If you don't take three-point shots into account, you cannot judge basketball players' relative scoring ability.
OK, so there are lies, damn lies and statistics. Still, we use statistics all the time in sports: ERA, batting average, on-base percentage, yards per carry, completion percentage, free-throw shooting percentage, rebounds per game, field goal shooting percentage.
The last three are from basketball, and two of them, if not damn lies, at least don't actually show what they imply.
Let's start with the easy one: rebounds per game. This is one of very few statistics in the three major sports that is presented without qualification; it is presumed to show how good a rebounder a player is.
In baseball, we don't show hits per game, we show hits per time at bat, commonly called batting average. In football, we may show total yards gained, but that is accompanied by yards gained per carry.
But in basketball, we only get rebounds or points per game, not the much more informative points or rebounds per minute played.
And that brings us to the second statistic which is extremely misleading: shooting percentage. The problem is that some shots are worth two points and some are worth three.
A player who takes mostly three-point shots and averages 39% is a better scorer than one who shoots 51% and only shoots twos.
One way to present a meaningful statistic would be points per shot. But I propose a different and more insightful, though equivalent, measure that I call ESP---Equivalent Shooting Percentage. Bear with me.
The ESP is the percentage of two-point shots a player would have to make to score as many points as he gets with his total number of twos and threes.
For example if Joe Johnson shoots 40 for 100, his "shooting percentage" is 40%. If 50 of those shots taken were three-point shots, and if he made 30% of those, he would have scored 95 points total in his 100 shots. His points per shot would be 0.95, and his ESP would be 47.5%.
For players averaging 10 points per game or more, the leading shooter in the NBA this season (as of 3/7/11) is Nene Hilario of Denver. His shooting percentage is 63%, and since he doesn't shoot any three pointers (1 for 4 this year), his ESP is also 63%. Nene averages 15 points per game.
The leader among those who score more than 16 points per game is Dwight Howard of Orlando; his shooting percentage is 60% and he also doesn't shoot any threes, so his ESP is 60%. Howard averages 23 points per game.
Kevin Durant is the leading scorer in the league, based on points per game. His shooting percentage is 46%. He shoots a little more than five three-point shots per game, making 34%, and his ESP is 51%. His shooting percentage for two-point shots is 50%.
His scoring is balanced; he is taking the right percentage of each type of shot.
LeBron James is the second leading scorer; he averages 50%, with an ESP of 52%. Again, this is very close to the proper balance.
When it comes to the best shooters on a points per shot basis, or equivalently those with the best ESPs, not many surprises turn up. Dirk Nowitzki shoots 53%, with an ESP of 56%. But Ray Allen of the Celtics takes first place among the NBA marksmen.
He shoots 50%, with a spectacular ESP of 59%. It is interesting to note that if Ray Allen took only three-point shots and made them at the same 46.7% that he has so far this year, his ESP would be an amazing 70%. Since his shooting percentage on two-point shots is 53%, Allen should attempt more three-point shots.
Just as a footnote to Allen, his teammate Paul Pierce shoots 50%, with an ESP of 56%. His 2 point shooting average of 55% means he takes about the right number of threes.
And as a footnote to the footnote, Shaquille O'Neill, oft injured and averaging just nine points per game when he does play, is the undisputed leader this season in both shooting percentage and ESP at 66%. Maybe that's what happens when you play beside Paul Pierce and Ray Allen.
There should be a lesson for coaches in this mathematical morass: many players should attempt more three-point shots; and some should shoot fewer. In fact, let's take the case of Joe Johnson (the real Joe Johnson of the Atlanta Hawks, not the fictitious Joe Johnson of the first paragraph).
His shooting percentage is 44%, and his ESP is 48%. He makes 50% of his two-point shots. He should shoot fewer three pointers.
On the other hand, Daniel Gibson of the Cleveland Cavaliers has a shooting percentage of 40% and an ESP of 49%. In fact, Gibson shoots three pointers at a higher percentage than two pointers. He should never venture close to the basket.
The NBA should publish percentages for two-point shooting, three-point shooting, and ESP (or points per shot), so that coaches and fans can better judge the scoring potential of each player.
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