviates most from what this simple model predicts?

As such, below are two leaderboards. The first features those players whose expected OAA, or “xOAA” (as given by this simple model), are far greater than their OAA from Baseball Savant. In other words, this leaderboard includes those players who underperformed OAA expectations based on their sprint speed alone.

Average sprint speed in the Majors is roughly 27 ft/sec according to Baseball Savant. Most of the players listed above are either average or above-average runners. Despite that, they earned poor grades in OAA. Andrew McCutchen in particular appears to be disproportionately fast in relation to his sprint speed, but Nick Castellanos‘ 2018 season represents the great discrepancy between OAA and xOAA by a fair margin. It should be noted that outfield metrics have developed a reputation as being a bit unreliable, so OAA alone probably shouldn’t be the be-all and end-all, particularly as it only considers range/catch probability.

Next, those players who overperformed in OAA as compared to what the single-variable linear sprint speed model expected. The clear leader here is Ender Inciarte, who seems to make the most of his pedestrian speed in center field. Lorenzo Cain and Mookie Betts are the other players to appear on this leaderboard more than once. Despite that roughly average sprint speed, Inciarte three times posted OAA of at least 20. Notably, this list only includes players with average or above-average speed: no season listed below features a player whose sprint speed is less than 27 ft/sec. Still, even considering their speed, the single variable model clearly underestimated the value of these athletes across the board.

Should the single variable model be refined, including a variable for whether an outfielder plays in center or in a corner is probably a good place to start. At a glance, it appears as though center fielders were generally underestimated whereas corner outfielder performance was overestimated. Additionally, including a metric like “Outfield Jump” would probably be of use in further contextualizing a player’s speed as it related to his range. In any event, speed appears to impact the game by way of player defense.