# Rethinking Basketball Statistics: Slightly More Accurate Scoring Efficiency Metrics

Just how efficient is Kevin Durant? Photo Credit: Keith Allison, Flickr.com

Carmelo Anthony led the NBA in scoring last season beating out Kevin Durant by just over half a point per game for the scoring crown. Despite his place atop the points per game charts, though, it would be hard to find many people who ranked Melo as the best scorer in basketball last season (well except the irrational New York Knicks that I assume exist as East Coast dopplegangers of the *totally rational *Los Angeles Laker and Kobe Bryant supporters). Because at the end of the day, any basketball analyst worth his opinion understands that conventional points per game numbers do not really indicate scoring efficiency and proficiency, and have realized there are much more capable statistics out there that reveal scoring efficiency.

There are three main scoring efficiency statistics to be exact, each of them having a different level of success in evaluating a players ability to score.

**Field Goal Percentage**

You can turn to any LeBron vs Kobe debate and find this statistic being used to its full effect. Kobe may put up more points per game but LeBron makes a much higher percentage of his shots. Field Goal Percentage tells us just that: how man field does a player make compared to the amount of field goals they have attempted; the simple formula of course being

"FG%=FGM/FGA."

The statistic is a quick and easy way to get a gauge of how often a player is putting the ball in the basket, but it falls short in a couple of areas. That is, it falls short in the typical way more traditional stats do, by disregarding the fact that threes are worth more than twos and by ignoring the fact that there is another way to score aside from making a field goal — namely free throw makes. As a result of these shortcomings, big men seem to dominate this category. Perimeter players are not necessarily less efficient offensive scorers, but they earn their extra points by taking and making threes — a lower percentage shot that is, again, worth an extra point — and by getting to foul line slightly more often. The top field goal percentage guys last season were DeAndre Jordan (64.3), Dwight Howard, Javale McGee, and Serge Ibaka, and LeBron James (who can ruin any point you are trying to make by being really, really good at basketball), while Tyson Chandler was the only ‘big’ to crack the top five in points per game or true shooting percentage. The fact that field goal percentage not only leaves threes and free throws out of the equation, but actively punishes players for taking threes are the main reasons it does not cut it as a legitimate scoring metric.

**Effective Field Goal Percentage**

Effective Field Goal Percentage at least partially solves this issue. It does so by taking the actual point value of two and three point field goals into account. Specifically a made field goal is valued as two of two point and a three point field goal is valued at three of two points. The formula then looks like this:

"eFG%=(FG+.5*3FG)/FGA"

In setting it up like this, Effective Field Goal Percentage at least solves the problem of truly garner the added value of a three point shot. As a result last year’s top ten Effective Field Goal Percentage players consisted of four non big men — LeBron, Jose Calderon, Chandler Parsons, and Durant — while the only non big to crack the top ten in Field Goal Percentage was LeBron. The statistic still falls short, though, because it still leaves the very important aspect of free throw shooting our of the game. So while all around great shooters are shown plenty of love with this stat, free throw line frequenters like Kevin Martin, Kobe Bryant, and James Harden are not credited for their ability to rack up points without a field goal attempt.

**True Shooting Percentage/PPWS**

The end all solution, then, that takes all three aspects of scoring — two point field goals, three point field goals, and free throws — into account is Points Per Weighted Shot and its prettied up sister True Shooting Percentage. The statistics are actually exactly the same except for a decimal difference and the factor the ‘pretties up’ True Shooting Percentage. The formulas:

"PPWS=PTS/(FGA+.475*FTA)TS%=PTS/(2*(FGA+.44*FTA)"

So outside of the difference between .44 and .475 True Shooting Percentage is just Points Per Weighted Shot cut half to make it look more likea ‘percentage’ (even though it is not a percentage and is literally an estimation of points per scoring attempt cut in half). Either way, both numbers are fairly accurate estimates of points scored per scoring attempt. They are still estimates, though, since the .44 and .475 factors are arbitrary numbers. The purpose of these numbers are to take into account there is not a one to one relationship between free throw attempt to scoring attempt. Instead every two free throw attempts is usually representative of a scoring attempt (getting fouled and taking two shots) with the skew just under .5 because of and ones — which are recorded as field goal attempts — and technical free throws. So it is a really accurate estimate as opposed to the direct number of points a player scores on a given scoring try. It is still an extremely accurate estimate — as we will see shortly — and is still the best way we can evaluate a players ability to score on any particular possession.

**Slightly More Accurate**

I want to propose a slightly more accurate statistic, though; one that does not need estimates as it directly calculates points per scoring opportunity. The statistic — called Points Per Ended (non turnover) Ended Possession — is essentially points per weighted shot, except it takes out the guess work of the .475 number — by using two shot and three shot fouls drawn; numbers recorded by NBA.com’s play-by-plays — and does not credit players for points earned via technical free throws (since these points are not actually earned via scoring opportunities). The formula then is:

"PPEP=(PTS-TPTS)/(FGA+2SFD+3SFD)"

where Technical Points (TPTS) are points earned via technical free throws, Two Shot Fouls Drawn (2SFD) are fouls drawn that earn two free throw attempts and Three Shot Fouls Drawn (3SFD) are fouls drawn that earn three free throw attempts. This, again, is the exact measurement of points scored per ended possession — excluding turnovers (which will be accounted for in the Possession category) and dealing the RBS definition of possession — as field goal attempts and And Ones are taken into account by Field Goal Attempts and earned trips to the foul line are taken into account by Two Shot Fouls Drawn and Three Point Fouls Drawn. The resulting number will be only slightly more accurate than Points Per Weighted Shot, but why not be more accurate when you can.

**Results**

To close here are some examples of Points Per Ended Possession compared to its other scoring efficiency counterparts. These numbers are from individual games — specifically from November 20th’s Rockets-Mavericks match up and November 21st’s Thunder-Clippers game — because there is no Two Shot Fouls Drawn and Three Shot Fouls Drawn statistics readily available to pull from the internet. Basketball-Reference does not keep these statistics and while NBA.com has them available in their game to game play-by-play (where I got the numbers from) they do not actually compile the numbers themselves — and the NBA does not allow access to any of their data for personal, professional, or academic use. Hoopdata could also be keeping these numbers — they already keep track of And Ones — but as of now do not keep these statistics (though I am hoping they will some day). So I can only use this extremely small sample size, but it should get the job done. Here are Kevin Durant and Russell Westbrook’s scoring numbers from last night’s win against Clippers and James Harden and Dwight Howard’s numbers from Wednesday’s loss against the Mavericks:

FG% | eFG% | TS% | PPWS | PPEP | |

Kevin Durant | 0.53 | 0.58 | 0.61 | 1.2 | 1.23 |

Russell Westbrook | 0.38 | 0.38 | 0.41 | 0.81 | 0.86 |

James Harden | 0.43 | 0.5 | 0.61 | 1.2 | 1.21 |

Dwight Howard | 0.75 | 0.75 | 0.76 | 1.49 | 1.5 |

Box Scores for Durant and Westbrook and Harden and Howard

There are a few things to note here. Mainly we can see how Kevin Durant and James Harden actually had similarly efficient shooting nights even though Durant shot a much better percentage from the field and had a better Effective Field Goal Percentage. This is because Harden went nine for 11 from the line in is his game while Durant struggled a little bit only going six for nine. Also, we can see that True Shooting Percentage, Point Per Weighted Shot, and Points Per (non turnover) Ended Possession produce very similar numbers — with True Shooting percentage being around half of PPWS and PPEP. This again highlights the fact that these numbers are essentially the same. But, again, Points Per (non turnover) Ended Possession is slightly more accurate because it does take the last little bit of guess work out of the equation. For instance Durant had two and ones in his game while Harden had only one. So while using an arbitrary .475 factor with free throws left the numbers even with Points Per Weighted Shot, Durant got the slight edge with the true ended possession number because their is no redundancy of counting one of his and one in both the field goal attempt and free throw attempt category. It is a little thing but it makes the numbers that more accurate.

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