# A New Way to Measure Efficiency

Today, many different stats trying to quantify NBA efficiency are out there, whether its Real Plus Minus, Box Plus Minus, Win Shares, and many others. Recently I wrote how PER is a bad statistic( a lot of the reason may be because of its arbitrary weights it places on its inputs); they all have pluses and flaws. Today I decided to throw my hat into the ring and take a stab at an overall offensive efficiency metric. While part of the inspiration to do this was because I hate the idea of bringing up a problem and not solving it (pretty much what I did with PER), I could not think of a way to properly account for players who have the ball in their hands an unreasonable amount (Harden, Westbrook, especially Westbrook, Westbrook again, etc.). These players tend to have inflated stats, so it can be difficult to trust the advanced metrics that cannot rule this out (such as PER).

The answer, or at least a possible answer, ended up being a lot simpler than I thought it was going to be. It did not require any complex formulas, arbitrary assumptions (my assumptions are valid, and there are only two of them), or convoluted concepts. It is by no means a perfect answer, but it is a worthwhile answer to say the least.

Hopefully I provided enough buildup. A lot of my new analysis hinges on a metric that I calculated to account for stat hogs. This metric is called player opportunities. To step away from the excel spreadsheet, let’s envision what a player can do with the ball in his hands. He can attack, trying to get into the lane and get fouled, score, or create for others. He can shoot over his defender. He can engage in a pick and roll. He also could pass, if he decides he doesn’t have the best matchup on the court. If a player is constantly attacking and shooting, he will naturally have higher assist levels, since he is causing the defense to react more often and opening up lanes for others. If a player is just a spot-up specialist, then he will have lower chances to record an assist, since every time he has an opening he is going to fire. A custodian-like player may only finish lobs and secure rebounds. There are multiple iterations of different player types and I could go on, but hopefully you see the bigger idea. While players may be on the court the same amount, the times they actually are probing the defense and attempting to create vary.

Now that I’ve explained the background of the metric, I will explain my calculations and rationale. The most obvious opportunity to create points (not necessarily score) that a player has is by shooting the ball. Thus, any time a player shoots the ball he is creating an opportunity to score. Therefore, field goal attempts is my first input. A player can get fouled in the act of shooting, so getting to the line is another opportunity, and .42*FTA is the next input (.42 is not arbitrary). A player can attempt to score, but turn the ball over. This was an opportunity nonetheless, so turnovers are included. Lastly, a player can create an opportunity by setting up another player. Hence, assists are an opportunity (I may be double counting here, since there are more than one opportunities per possession if a basket is assisted, removing assists may be a way to correct for this, but I did not think it was harmful).

Because a player can technically create an opportunity via a pass and not be credited with an assist (because the shot missed), I may be missing some opportunities (another reasons taking out assists may not be a bad idea) as players can set up chances but not be rewarded. I am rationalizing this by admitting that most teams miss shots at a reasonably similar metric and accounting for this difference while taking into account a player’s assist rate would make the metric too complex. Another issue with removing assists is that players who are pass-first, like TJ McConnell, may be overvalued as a result of not shooting too often. He should still be credited for plays where he sets up others.

After all of this explanation, which was admittedly pretty lengthy, I will finally arrive at my final calculation.

Opportunities = Field Goals Attempted + Assists + Turnovers + 0.42*Free Throw Attempts

Using Opportunities as a scale, I then created similar metrics, points per opportunity, assists per opportunity, and points created per opportunity. Points and assists per opportunity is simply dividing points scored and assists by opportunities, respectively. Points created per opportunity is points per opportunity + 2*assists per opportunity. I know some baskets are worth three points, but I felt this simplification kept the metric from overvaluing those pass-first players.

This final metric, points created per opportunity, can be used to judge overall efficiency of players. It does not weigh high volume scorers too highly, and it shouldn’t, because high volume scorers just aren’t that good for winning basketball games. It rewards the 3, making free throws, and not turning the ball over. Even with my checks in place, it likes players who can set up others, and it should, since assists often lead to easy baskets. Overall this stat attempts to show how many points a player creates on the floor while adjusting for the time he actually has the ball in his hands. This helps players like Ricky Rubio, who have a lower than average shooting percentage (not breaking news) but who don’t take too many shots. If he is only shooting 8.7 times per game, then he is only missing 5 shots. What are 5 shots over the course of an entire game? This is the reason to account for opportunities, to segment between high volume scorers and non-shooters who don’t shoot as often. Here are the results:

One flaw in this metric is that it does not account for rebounding. This stat is meant to measure playmaking efficiency, and the fact that Nikola Jokic, Al Horford, and KAT are top players in this metric speaks to their offensive abilities. Other metrics can compare rebounding directly.

To cross-validate my metric (using that term loosely), I ran a regression between points created per opportunity and Offensive Real Plus-Minus (my favorite of the advanced stats above). ORPM is supposed to incorporate all facets of the game, including rebounding and others (screening, cutting, etc.), so naturally not all facets of the game will line up, but I thought it would be interesting to see non the less. Here are the results:

There are some major outliers (Rondo and TJ McConnell), but in general, these stats correlate pretty well. Even without accounting for rebounding, 42% of the variation in points created per opportunity explains variation in ORPM. This shows that this stat is meaningful, and has validity. Here are the rankings of players rated highest by points created per opportunity.

The players that I used recorded over 1200 opportunities throughout the year, to make sure I left out those who are especially confined to spot up shooting. Naturally, as I become stricter about the opportunities requirement, the regression improves, as I am picking off more and more outliers. They are by no means the top 80 in the league, but they are the ones who I was able to get the most trustworthy data from, when accounting for injuries, minutes played, etc.

If I further constrain opportunities (say, greater than 1300 over the entire season), as mentioned, here is the result of a better regression:

Note the improvement, as the R-squared term is nearly .15 units greater. Note that outliers McConnell and Rondo are both filtered out.

Excel Data: PCpO