When ranking players, fans must always reach a balance between going on individual vs team success. There have been many players with stellar box score stats but a lack of team success, as well as many with worse box score stats but better team success (for example, Wilt Chamberlain vs Bill Russell). An attempt to solve this has been advanced stats, which aim to quantify how much a player actually makes their team better, which after all, is the goal of basketball. There are many advanced stats, and it’s not immediately obvious which ones are the best. In this post we’ll aim to determine which advanced stats are best to use for individuals by seeing how well they correlate with various metrics of team success in the regular season and playoffs.
1. Preliminaries
We start by introducing all the advanced stats, dividing them up by those which measure player success and those which measure team success.
Player Stats:
PER (Player Efficiency Rating) – This a per minute stat that is meant to represent a combination of all box score stats. It basically measures how well a player “stuffs the statsheet” in a single number, and it’s arguably the most popular advanced stat. That said, it’s received criticism for not valuing defense enough and potentially overvaluing centers.
VORP (Value Over Replacement Player) – This is an estimate of how many more points a player contributes per 100 possessions compared to a replacement-level player on an average team. This takes minutes into account, unlike BPM stats.
DBPM (Defensive Box Plus Minus) – This is a box score estimate of the defensive points per 100 possessions a player contributed above a league-average player, translated to an average team.
OBPM (Offensive Box Plus Minus) – A box score estimate of the offensive points per 100 possessions a player contributed above a league-average player, translated to an average team.
BPM (Box Plus Minus) – Sum of DBPM and OBPM.
DWS (Defensive Win Shares) – This is an estimate of the number of wins contributed by a player due to defense.
OWS (Offensive Win Shares) – This is an estimate of the number of wins contributed by a player due to offense.
WS – Sum of DWS and OWS. This estimates how many wins a player contributed to their team, and the sum of the win shares for each player on a team will roughly add up to the total wins a team had that season. In previous posts this has been our default advanced stat for evaluating players.
Team Stats:
Wins – This is simply the amount of wins a team gets in a season.
W/L% – This represents a team’s win percentage in a team (i.e. wins / games played).
Playoffs – Amount of playoff series won.
DRtg – Defensive Rating is the amount of points a team allows their opponents to score per 100 possessions.
ORtg – Offensive Rating is the amount of points a team scores per 100 possessions.
Rel DRtg – Relative Defensive Rating represents the difference between a team’s defensive rating and the league average defensive rating during a given season.
Rel ORtg – Relative Offensive Rating represents the difference between a team’s offensive rating and the league average offensive rating during a given season.
Net Rtg – Net Rating is the difference between offensive and defensive rating. It represents how many points a team outscores its opponents by per 100 possesions. Note net rating is the same as relative net rating since the average net rating in a given season is always 0.
SRS (Simple Rating System) – This is a modified version of net rating which takes into account strength of schedule.
2. Stats
Looking at every team in every season, we calculated the weighted average of all advanced stats for players on that team. We then compared these with the advanced stats for the team to see the correlations. All player and team stats are done exclusively for the regular season (except for the Playoffs stat). The R2 values for each pair are shown below, with higher values corresponding to a stronger relationship:
It’s important to point out that some of the low R2 values happen due to defensive stats and offensive stats not being related. We also see high R2 values in several places where we’d expect. For example, Box Plus Minus stats are almost perfectly correlated with their corresponding relative rating stats, as both are a measure of points per 100 possessions relative to league average. These matches are OBPM – Rel ORtg, DBPM – Rel DRtg, and BPM – Net Rtg.
Another thing to note is that player advanced stats are much better correlated with relative ratings as opposed to absolute ratings. This is because player advanced stats are already relative in the sense that they are determined based on the production of average players.
When determining which single advanced stat is best, the most important team stats to predict are winning, SRS, and playoff success. For all of these, the top three player stats that have by far the highest R2 values are VORP, BPM, and WS. Of these three, WS actually looks to be the worst as it less related to playoff success and SRS while still being approximately equally related to winning as VORP and BPM. We also note that WS are about equally correlated between offensive and defensive metrics for team success, while VORP and BPM are a little more correlated with offensive metric, and this might be explainable by the gap between elite and average offensive production being bigger than the gap between elite and average defensive production.
The one all-encompassing stat that falls short is PER, as even though it’s highly correlated with offensive success, it has very low correlation with defensive success, which supports the criticism it has received for not accurately taking defense into account.
3. Conclusion
We can conclude that VORP, BPM, and WS are the three best advanced stats to use when evaluating players, as they are by far the most related to team success. In the next part we’ll dive deeper into these three stats and discuss the situations where one might be better than the others.
All-Star Analytics 