Posted: Fri Oct 26, 2007 3:39 pm Post subject: Are top-rated point guards under-rated by PER?
First of all, there is no question that summary stats like PER have value. They are easy to read, incite discussion among fans and help promote the game. They also have some use on the analytical side, where they can be helpful in tracking an individual's career development. Suppose a player's scoring drops three points a game, but his offensive rebounding and scoring efficiency increase. Is he still as valuable to the team, or has he begun to decline? In providing a rough summation of a player's contributions, PER offers a reasonable starting point for answering this kind of question.
However, when it comes to comparing players - especially, players with different roles - this type of stat can be very misleading. After all, it's possible that a logic based system might do a solid job of comparing the value of free throw to that of a field goal or even estimating the value of an isolated event like a steal. But, how do you "logic out" the value of an individual defensive rebound or an assist? You can't. Those kinds of questions require more than logic; they require research.
This is the problem. Although, a rational stat like PER might appear to be scientific, the best it can really do is mimic the opinions of its author. Those opinions may be well informed and the formula may be well thought out. But, concrete answers require empirical evidence.
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Okay, are point guards under-rated by PER? I think they are ridiculously under-rated.
Let's start with the basic: how much is an assist worth? For each assisted field goal PER assigns one-third of the credit to the assister and two-thirds of the credit to the scorer. The rationale behind this is that the play maker has done one thing (pass), while the finisher has done two things (get open and make the basket.)
But, is that a reasonable basis upon which to assign weights?
Dwyane Wade drives through the paint and begins his upward trajectory to the rim enticing both his own defender and the weak side help to leave their feet. Then, at the last instant, Wade flips the ball behind his back to Udonis Haslem for a quick little, jack-knife slam. Wade is credited with an AST, Haslem with a FGM and the PER translation is one-third credit to Wade, two-thirds credit to Haslem. But, Wade has utilized a rare talent, while Haslem has simply completed a play that should be routine for any competent NBAer. Wade clearly deserves more of the credit in this sequence.
To Hollinger's credit, he acknowledges this as a problem in the introduction to PER. Unfortunately, rather than dealing with the issue empirically, he defends the weights by stating that "point guards are not under-represented among the top-rated players." Well, if there is evidence to that affect, perhaps it would be a defense, but (as far as I know) no evidence is offered. It seems as if the "galvanizing" evidence is simply that PER succeeds in echoing Hollinger's opinion on the value of point guards.
Now, checking your output against expert opinion is certainly worthwhile. But, rather than just rely on just the author's opinion, let's see how PER's assessment of top-rated point guards stacks up beside some objective expert opinion.
Ten point guards made the Hall of Fame's "NBA's 50 Greatest Players" list. Here they are along with their best single season PER (pre-1988 PERs are taken from the estimates at http://www.basketball-reference.com/about/per.html.)
Code:
Player MaxOfPER
Nate Archibald 25.2
Dave Bing 22.5
Bob Cousy 21.6
Walt Frazier 21.6
Magic Johnson 27.0
Earl Monroe 19.3
Oscar Robertson 27.6
John Stockton 23.9
Isiah Thomas 22.2
Lenny Wilkens 20.3
The base PER is 15.0, so those are fairly high numbers. But, considering that the season best PER over the past twenty years has averaged 29.8, are they high enough? Here is where each HOF point guard's best season ranks among the best PER seasons of all players at all positions.
Code:
Player Rank of best single season PER
Nate Archibald 137th
Dave Bing 378th
Bob Cousy 492nd
Walt Frazier 504th
Magic Johnson 65th
Earl Monroe 1,038th
Oscar Robertson 55th
John Stockton 222nd
Isiah Thomas 404th
Lenny Wilkens 753rd
And, here are some newer additions based on ESPN.com "10 greatest point guards of all time."
Code:
Jason Kidd 375th
Steve Nash 228th
Gary Payton 252nd
I'm not a fan of the "smell test", but that seems to be the basis of validation for logic based, summary stats, so let's check the aroma from PER's ratings of elite point guard.
McGrady, Wade (twice), Nowitzki (twice), Kobe and LeBron have all registered PERs at least one to three points higher than any of Magic Johnson's MVP seasons. Magic Johnson. Magic.... Johnson.
After Magic and Oscar - who get a lot of PER for being the two top rebounding point guards of all-time - things get really hairy (btw, according to B-R.com the top five rpg guards (no G-Fs) of all time are... Oscar, Magic, JKidd, Fat Lever and Walt Frazier... all point guards. Oscar and Magic both averaged better than one rebound a game more than MJ or Clyde Drexler.) All right, continuing...
Amare Stoudemire and Elton Brand both have PERs which rank among the top one hundred of all time, while John Stockton can't crack the top two hundred... Isiah Thomas and Clyde Frazier can't even crack the top four hundred. You might convince me that Karl Malone should rank ahead of John Stockton, but PER is telling me that Elton Brand (26.5) is a much more valuable player than John Stockton (23.9) or Isiah (22.2). Really?
Bob Cousy's best PER was 21.6 placing him in a tie for 492nd place with, among others, -- Larry Hughes. Yes, the same Bob Cousy who was MVP and made first team All-NBA ten consecutive seasons. Let's see Cousy or Hughes? Hughes or Cousy...? Well, at least Cous gets more respect than "50 Greatest of All-time" teammate Earl Monroe. Earl the Pearl's best PER weighs in at one thousand and thirty eighth -- same spot as Ruben Patterson and Matt Harpring.
If PER does not under-rate elite point guards then the history of the NBA needs a serious re-write.
Joined: 27 Jan 2005 Posts: 530 Location: cleveland, ohio
Posted: Fri Oct 26, 2007 5:03 pm Post subject:
Bob Cousy's best PER was 21.6 placing him in a tie for 492nd place...
i'm certainly not saying bob cousy was not a great basketball player - he was. but if you are looking for a statistical reason as to why he doesn't rate higher in a statistically based rating system, one key reason would be his shooting. looking at his best 10 year stretch, say 1951-52 to 1960-61, his FG% was .373 when the league average was .388, and his ScFG% (overall shooting) was .441 when the league average was .444....
during those 10 years he scored 19.7 pts/g, and if you look at the 20 players who averaged at least 17 pts/g during this same time period, cousy had the worst FG% and worst ScFG%...
on the other hand, a PG like john stockton for example, although not the scorer cousy was, did score 15.6 pts/g during his best 10 year stretch, but shot overall a ScFG% that was 8% better than the league average...
The issue of shooting % raises another interesting question about stats like PER as they relate to point guard. PG's, more so than any other position, are likely to take lower % shots with the clock winding down, simply by virtue of handling the ball more. This is not universally true, and I'm not sure how big an impact it would have on shooting %, but it certainly does have an impact. Are PG's to be punished for taking the only available shot late in the clock, even if it is a bad one, rather than risk a 24-second violation and a turnover?
Ive always agreed with what you mentioned about dishing, there is no stat that is more opinionated than the assist as some are clearly worth more than others. I like to give both players equal credit but I know there are cases when the shooter did more of the work and the creator did more.
So yea PER does seemingly underrate PG's but much of what they do is intangible, they are looked upon as leaders but does it really end only at PG's? What about players who rack up alot of assist but are also scorers. Say Joe Johnson vs Michael Redd. JJ is obviously not the scorer Redd is but hes more of an all around threat. Personally I think Redd is the better player I just find it odd that his PER is that much higher than JJ's.
Im curious as to how much better PG's would be rated if they were given 2/3 the credit.
PER formula tends to place scorers high and that may disadvantage pass first or traditional PGs especially those from much earlier eras.
Career PER list for PGs depends on filter, using 20,000+ minutes I see the rank order of Magic, Robertson, Stockton... Iverson, K Johnson, Nash, Cassell, Brandon Cousy,
Price, Marbury, Frazier, Kidd, Payton. Hardaway, Billups, Francis, I Thomas, Rod Strickland Archibald Lever, Terry, Bing, A Hardaway, Porter, Monroe Bibby Wilkens, etc.
Last edited by Mountain on Sat Oct 27, 2007 3:56 pm; edited 1 time in total
Bob Cousy's best PER was 21.6 placing him in a tie for 492nd place...
i'm certainly not saying bob cousy was not a great basketball player - he was. but if you are looking for a statistical reason as to why he doesn't rate higher in a statistically based rating system, one key reason would be his shooting. looking at his best 10 year stretch, say 1951-52 to 1960-61, his FG% was .373 when the league average was .388, and his ScFG% (overall shooting) was .441 when the league average was .444....
during those 10 years he scored 19.7 pts/g, and if you look at the 20 players who averaged at least 17 pts/g during this same time period, cousy had the worst FG% and worst ScFG%...
True. However, very few of those scorers were guards. And the problem is that while Cousy's best PER of 21.6 stacks up well against other point guards, it stacks up poorly against players at other positions. Oscar Robertson's 1960-61 was the only PER by a guard higher than Cousy's 21.6 during the period you define, but there were 53 higher PERs recorded by forwards and centers.
Bob Cousy was the dominant passer and dominant guard for a decade, but his best PER rates 492nd? There must be some reason these point guards were voted among the 50 Greatest players of all-time. PER just doesn't get it.
The issue of shooting % raises another interesting question about stats like PER as they relate to point guard. PG's, more so than any other position, are likely to take lower % shots with the clock winding down, simply by virtue of handling the ball more. This is not universally true, and I'm not sure how big an impact it would have on shooting %, but it certainly does have an impact. Are PG's to be punished for taking the only available shot late in the clock, even if it is a bad one, rather than risk a 24-second violation and a turnover?
That's a good point Conan
Here are a few other reasons elite point guards are under-rated by PER:
1. While the ball is being advanced in the back court and a play set up there is very little good that can happen statistically from the ball handler's perspective. It's generally either a turnover or nothing.
2. The one-third weight given assists is much too low for many elite play-makers because the impact of individual assists on team scoring is distinctly non-linear.
3. There is no allowance for the psychological boost provided by strong floor leadership. It may be difficult to quantify, but, in a fast paced game like basketball where it is impossible to maintain one hundred percent effort every second of every game, motivation is a huge factor. This responsibilty often lies primarily with the point guard and, just as in every walk of life, some ball players are simply more inspirational than others.
4. I can hear the teeth gnashing over number 3, so here is one that may hold more appeal to people focussed strictly on manipulating traditional stats.
PER assumes that each shot has the same likelihood of being assisted as the team's over-all AST/FGM rate. However, point guards typically have a lower percentage of their shots assisted than the team average.
For example, 63% of Phoenix' baskets were assisted. So, PER assumes that 324 of Steve Nash's 517 made field goals benefited from an assist. But, according to 82games.com, only 23% (or 119) of Nash's baskets were actually assisted. Therefore, one-third of the credit for 205 of Nash's baskets went to a "phantom" assister. That's 137 points that should have stayed in Nash's column.
That's a rather large error and, of course, it's not just Nash. B.Davis (26%), Billups (33%), Miller (29%), Paul (17%), Ridnour (29%), Arenas (36%) and Parker (33%), as well as a few play-making, non-PGs like Wade (27%) and Iverson (26%) are significantly affected by this. Chris Paul had more than two hundred points siphoned off to teammates for phantom assists.
This obviously works in reverse for players who have a higher percentage of their baskets assisted than the team average.
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PER assumes that each shot has the same likelihood of being assisted as the team's over-all AST/FGM rate. However, point guards typically have a lower percentage of their shots assisted than the team average.
"Another interesting pair is Steve Nash (assisted 20% of the time) and Shawn Marion (73%). By PER, they were basically equivalent per-minute; 21.55 and 21.17, respectively. Add in assists and Nash has a commanding 23.61-20.21 advantage."
PER assumes that each shot has the same likelihood of being assisted as the team's over-all AST/FGM rate. However, point guards typically have a lower percentage of their shots assisted than the team average.
For example, 63% of Phoenix' baskets were assisted. So, PER assumes that 324 of Steve Nash's 517 made field goals benefited from an assist. But, according to 82games.com, only 23% (or 119) of Nash's baskets were actually assisted. Therefore, one-third of the credit for 205 of Nash's baskets went to a "phantom" assister. That's 137 points that should have stayed in Nash's column.
That's a rather large error and, of course, it's not just Nash. B.Davis (26%), Billups (33%), Miller (29%), Paul (17%), Ridnour (29%), Arenas (36%) and Parker (33%), as well as a few play-making, non-PGs like Wade (27%) and Iverson (26%) are significantly affected by this. Chris Paul had more than two hundred points siphoned off to teammates for phantom assists.
This obviously works in reverse for players who have a higher percentage of their baskets assisted than the team average.
Couldn't this be at least partially addressed by determining the average % of baskets assisted for each position, and weight for assist credit accordingly? I know this gets into gray areas about positional definitions (is Wade a PG or SG?), but it seems like it might be a worthwhile endeavor if no one's done it before.
The PERs I got are slightly off from Hollingers and elsewhere, but this is just for a quick example:
nash,steve 23.6
stoudemire,amare 23.0
marion,shawn 20.7
barbosa,leandro 18.3
diaw,boris 12.9
bell,raja 11.9
thomas,kurt 11.4
banks,marcus 11.2
jones,james 10.7
Using assisted rate from 82games.com, I get:
nash,steve 26.0
stoudemire,amare 22.8
marion,shawn 19.8
barbosa,leandro 18.3
diaw,boris 13.2
banks,marcus 12.3
bell,raja 11.2
thomas,kurt 10.9
jones,james 9.8 _________________ a. stat. n00b.
Joined: 14 Jan 2005 Posts: 1747 Location: Delphi, Indiana
Posted: Sat Oct 27, 2007 7:35 am Post subject:
I don't know when the basics of PER were being hatched out, but not that long ago PG's were very well represented in annual player rankings.
Using b-r.com's Player Stats Search, I looked for best PER seasons by PG's. Actually I selected the position "Guard" and looked for seasons with at least 2000 minutes and an Ast/40 rate of >6. This lets in a few Jordan and Wade seasons, but they were defacto points anyway, for many of their minutes.
If PG is an 'underrated' position, then on average there might be fewer than 10 PGs among the top 50 PER's, fewer than 20 among the top 100, etc. Actually, by my operational definition (>6 Ast/40), I've added a positive attribute, and I expect more than 1/5 of any slice to be PG's (so defined).
In the 5-year interval 1988-1992, the 20th best PER among 'PG' was 22.2, while the 100th PER among all players was 19.7. So we might say the positional-median #20 season was 19.7, which was 2.5 PER points lower than the #20 PG season.
At every level, the PER status of point guard has fallen steadily since the late-'80s. I am pretty sure there was just a wealth of talent at the position, until it fell off in the mid-late-'90s. (From '98-'02, there weren't even 100 qualifying PG seasons, and I pro-rated 1999).
John H may have tested his PER formula on the recent past and found plenty of PG's among the best players every year. At that time, perhaps the late '90s seemed like an anomaly that would pass; but in fact, the trend has continued. Top-notch PG's are fewer, and 2nd-tier and middling PG's are in even shorter supply than 10 or 20 years ago.
Note that with expansion, total numbers of players at any PER level have risen. This is part of the PER definition. Counter to that trend, PG PER's have dropped in number. Per-team, that trend is even worse. _________________ 40% of all statistics are wrong.
1. While the ball is being advanced in the back court and a play set up there is very little good that can happen statistically from the ball handler's perspective. It's generally either a turnover or nothing.
Quote:
PER assumes that each shot has the same likelihood of being assisted as the team's over-all AST/FGM rate. However, point guards typically have a lower percentage of their shots assisted than the team average.
The A/FGM and even Assists weights is something that could probably be fixed some day by linear ratings. But about the first point, Ratings compute points and gain/lost possessions translated to points (one final economical result, not the total cost of each part involved in the process). Thereīs no value nor sharing for keeping the possession saved or processing it (ballhandling, the relationship Passing (Pot. assists)/TO, etc.) and thatīs assumed like intangibles (in other words, pont guarding is assumed like intangible). Some ratings adjust for no tangible defense (also pseudo-arbitrary), probably an offense adjust could be also made in this case, but something better and wider than "overall A/FGM rate". At least PERīs usage is a step ahead from others ratings.
I don't have much background in statistics, but I too have thought PG are underrated by PER. I've wondered why you guys don't consider factoring in team stats into your individual evaluation.
To me there is a stat that doesn't really exist for PG but is critical to their evaluation
If you watch the Suns, Nash holds the ball for an inordinate amount of time during a teams's possesion. As a result he accumulates a lot of assists and turnover BUT his teams are perenially among the lowest in Turnovers. Shouldn't he get dome sort of statistical brownie point for that.
Ideally there would be a stat that somehows incorporate team offensive effeciency and TO per time the ball is in a player's hand.
IMO there is a chance that Hollinger's dictum that players can't make other players better is wrong. From what I remember he used PER to make that assertion, but in my opinion the equation for PER has some potential ways of masking this phenomenon of "making teammates better". I'd love to see Hollinger repeat his study b/c I suspect guys who maintain the same PER with different PG might see an increase in their own TO, which is masked by their increase in usage rate. If a PG reverses those two stats isn't he really making others better, even if they maintain the same PER.
Couldn't this explain why the AI to Denver experiment didn''t work the way he expected. After all isn't there only so much "usage rate" to go around. I would expect the aggregate usage rate of teams across the NBA to be pretty universal regardless of personnel. Isn't their value to the PG playing alchemist and figuring out who to distribute to in hope of finding gold (i.e higher tema percentages lower TO, something that wouldn't be attributed to the PG in PER)
I'm curious to know how statistician feel about this.
Joined: 30 Apr 2006 Posts: 225 Location: Pleasanton, CA
Posted: Sat Oct 27, 2007 2:34 pm Post subject:
I think you're definitely on to something when you talk about how players can influence each other in multiple ways -- such as decrease turnovers but decrease usage rate as well. Too often people focus on one aspect and then make an overall claim.
I think Hollinger is still more right than wrong about the "making players better" argument because it is ultimately too simplistic. Players influence each other in a lot of ways and it's usually not a simple better or worse outcome.
Shaq gives you better shots but fewer of them. He's not making you better or worse as much as he's changing your role. Joe Johnson left the Suns for Atlanta and his shooting percentage went down but his usage went up. His role changed.
If you took a terrible player and substituted him in for Kobe Bryant a lot of the Lakers would get better because they'd suddenly have a lot more possessions to use their talents. But you'd never see that terrible player get credit for making his teammates better.
Mike I wonder what your PG vs all positions comparison thru time would show on assist/40 for PGs and for 3 point shot frequency and accuracy for PGs and everyone thru the distance changes and perhaps also FTAs for each thru changes in handcheck enforcement if that can be segmented agreeably.
Did the 3 point shot and the increase in the number of players who could take them proficiently make PGs somewhat less valuable as a passer? Has it cut into their usage?
Does the decline of post players also contribute to a decline in PG PER value from assists?
Would you have interest in breaking out the parts of the PG PER decline?
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