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Love and Mathematics

tziller posted 9/8/2007 from ballhype.com

Last week, Carter Blanchard of Plissken at the Buzzer gave a spirited (and well-received) refutation of John Hollinger's PER, as well as a major tenet of the APBRmetric methodology (the per-minute statistic). On numerous counts, Carter slapped the baby on its ass -- namely, his assertion that 'using any one measure to fully describe a player is fool's work' is golden. Carter endorses looking at the full stat line in analyzing a player's contributions performed and expected. I heartily agree.

But Carter's claims that PER and per-minute statistics equate largely to 'nonsense' are off-target. He says combining numbers, in many cases, serve to obfuscate truth, using the example of Ike Diogu's 19.3 points-per-40-minutes in comparison to the algebraically identical statistic that Ike scored 7.2 points per 13.1 minutes (which happens to be his minutes per game). (Carter says Ike scores 22-per-40, which he did in Golden State. His full-year p/40 was 19.3.) Why do we use the per-40 stat in lieu of per-game? Quick: tell me who's a more prolific scorer, Ike Diogu or Danny Granger. Last season, Granger scored 13.9 points per game (to Diogu's stated 7.2 points per game). Granger played 34 minutes a contest, Diogu 13.1 minutes. You need offense, your options are Diogu and Granger. Pick one.

Looking at points per game and minutes per game, who do you pick? It's cloudy, right? Unless you look to a per-minute figure... where Diogu clearly outshines Granger (19 p/40 to 16.4 p/40). Carter writes "most players don't get buried on the depth chart without a reason." Using this reasoning would insinuate NBA coaches all know what they are doing -- that Granger, Troy Murphy and Mike Dunleavy are all better than Diogu because they all got more minutes from Rick Carlisle than Ike did. Anyone willing to agree with that statement? Me and my two buddies here thinks that's pretty damn funny.

We use per-minute statistics because we don't trust NBA coaches. Relying on per-game -- a minutes-dependent metric -- relies on the assumption NBA coaches make the correct rotational decisions. It's not a bold statement to reject that thinking... and if it is, people should stop criticizing Carlisle, Doc Rivers, Flip Saunders and every other coach that gets killed by fans every single season. On the surface, it's not Ike's fault Troy Murphy got more than double the minutes he did in Indy. When given the opportunity, Ike scored his ass off (something Indy surely needed, with the worst offense in the league). This we know -- the numbers tell us so. Taking Carter's '7.2 per 13.1' and altering it to '19.3 per 40' doesn't obfuscate, it provides ease of comparison. We aren't saying Ike will ever or should ever get 40 minutes per game -- it's a reasonable standard measure to help quick comparisons and quick recognitions. Based on my countless internal references to per-40 numbers, I can tell you 19 p/40 is pretty darn good, but not elite. I could've told you last summer (and did) Kevin Martin would be a tremendous scorer if given minutes, based on looking at his per-40 rates. Of course, per-40 rates don't tell you everything -- in some cases (such as rebounding), they aren't even the best measure of comparison. (That'd be rebound rate, which is so far removed from minutes-dependent I'd expect mutiny from those endorsing per-game numbers.) But as a part of both quick-look comparisons and in-depth qualitative judgment, they are key and much more lucid than per-game or raw statistics.

Which brings us to the ultimate kitchen-sink statistic, Hollinger's PER. I'm not the biggest fan of PER, actually -- like Carter, I endorse using a number of numbers in analyzing a player's contribution -- scoring rate, scoring efficiency, rebound rate, plus-minus, various on-off comparisons, usage rate, assist rate, turnover rate, block and steal percentages, etc. PER is, essentially, all of things wrapped into one. That makes it messy, it makes it complex. Honestly, it makes it so messy and complex it's hard to get more than one qualitative figure out of it. Luckily for those who like PER to some degree, that qualitative figure we can get from it happens to be an important one: quality.

PER tells us who did good and who did bad, regardless of what the player's coach thinks of him. I could go on for kilobytes explaining how this is valuable or lining up example after example of the usefulness of having a sensical metric which quickly reveals a measure of minutes-independent quality. It doesn't tell you who is a good defender, and the fact it includes any defensive stats at all actually cloud things. (Many in APBRmetrics have endorsed 'Offensive PER' -- a stat much like PER but with steals, fouls and blocks removed since PER is not a credible measure of defensive ability anyway.) And of course, PER can overrate players (including Carter's examples of Earl Boykins and Bernard Robinson, who fared better than Lamar Odom in the measure last year). Like any stat, PER can be fooled. Boykins' scoring tear in weaponful Denver boosted his PER into the above-average category when his Milwaukee malaise was much more telling. Bernard Robinson played less than 300 minutes, and no statistic for any player at less than 1,000 minutes in a season should ever really be trusted... including PER. Lamar Odom is better than both Robinson and Boykins, every basketball fan knows this to be fact. But Boykins is no slouch offensively. He scores often, creates a ton of shots with turning the ball over and shoots fairly efficiently (when you consider how many shots he takes from deep). Various individual stats (usage, scoring per-minute, effective field goal percentage) tell us this; PER sums it up. Now look at minutes per game (21 for his career) and points per game (9.8) and tell me Earl Boykins is a really good offensive player. And then score one for PER.

No one statistic is ever going to be the be-all-end-all Holy Grail of individual measures. Hollinger nor his acolytes/peers have never come close to claiming PER is that golden chalice. But when you endorse raw numbers instead of PER and then tell me "most players don't get buried on the depth chart without a reason," you're begging for this (admittedly unfair, but nonetheless cogent) graphic: 

PER isn't the final answer, but it's damn sure better than the alternative.