Basketball’s Perfect 10

What is a perfect game in basketball? We all know about the perfecto in baseball and perfect 10 in gymnastics. Even the NFL’s passer rating metric has a maximum value. But is there a way to quantify that a player had a flawless game in hoops? Do they need to make every shot? A pitcher does not need to throw entirely strikes to pitch a perfect game, neither does a quarterback need to complete every pass to obtain a perfect passer rating. But, they need to avoid major mistakes, such as base hits, interceptions, or, in basketball’s case, turnovers. So, I tried to find a method to rate a basketball player’s single game contribution to a team out of a possible 10 points. The famous statistician Dean Oliver came to my aid in this project stating the importance of several factors in the game of basketball.

 Shooting – 40%
 Turnovers – 25%
 Rebounding -20%
 Free Throws – 15%

The first metric is shooting, which is by far the most weighted of the Four Factors. Does this make sense? Certainly. Shooting determines the end result of most possessions and is the only measure (along with free throws) that points are added to a team’s and player’s totals. A player’s shooting performance can ultimately make or break a team’s performance, and we saw it in Davidson’s win over St. Bonaventure in the Atlantic 10 Tournament, and unfortunately also in their loss in the NCAA Tournament to Kentucky (albeit the 6 for 11 night by Jon Axel Gudmundsson).

An ideal way to measure shooting performance is to weight three point field goals higher than two point shots, and that is done by the metric of effective field goal percentage, which weights three pointers 1.5 times more than twos. A 100 percent performance is not needed; any effective field goal percentage of over 70 is an outstanding day; it is rare to do better. Hitting every field goal in a game is next to impossible, so a perfect score would be nearly unattainable If the bar is set higher.

Maybe the most important metric stressed by a coach is that of avoiding turnovers. Giveaways not only lose a team possessions, but also allow a much easier opportunity for the opponent to score on the fast break. Turnovers can also have negative effects in loss of confidence and momentum, and can lead to large scoring runs by the opposition. For a player to have a perfect game, it is essential to play turnover-free basketball for the entirety of the contest, because they are almost always caused by poor decision making and/or lack of execution. However, a player can also force opponent turnovers through steals, which is why turnover percentage minus steal percentage is the best way to find out the rate of a player taking away opponent’s possessions to a player losing his own possessions. To calculate this part of the metric, we use turnover percentage and steal percentage, which is the estimate of a player’s giveaway and steal rate per 100 possessions, respectively. Thus, it is possible for a player to still obtain a perfect rating with a turnover or two if it is highly offset by multiple takeaways.

Rebounding is the next most important factor. Collecting boards allows for extra shots and decreases the opponent’s chances at extra shots. For this experiment, we are looking at total rebound percentage (percentage of all offensive and defensive rebounds that are grabbed per 100 possessions), Why not just offensive rebounds? Yes, getting the board on the offensive end gives your team an extra opportunity to score. But missing a defensive rebound can give an offensive board to the opposition, while collecting it saves from an opponent’s extra opportunity. In baseball, a strikeout and a flyout to the warning track both count towards a perfect game. Many analysts apply Four Factors to both offense and defense, and improving your “defensive” offensive rebounding percentage means simply to grab more defensive rebounds. Perhaps if we were evaluating a player’s rebounding skill alone we would make offensive boards more valuable due to them being more challenging to obtain (again, like strikeout percentage in baseball). Additionally, not all total rebounding percentages are created equal. Centers and forwards tend to collect more due to their height and play style, so the metric is adjusted for each position, in such a way that centers need to collect a higher percentage of rebounds than guards to get full marks.

Finally, if I said earlier that coaches will harp on turnovers the most, maybe I was wrong. Free throws are such an important aspect of basketball, and decide the outcome of seemingly every close game. Free throws are “free” meaning there is no defensive pressure, thus players should be able to sink every free throw opportunity they are given to keep a perfect rating. Missing a tough shot guarded by a defender is excusable, but missing a straight shot at the basket without any hands near your face should be considered a mistake. Free throws are meant to be made, not missed. Thus, a player who misses a free throw should not be deserving of playing a perfect game. If the player attempts no free throws during a game, I give 75 percent credit, but I do not give 100, due to the player’s lack of effort to get to the free throw line, which denies the team chances for easy points.

Using these four different calculations, I weighted them accordingly to produce a rating out of 10 (similar to player ratings in professional soccer) to reflect a player’s overall contribution to the team in a particular game. Here are the ratings for each starter from the four games of this year’s NBA Finals:

We can see here some interesting trends about what happened in the Finals. For the Cavaliers, Kevin Love’s impact was shown when looking at his great shooting efficiency and high rebounding totals, even when adjusted for the center position, and was consistent in bringing returns all series long when other players struggled, except for when they basically gave in during Game 4. Although not talked about much, George Hill’s and JR Smith’s poor shooting significantly hurt the team in Games 2,3, and 4. LeBron’s turnover rates were not spectacular enough to earn him high overall ratings, and his shooting was great but not amazing, aside from Game 1. On the Warriors side, Kevin Durant’s numbers supported the decision to give him the Finals MVP award, averaging an 8.49 rating over the series compared to Curry’s 8.2. His performance during Game 3 was nearly flawless except for three turnovers committed. It seemed that if either Curry or Durant was having a less than ideal game, the other made up for it. Finally, the performance of both Kevon Looney and JaVale McGee was underappreciated but extremely helpful in taking high-percentage shots and limiting turnovers, which are huge in winning basketball games.

So, have we seen any perfection lately? It is hard to come by. Davidson’s own Stephen Curry has received two flawless 10.0 ratings: one on January 18, 2016 against LeBron’s then Cleveland Cavaliers making 7 of 12 from three point range for 35 points in a 34 point win. Steph did have one turnover, but it was offset by three steals on defense to overcome the giveaway. The other perfect outing was last December 30 in a 141-128 triumph over the Memphis Grizzlies. Steph made an insane 10 of 13 from 3 and did not give the ball away all night, while making all his free throws. All this on his first game back from an ankle injury, which shows how impressive this Davidson product continues to be. Is more perfection in the future for 30-year-old Steph Curry? Why not? This rating system can help identify players that have recently contributed to their team through the most important ways in games and showcase the players who are helping their teams succeed the most.

Image by © Ellen H. Wallop/CORBIS