Injury Impact in the NBA

Led by Davidson’s own Stephen Curry and Finals MVP Kevin Durant, the dynastic Golden State Warriors completed the first NBA Finals sweep since 2007 over LeBron’s Cleveland Cavaliers. The decisive victory showcased both the star power and depth of this juggernaut team over a James- led Cavs squad with minimal other effective role players. The arsenal of weapons the Dubs had at their disposal this series was tremendous, which begs to question how dominant they could still be if key players were injured. How would the probability of one team winning the series change, say, if Curry was unavailable? We need a way to judge how much of an impact each player makes to his team through both offense and defense. We have that in win shares, which takes player contribution into account. The total amount of regular season wins that one team has is divided into win shares for each player on the team. On offense, the calculation takes points produced largely into its measure. The statistic represents the amount of points that a player makes possible during a game through made field goals and free throws, assists, and offensive rebounds leading to scores. We normalize this value with the league’s average PPP and the number of the player’s offensive possessions played in. We then take the team’s pace into account using marginal points per win by multiplying a constant of 0.32 by the league’s average PPG by the ratio of the specific team’s pace to the league’s average pace. Offensive win shares are calculated by dividing a player’s marginal offense by its team’s marginal points per win.

Similarly, defensive win shares are found by dividing a player’s marginal defense by the aforementioned marginal points per win. Marginal defense takes into account the number of points allowed by the player per 100 possessions, as well as a player’s minutes, team defensive possessions, and the league PPP. The sum of a player’s offensive and defensive win shares is their total number of win shares. For example, Steph Curry’s win shares for 2017-18 is 9.1 and Lebron James’ is 14. Note that the sum of each players’ wins shares on a team is the number of wins obtained through win shares, which should be very close to the amount of wins in the regular season. Normally, the more minutes a very efficient player has, the more win shares obtained because more minutes mean more opportunities to assist and score, as well as a higher ratio of minutes played to team collective minutes. Thus, an injury to a player like Curry that would cause him to miss time during the regular season will bring down his total win shares from what they should be. To adjust this, adding minutes to Curry’s total to what it would be if he never got hurt and subtracting minutes from lower guards in the depth chart would be an acceptable estimate to show how good the Warriors are when they are at full strength. That way, we can use these win totals to find the probability of beating teams in the playoffs with all players healthy. With Curry’s limited time in the season, GSW’s win shares total was 57.21. But with the adjustment to an always-healthy Curry, the total would jump to 61.25. But what if Curry was completely sidelined for (*gasp*) the NBA Finals? Then Stephen’s minutes would drop to zero and his time would need to be allocated by guards lower on the depth chart, most likely. Quinn Cook and Shaun Livingston would be the best candidates for seeing more time without Curry. Those players are not as efficient, with win shares/48MIN much lower than Steph’s. Since win shares are based on player involvement in minutes and not just performance, win shares/48MIN is a great metric to showcase how players are performing given their limited window of minutes. Curry’s is .267, the second largest in the league behind likely NBA MVP James Harden. So, as you may have figured out, the win share total of GSW would drop without Curry, and it turns out that it drops by a significant total. Without Curry, the Warriors would only have 51.15 wins, which is a 10-win dropoff from full-time healthy Curry, which is ENORMOUS in the NBA. But hey, 51.15 wins is still more the Cavs would have WITH Lebron (46.71). Even if Durant is lost too, the Warriors were still projected to win 48.7 games. Why? The answer is the depth that Golden State has with its forwards. Players like David West, Kevon Looney, Jordan Bell, and JaVale McGee all have above average win shares/48MIN , meaning that each player on the team is making efficient contributions to the club as a whole. The Cavs have only six active players that have a win share/48MIN rating of over .1, while the Warriors have nine of them. Golden State has more efficient pieces that can run the offense well and play defense compared to a bunch of below average bench players plus a couple starters and LeBron. It is worth noting that if LeBron also got injured, it would bring the Cavs from a 46.71 win team to a 39.51 win team, which more often than not  does not make the playoffs. So losing LeBron would have sunk the Cavs from a mid-playoff seeded team to most likely a non-playoff team. And it didn’t hurt that much compared to Curry because James is ninth in WS/48 compared to Curry’s second place spot.

Even if Lebron stayed healthy and Curry plus KD got freak injuries, all hope may not have been lost for GSW, but it would have been a much closer series and would likely go 6 or 7 games. Just for fun, I used the same technique to find how much that Chris Paul injury hurt the Houston Rockets late in the Western Conference Finals. Paul’s WS/48 is .265, just 2 thousandths behind Steph Curry for third in the NBA. At full strength, Paul brings the 2017-18 Rockets 65.72 wins, and without CP3 that number drops to 57.47. This is on par with the Warriors with limited Curry and less than the Warriors with full-strength Curry. Needless to say, Paul’s injury ended up having a devastating effect on Houston’s chances of eliminating the Warriors, as they went from being favored to being the underdog versus GSW.

To calculate win probabilities, I used a formula developed by the Society for American Baseball Research, which takes into account the winning percentages for both teams and finds the probability that team A defeats team B. The calculation is defined here.

P_(A,B) = (WP_A (1 – WP_B))/(WP_A (1 – WP_B) + WP_B (1 – WP_A))

where WP represents “win percentage” of team A or B. The probability found is the chance that team A defeats team B.

I made several scenarios regarding injuries to specific players, and found these different probabilities relating Houston, Golden State, and Cleveland.

Is it surprising seeing the Warriors being favored without their two best players against the Cavs? I do not. The Warriors are a well-oiled machine that can still run without their most efficient parts due to their high efficiency win share numbers with bench players that can come in and play great team basketball to still give the Dubs a chance. We saw that in this year’s finals as the many role players such as West, Bell, and McGee gave Golden State quality efficiency in limited minutes, while the Cavs supporting cast failed to consistently produce, especially on defense. And yes, this is further proof that Chris Paul’s injury could have very well derailed the Rockets from vanquishing the juggernaut Golden State Warriors. Overall, injuries can definitely affect a team’s chances of winning it all, but basketball is a collective team game, and a great supporting cast can minimize what would be lost by losing a star player.