Relationship between advanced stats and winning

While a growth in advanced metrics provides a more robust picture of a player's value, the true measure of a metric should be it's ability to correlate with his team winning. I took six advanced metrics from basketball-reference.com for the 2014-15 season* and focused on only players that had played a minimum of 100 minutes this season through the December 5 games (this resulted in a population of 342 players). 

I compared each player's team's winning percentage (win %) with i) usage %, ii) player efficiency rating (PER), iii) true shooting % (TS%), iv) box plus-minus, v) value over replacement player (VORP) and vi) win shares per 48 minutes (WS/ 48). The definition for each are pulled mostly from basketball-reference.com's glossary. Below each definition the specific matrix is plotted on the vertical/ y axis and win % is plotted on the horizontal/ x axis. 

Each blue dot represents one of the 342 players that qualified. I included a yellow linear regression line to exhibit the direction of the relationship. If there is a very strong relationship between the metric and win % then the yellow line will begin at the bottom left of the chart and rise steeply to the top right of the chart, which would indicate that as the metric increases so too does win percentage. I include an R-square to indicate how well the model fits the data (or how well the metric explains win %). The lower the R-square means that the metric does a poorer job explaining win %.

Usage %: Usage Percentage (available since the 1977-78 season in the NBA); the formula is 100 * ((FGA + 0.44 * FTA + TOV) * (Tm MP / 5)) / (MP * (Tm FGA + 0.44 * Tm FTA + Tm TOV)). Usage percentage is an estimate of the percentage of team plays used by a player while he was on the floor.

PER: A per minute rating that adds accomplishments and subtracts failures (see formula here).

TS%: True Shooting Percentage; the formula is PTS / (2 * TSA). True shooting percentage is a measure of shooting efficiency that takes into account field goals, 3-point field goals, and free throws.

Box plus-minus: A box score estimate of the points per 100 possessions a player contributed above a league average player, translated to an average team.

VORP: A box score estimate of the points per 100 team possessions a player contributed above a replacement-level player, translated to an average team.

WS/ 48: An estimate of the number of wins contributed by a player per 48 minutes (league average is approximately .1000).

The above shows that while all six of these advanced metrics has a positive correlation with team win%, usage, PER and TS% are weakly related (they have relatively flat lines). Box plus-minus, VORP and WS/ 48 have a stronger positive relationship but the r squares indicate that they only explain ~15-18% of the relationship between the specific metric and team win %. However the includes a player's team's wins are included as a component in the formula for ws/ 48, thus the stronger positive correlation and larger R-square with ws/ 48 are expected. As a result, box plus-minus and VORP, which includes box plus-minus in its formula, should be considered the best metrics in terms of correlating with team win % that don't also include a team's wins in the formula (based on this small sample).

*A major limitation of this approach is that it focuses only on one incomplete season (2014/15). I will try to run a similar analysis on these metrics over several completed seasons, which should give a more accurate picture of the correlation with winning.