By Matty Cheng
Not just any other game. December 2nd, 2010: new Miami Heat LeBron James’ revenge game against his former team, the Cavaliers. April 13th, 2013: Carmelo Anthony’s homecoming game against the Denver Nuggets he forced a trade from. Or March 11th, 2018 when IT gets his chance for revenge time against the Cavaliers. Or what about when Channing Frye plays his revenge game against the Cavaliers? Wait, Channing who?
Do NBA players perform better in revenge games? Do superstars like Kevin Durant fare better than role players like Channing Frye who are used to switching teams?
To determine the performance of players in revenge games, I analyzed the careers of 486 qualified NBA players (minimum 10 games played in 2017). To quantify the performance of players, I used a player’s GameScore, John Hollinger’s measure of a player’s performance (10 is an average GameScore, while 40 is an amazing game).
Game Score Formula = .4*(Field Goals Made)+.7*(Offensive Rebounds)+.3*(Defensive Rebounds)+Steals+.7*(Assists)+.7*(Blocked Shots)-.7*(Field Goal Attempts)-.4*(Free Throws Missed)-.4*(Personal Fouls)-(Turnovers)
I compared a player’s GameScore in a revenge game to their average GameScore during that season. For example, consider LeBron James’ homecoming games (first game played at former team’s arena).
LeBron James had an incredible homecoming game in 2010, exacting revenge on the Cleveland Cavaliers with a 55.3% increase in GameScore compared to his season average. In 2014, after going back to Cleveland, LeBron’s homecoming game against the Miami Heat was not quite so spectacular, but still a 9.6% increase in GameScore.
While the incredible revenge games are seared in our memories, there actually seems to be minimal performance increases when looking at all qualified players in homecoming games (Figure 1). Perhaps we can easily recall the spectacular games, but the GameScore for homecoming games increased on average by a mere 1.57% with players scoring only 2.04% more GameScore points. However, note the large variation in performances, with some players performing extraordinarily but most who do not. For example, Corey Brewer had a 600% increase in GameScore in his Homecoming game.
[Figure 1. GameScore percentage change in homecoming games vs season average]
But perhaps the extraordinary revenge games are from superstars like LeBron James. Using John Hollinger’s PER (Player Efficiency Rating) thresholds, we can just analyze “All-Star” players’ homecomings with the PER cutoff being at least 22.5. They had an average GameScore decrease of 9.73%, scoring 4.58% less points, however there is a small sample size here. So, All-Stars actually performed worse in homecoming games compared to their season averages.
BELOW AVERAGE PLAYERS:
Next, I considered below average players by Hollinger’s PER (players with less than 13.0 PER). This group saw an increase of 11.77% in GameScore coupled with 8.73% more points. Figure 2 shows the interesting difference between below average players and all stars homecoming performance. I also calculated the z-score for each homecoming GameScore, which shows how many standard deviations the GameScore is from the season average GameScore. By Z-scoring, we are able to more effectively compare the all-stars to below average players since the below average players will naturally have more variance. The z-score plot (Figure 3) supports the finding that all-stars perform worse (-0.169 standard deviations below season average) than below average players (+0.0450 standard deviations above season average). After running t-test, we found that the means of all-stars and below average players are not statistically different. This is likely due to the low sample size of All-Star homecoming games, making it harder to show statistical significance.
[Figure 2. GameScore percentage change in homecoming games by player type]
[Figure 3. Z score of GameScore in homecoming games by player type]
ALL REVENGE GAMES:
I also looked at all revenge games. For example, this includes all of James Harden’s games against his former OKC team that he was last on in 2012. This group shows a similarly small increase in GameScore (+3.07%). The difference between All-Stars and below average player performances follow the same trend of a decrease for All-Stars (-3.41%) and increase (+2.99%) for below average players, but the changes are less pronounced (Figure 4). The z-score plot (Figure 5) supports the finding that All-Stars perform worse (-0.0997 standard deviations below season average) than below average players (+0.0610 standard deviations above season average). The t-test does find that the means of all-stars and below average players show a difference that is statistically significant.
[Figure 4. GameScore percentage change for all revenge games by player type]
[Figure 5. Z score of game score for all revenge games by player type]
There could be a couple of reasons why All-Star players perform worse than below average players. Some of the difference could be explained by minutes played. All-Stars played roughly their season average minutes (0.2% more minutes) while below average players played slightly more than their season average of minutes (2.63% more minutes). My theory is that homecoming games for a player brings extra motivation and focus to the entire former team, resulting in a concerted defensive effort against the homecoming player. In Carmelo Anthony’s return game to Denver as a member of the New York Knicks, he put up a GameScore that was 85% lower than his season average. This could have been due to the fans and players being extra motivated by the return of their former superstar after he forced a trade through to the Knicks in 2010. This is one possible explanation for the decrease in performance.
There is likely little extra team motivation when a below average player returns since he was not famous or the focal point of the team. But, the homecoming player still has his personal motivation, which could explain the positive increase in performance.
In exploring the potential relationship between revenge game performance and skill of the player, we plotted every player’s GameScore percentage change by their PER (Figure 6). The regression line suggests a small but negative correlation between revenge game performance and PER.
[Figure 6. GameScore percentage change for all revenge games by PER rating]
In conclusion, the homecoming games exhibit the greatest changes in player performance. All-Stars tend to perform worse in homecoming games while below average players tend to perform better. Perhaps this can be attributed to the fact that when an All-Star returns home, his former team and the fans get riled up, while few notice when a below average player returns. The changes in performance compared to season averages diminish in subsequent revenge games, likely owing to the fact that the players are less emotionally charged after the first homecoming game. One implication of this study is that for Daily Fantasy Sports players, instead of locking in the big name players in homecoming games such as IT, one should perhaps target the “below average players” like Channing Frye. Especially considering ROI with respect to salary, one should use the low priced Channing Frye’s of the league instead of the high priced ITs of the world. In revenge games, perhaps it is not the gigantic, flashy sword, but instead the unassuming, understated small knife that cuts deepest for some sweet revenge.
If you have any questions for Matthew about this article, please feel free to reach out to him at firstname.lastname@example.org