« My Hero | Main | Obama, Tables, Health Care »

March 24, 2007

Rate States vs Cumulative Stats

by Nicholas Beaudrot of Electoral Math

Comparing the top performers in WP-48, which is a rate statistic, to the top-PER performers, which is dependent upon playing time (as well as how many opportunities your coach and teammates give you handle or shoot the ball), is definitely an apples-to-oranges comparison, roughly akin to comparing total rushing yards with yards-per-carry. A better comparison would be the All-PER team to the All-PAWS team, which consists of either Jason Kidd, Kobe Bryant, Kevin Garnett, Dirk Nowitski, and Marcus Camby; or Kidd, Kobe, Shawn Marion, Garnett, and Camby (Dirk is the only "power forward" in the top 30). Just eyeballing things, the all-PER team scores more (except at the 2-guard), while the all-PAWS team does more "other stuff" (rebounding, fewer turnovers, etc.) while still scoring at a healthy clip. Update: a commenter points out that PER is in fact a rate stat. Surprising, because I've rarely seen PER formula put a high-quality bench player was as effective as many starters (Zach Randolph in '02-03 is one of those cases). PER seems to downgrade David Lee and his off-the-chart field goal percentage because he only scores 17.5 or so points per 48 minutes, compared to 27 for Garnett and 36 for Yao Ming (!).

As for game-to-game consistency, there's always the old "hot hand" paper, and the fact that a single game's sample size is too low to glean any real information. Given 18 shots in a game, it's impossible to tell the difference between someone who shoots 45% and someone who shoots 47%. It's highly unlikely, therefore, that shooting performance in game n has any meaningful correlation with shooting percentage in game n+1, though obviously Real Data would be nice.

March 24, 2007 | Permalink

Comments

PER is not dependent on playing time because it's adjusted for minutes played. And all basketball stats are, to some degree, dependent on how much a player is allowed to handle the ball, right? The main difference is that PER doesn't claim to be able to explain wins (which is logical, because systems based on boxscore stats lack too much information about the defensive side).

Posted by: Carlos | Mar 24, 2007 1:22:09 PM

Since when does Big Media Matt post here...?

Posted by: Thlayli | Mar 24, 2007 1:48:13 PM

PER is playing-time adjusted? Really? Does David Lee come close to the PER leader boards? I mean, his season is just off the charts in so many ways, notably FG%, that he ought to show up there ... ditto Zach Randolph when he wasn't a starter, etc.

I have been staring at the formula trying to figure out why this is. My gut says that PER ends up being a rate stat by accident, but I'm having a hard time demonstratin g it.

Posted by: Nicholas Beaudrot | Mar 24, 2007 2:12:55 PM

I'm having a hard time demonstrating it

Maybe it's too obvious :). Unadjusted PER is simply a sum of the individual values of each of a player's statistical events, with the whole thing divided by minutes played. That last bit is crucial ;).

D Lee is currently 34th for the season.

Posted by: sidereal | Mar 24, 2007 6:33:25 PM

And as to the lack of small-denominator outliers in PER, it could be because it aggregates a large number of individual events, reducing the chances of outliers. Meaning you couldn't just come off the bench and bomb 3s for 5 minutes. You'd have to bomb 3s and hand out assists and get rebounds and avoid turnovers etc, which greatly reduces the chances of a large numerator in a small amount of time.

Also, it could be taken as evidence of meritocratic distribution of playing time in the NBA. It looks like players who make consistent positive contributions are given a lot of playing time.

I'm trying to think of counter-examples. . probably players in their declining years who don't have the endurance to play a lot of minutes but contribute when they're in. Shaq's probably the best current example. He's playing 26 minutes a game and is 16th in PER.

Posted by: sidereal | Mar 24, 2007 6:45:08 PM

It could also be that the KB leaders list has a minutes cut-off. Kyle Lowry for example has a PER of 18.6 but he doesn't show up on the leader list because he's only played 175 minutes.

The important thing to remember about PER is that it is a rate stat, but it isn't really an efficiency stat. It measures how much a player does (good and bad), which gives credit for efficiency but it really just total production. So David Lee gets credit for being efficient but not as much credit as another player that did more less efficiently.

Posted by: NickS | Mar 25, 2007 3:04:43 PM

The simple answer: you use both. Everyone at FO uses DVOA and DPAR in tandem to discuss players, because otherwise you miss significant things (like 2005 Roethlisberger being dismissed because of his low stats/DPAR, but DVOA (per play) tells us that he was a top-five quarterback, but he just didn't have to throw as much as other quarterbacks).

Posted by: Fnor | Mar 25, 2007 4:33:07 PM

Yeah, Knickerblogger's site uses a cutoff for his leaders's list (It's the meaning of the Q column, the one with the Y or N in it)

Posted by: Carlos | Mar 26, 2007 12:22:34 AM

The answer on PER is that PER gives you credit for the share of the team's work that you perform on the floor. That is, if Dirk Nowitski takes 40 shots while everyone else on the floor takes 60, and LeBron James take 35 shots while everyone else on the floor takes 65, then Dirk is better than LeBron in PER, all things being equal, but they show up as equal in WP48.

Posted by: Nicholas Beaudrot | Mar 26, 2007 1:07:35 AM

托盘
托盘
钢托盘
钢制托盘
塑料托盘
木托盘
木制托盘
纸托盘
木塑托盘

托盘
钢托盘
钢制托盘

托盘
钢托盘
钢制托盘
塑料托盘
托盘

托盘
钢托盘
钢制托盘
钢托盘
木托盘
钢制托盘
托盘
塑料托盘

托盘
钢托盘
钢制托盘

托盘
钢托盘
钢制托盘
塑料托盘
木托盘
南京托盘
南京钢托盘
上海托盘

托盘
钢托盘
钢制托盘
塑料托盘
木托盘
南京托盘
南京钢托盘
上海托盘

托盘
钢托盘
钢制托盘
塑料托盘
木托盘
纸托盘
南京托盘
上海托盘
北京托盘
广州托盘
杭州托盘
成都托盘
武汉托盘
长沙托盘
合肥托盘
苏州托盘
无锡托盘
昆山托盘

托盘
钢托盘
钢制托盘
塑料托盘
木托盘
纸托盘
南京托盘
南京钢制托盘
南京钢托盘
上海托盘
北京托盘

托盘
托盘
托盘
托盘
钢托盘
钢制托盘
塑料托盘
塑料托盘
塑料托盘

托盘
塑料托盘
钢托盘
钢制托盘
铁托盘
托盘
钢托盘
铁托盘
钢制托盘
塑料托盘

托盘
钢托盘
铁托盘
钢制托盘
塑料托盘
托盘
钢托盘
铁托盘
钢制托盘
塑料托盘

托盘
托盘
钢托盘
钢托盘
铁托盘
铁托盘
钢制托盘
钢制托盘
塑料托盘
塑料托盘

托盘
钢托盘
铁托盘
钢制托盘
塑料托盘
托盘
钢托盘
铁托盘
钢制托盘
塑料托盘
托盘
钢托盘
铁托盘
钢制托盘
塑料托盘

托盘
钢托盘
铁托盘
钢制托盘
塑料托盘
托盘
托盘
托盘
钢托盘
铁托盘
钢制托盘
塑料托盘

托盘
钢托盘
钢制托盘
铁托盘
塑料托盘
木托盘
木制托盘
纸托盘
木塑托盘
柱式托盘
波纹托盘
镀锌托盘
南京托盘
上海托盘
北京托盘
广州托盘
托盘
钢托盘
钢制托盘
铁托盘
塑料托盘
木托盘
木制托盘
纸托盘
木塑托盘
柱式托盘
波纹板托盘
镀锌托盘
南京托盘
上海托盘
北京托盘
广州托盘

托盘
钢托盘
钢制托盘
铁托盘
塑料托盘
木托盘
木制托盘
纸托盘
木塑托盘
柱式托盘
波纹托盘
镀锌托盘
南京托盘
上海托盘
北京托盘
广州托盘
托盘
钢托盘
钢制托盘
铁托盘
木托盘
塑料托盘
木塑托盘
柱式托盘
波纹板托盘
镀锌托盘
南京托盘
上海托盘
北京托盘
广州托盘

托盘
钢托盘
钢制托盘
铁托盘
塑料托盘
木托盘
木制托盘
纸托盘
木塑托盘
柱式托盘
波纹托盘
镀锌托盘
南京托盘
上海托盘
北京托盘
广州托盘
托盘
钢托盘
钢制托盘
铁托盘
塑料托盘
木托盘
纸托盘
木塑托盘
柱式托盘
波纹板托盘
镀锌托盘
南京托盘
上海托盘
北京托盘
广州托盘


托盘
钢托盘
钢制托盘
托盘
塑料托盘

Posted by: judy | Sep 27, 2007 3:22:59 AM

The comments to this entry are closed.