Nylon Calculus: Predicting injury recovery for Klay and Durant

We’re building prediction models to estimate how much productivity injuries could cost Klay Thompson and Kevin Durant over the life of their new contracts.

Golden State tipped-off Game 5 of the NBA Finals with their once-again-fully star-studded lineup and a renewed swagger. Kevin Durant was back and — for a few minutes anyways — the Warriors looked as if they were unbeatable again. But then in the space of 68 minutes of play, they lost Durant and then Klay Thompson to a pair of catastrophic leg injuries. In a flash, Golden State went from being a team who was a sure bet to compete for the next few titles to a team with a suddenly uncertain future. By the end of Game 6, both Durant and Thompson were free agents and the Warriors had to decide who would continue to be a cornerstone of the franchise. Could they really bank on either of these guys to make a full recovery?

To predict how Thompson (torn anterior cruciate ligament, ACL) and Durant (ruptured Achilles tendon) will bounce back, we examined the league’s recent history with these injuries. We searched the Pro Sports Transactions archive to find all of the season-ending ACL (N=65) and Achilles tendon (N=40) injuries since the 2000-01 season (ie. during the play-by-play era).

It’s pretty obvious that either of these leg injuries can be a BIG problem for a professional basketball player. About half of the players who went under the knife for ACL operations ended up playing fewer than 100 additional regular-season games in their careers. On the contrary, there are also plenty of success stories of players who have had lengthy post-ACL-tear tenures. Current veterans like Jamal Crawford and Ricky Rubio have both played nearly their entire careers with a surgically-repaired ACL.

The league’s track record for Achilles rehab is bleaker — as 70 percent of players return for fewer than 100 games. Moreover, long-term successes have been exceedingly rare following season-ending Achilles injuries. Although current players like Rudy Gay — not to mention fellow 2019 Warriors Jonas Jerebko and DeMarcus Cousins — are offering road maps to recovery.

So, ACL injuries are bad. Achilles injuries are worse. And that’s probably about as far as you’ve heard this conversation go. But this type of simple analysis overlooks several important factors. For starters, how old were these players when they were injured? And how many more games would we have expected them to play if they hadn’t been injured?

Also, what can we say about how — specifically ––these injuries have impacted players in the past? Acknowledging that injury recovery is extremely personal and every situation is unique, could we use a stat like rim-attempt frequency as a surrogate for explosiveness in an effort to chart the shape of performance recovery curves? Can we use recent history to anticipate how Thompson and Durant will be forced to change their games in the impending post-injury future?

To help answer some of these questions we can use mixed-effects models. Collecting data from PBPstats.com for every player since the 2000-01 season we can relate the number of minutes a person played in a given season to his years of experience (raised to the first, second, and third power), the calendar year, and his injury status (ie, in the year of an ACL or Achilles injury, in the year after his injury, or in the two to five years after his injury). The model defines a common shape of the aging curve for any NBA player but with a different amplitude defined for each individual and it allows us to see the impact — in terms of minutes lost — of an ACL or Achilles injury.

Similarly, we created four skill-specific aging curves for at-rim frequency (percent of field goal attempts at the rim), at-rim accuracy (field goal percentage at the rim), 3-point frequency (percent of field goal attempts from 3), and 3-point accuracy (3-point percentage). Each of these outcomes was related once again to years of experience, season, and injury status to find the skill-specific effects of ACL and Achilles injuries. Again, the models use all of the available league data to determine the likely shape of the aging curves, but each player is assigned a unique starting point for his own individual curve.

So, for example, we can predict how many minutes Thompson will play during each of his next five seasons as well as looking at how often and how well he will shoot at the rim and from the 3-point line.

Our models indicate that — relative to a healthy aging curve — an ACL injury cost a player about 326 minutes in the following season (of course, Thompson is likely to miss even more minutes than this, due to the extreme timing of his injury). However, in the four seasons that followed, ACL survivors bounced back to a level approaching the healthy aging curve with only a 156-minute deficit observed. Still, the probabilities would suggest that Thompson is unlikely to regain anything approaching his customary 2500-minute routine over the next few years.

Our models found no statistically significant effects of ACL injuries on rim-attempt frequency, at-rim accuracy, 3-point frequency, or 3-point accuracy in the five years that followed.

We can use the same models to predict how many minutes Durant will play during each of his next five seasons as well as looking at how often and how well he will shoot at the rim and from the 3-point line.

Our models found that an Achilles injury cost a player 291 minutes the following year (again, the timing will be worse than usual in Durant’s case) and that the playing-time deficits persisted over the course of the next four years (284 minutes lost in each of years 2 to 5). Unlike the players recovering from ACL injuries, there was no apparent post-Achilles bounce-back in Year 2.

Interestingly, Achilles injuries were definitively linked to decreases in the percent of field goal attempts at the rim in the following year (four percentage points lower than would be expected with healthy aging) as well as over the next four years (five percentage points lower), presumably due to lost explosiveness. Correspondingly, players that suffered Achilles injuries tended to take a larger fraction of their shots behind the 3-point line. In contrast, there were no significant deficits in shooting accuracy at the rim or from 3.

Last night it was reported that Thompson will receive a five-year $190 million max contract from the Warriors whereas Durant accepted a four-year $164 million deal from the Nets (the most they were allowed to offer him). It’s a bit jarring to see Thompson ink the bigger deal than Durant (and to hear rumors that the lowly Knicks balked at offering Durant the max). But presumably, Durant got exactly the deal he wanted. All indications are that the Warriors were totally willing to offer him the even max-ier supermax deal (of five years for $221 million) and he just wasn’t interested.

But, based on recent history, Thompson is likely to play more minutes over the course of the next five years. Moreover, our models suggest that Durant will drive to the basket less frequently and rely more heavily on his 3-point shot after his return, making him more-or-less a taller version of Thompson. Perhaps, in the end, the Warriors will find that they have signed the right injured star after all.

Here’s wishing both players a speedy and sustained recovery.