In honor of Dirk: ‘Points Per Miss’ and his spot among the NBA’s all-time greats

Last night, Dirk Nowitzki turned in one of the most mind-bogglingly awesome individual basketball performances I have ever seen. As I tweeted near the end of the game: “Nowitzki is German for un-fucking-believable. Sometimes, only the f-word will do.”

Here are the raw numbers: 48 points, 6 rebounds, 4 assists, 4 blocks in 41 minutes. As impressive as those numbers are by themselves, they do not even begin to tell the story of just how close to perfect a basketball game Dirk played last night.

Here are the most impressive numbers: 12-15 from the field, 24-24 from the free throw line. Feel free to re-read those numbers a few times to ensure that they sink in.

As Bill Simmons tweeted: “48 points, 3 missed shots total (FG + FT). We need a stat like ‘points per miss’ to see if that’s a record for a 40+ point game.”

For the evening, Dirk’s “points per miss” (or PPM as we’ll refer to it henceforth) was 16. 16! 16 points for every missed shot. That is astounding, and it is a terrific way to appreciate what was one of the best single-night shooting performances on any level of basketball ever.

And as I went to bed last night, Simmons’ tweet had me thinking. Just how useful of a stat would PPM be? So I decided to get up this morning and investigate it a little further.

dirk-nowitzki-points-per-missImage source: AP Photo/Tony Gutierrez via

Points Per Miss (PPM)

First off, let’s assess what we’d hope to ascertain by comparing players’ PPM values.

By analyzing the number of points a player is able to score for every shoot he misses, we are assessing one component of his offensive efficiency. There are a number of ways to do this already, and PPM would simply add another layer to how we view a player’s worth to his team.

Specifically, because a missed shot equates to a missed scoring opportunity that could have perhaps been capitalized on by another player, PPM should give us some measure how efficient a player turns the shooting opportunities he takes for his team into points.

Points per game is an oft-cited stat, but it provides little in the way of efficiency. A player could score 40 points per game and lead the league, but if he just does it because he chucks up half of his team’s shots, his team probably is not very good or balanced on offense. Another player who scores only 25 points per game but who is highly efficient at turning shooting opportunities into points is maximizing his own scoring chances while, theoretically, not wasting his team’s scoring opportunities shooting lower percentage shots (by comparison) than what his teammates could get.

Obviously it is all relative, and the composition of a team goes a long way to determining who should be shooting and how often, so in no way am I positing that PPM can be anything close to a be-all, end-all comparative stat. But I do think it can be both fun and illustrative, especially at the superstar level, so let’s dig into the numbers.

Plus, looking at the average PPM numbers for the greatest players in history of the game will give you even more of an appreciation for last night’s ridirkulous performance in Dallas.

PPM in 2010-11

Here are the top 23 scorers in the NBA this season (based on total points scored during the regular season) ranked in order of their PPM:

Player TP FG Missed FT Missed PPM
Dirk Nowitzki 1681 569 48 2.724
Paul Pierce 1511 514 63 2.619
Pau Gasol 1541 527 76 2.556
Kevin Love 1476 544 75 2.384
Kevin Durant 2161 827 81 2.380
LeBron James 2111 727 160 2.380
Kevin Martin 1876 714 75 2.378
Chris Bosh 1438 532 87 2.323
Amare Stoudemire 1971 738 124 2.287
Dwyane Wade 1941 692 158 2.284
Dwight Howard 1784 425 370 2.244
LaMarcus Aldridge 1769 708 93 2.208
Zach Randolph 1504 590 96 2.192
Brook Lopez 1673 665 104 2.176
Carmelo Anthony 1970 819 98 2.148
Derrick Rose 2026 886 79 2.099
Al Jefferson 1528 665 69 2.082
Kobe Bryant 2078 899 100 2.080
Russell Westbrook 1793 776 100 2.047
Danny Granger 1622 725 71 2.038
Luol Deng 1430 624 83 2.023
Blake Griffin 1845 680 249 1.986
Monta Ellis 1929 885 91 1.976

As you can see, Dirk’s performance last night should not come as a complete surprise considering that he led the top scorers in the NBA in points per miss. More on the big German in a minute.

First, a few observations about the above chart:

  • Paul Pierce is much higher than I thought he would be, and this makes me appreciate his game more. Pierce took almost 300 3-pointers this season, but still managed to shoot almost 50% from the field while shooting 86% from the line. Not only does this show how well-rounded Pierce’s game is, it also shows the impact that a balanced offense and a good, pass-first point guard can have. The Celtics have many good players, so one player does not have to chuck up shot after shot for them to have a chance to score. Instead, the C’s can work the ball to get good, high percentage shots, and Pierce took great advantage of this. Ray Allen was not among the league’s top 23 scorers, but his surprisingly high PPM (2.521) for a guy who shoots a lot of threes is a testament to the Celtics stars’ shooting ability and keen shot selection.
  • Kobe Bryant is below Al Jefferson. That’s not good. It is illustrative, I think, not only of Kobe’s modus operandi as a high volume shooter but also his declining skill set and athletic ability. His inability to get to the basket and get easy shots, most notable during the sweep against Dallas, results in him taking more difficult jumpers and therefore missing more shots than he used to. For comparative purposes, Kobe’s career PPM is 2.140.
  • Some (though certainly not all) of the guys near the top of the list are older vets while the guys at the bottom of the list are younger players. This suggests to me that PPM is a decent indicator of a players’ relative strengths in the area shot selection, which is partly a function of experience. At the top of lists are vets like Dirk and Pierce while young guys like Blake Griffin and Monta Ellis are at the bottom of list. I’m not saying it’s a perfect indicator of shot selection, but it’s in the stew, so to speak.

Now back to Dirk.

A big part of Dirk’s offensive efficiency is his superb free throw shooting, which this PPM stat takes into account*. Dirk is an 87.7% free throw shooter for his career, which is outstanding, especially for a guy who stands 7-feet tall. And free throw efficiency should play a part in telling the story of a player’s overall offensive efficiency, which is one reason I like this stat.

* – I should mention at this point that I realize for this stat to be better there should probably be some kind of weighted adjustment to more accurately incorporate field goal attempts, worth two or three points, and free throw attempts, worth one point, into the same stat. I’m not smart enough to figure out exactly how that should go to make this stat more accurate, but I’m open to anyone’s ideas in the comment section.

UPDATE: After taking into account the bevy of excellent reader comments below, we have updated the PPM formula.

Let’s take a guy like Shaquille O’Neal. He was clearly a very efficient offensive player, but think how much more efficient he would have been had he converted just 60-65% of his free throw attempts, or if he had never been fouled in the first place and could have instead had more non-free throw attempts at the basket. Shaq getting fouled and going to the line for two shots resulted in at least one missed shot almost half the time. A guy like Dirk, on the other hand, has no shooting black holes like Shaq. Therefore, his efficiency at turning scoring chances into points is even better than a guy like Shaq’s because Dirk has no weakness that consistently turns into missed shots and, most likely, into the other team’s possession.

For his career, Shaq averaged 23.7 points per game. Dirk averages 23.0 points per game. Yet Dirk has a 2.386 career PPM while Shaq has a 2.127 career PPM. The difference in their case is mostly due to free throw shooting.

PPM and the All-Time Greats

And while we’re on the subject of all-time greats, which certainly both Dirk and Shaq are, how do their career PPM numbers stack up against the best scorers in the history of the game? Here are a handful of the best players ever and their career PPMs.

Player TP FG Missed FT Missed PPM
Kareem Abdul-Jabbar 38387 12470 2592 2.549
Dirk Nowitzki 22792 8755 797 2.386
Larry Bird 21791 8743 511 2.355
Michael Jordan 32292 12345 1445 2.342
Oscar Robertson 26710 10112 1491 2.302
Karl Malone 36928 12682 3401 2.296
Kobe Bryant 27868 11658 1365 2.140
Shaquille O’Neal 28596 8127 5317 2.127
Wilt Chamberlain 31419 10816 5805 1.890
Allen Iverson 24368 11439 1793 1.842

Update: I should explained this better when I originally posted. The above list is not top 10 all-time or anything close to it; I just chose a handful of players that I thought would make for interesting comparisons. I need to expand this list to be more inclusive of all NBA greats when I have a bit more time. For example, as a commenter points out, Magic Johnson’s career PPM is actually 2.671, higher than both Kareem’s and Dirk’s, and is yet another measure of just how incredible Magic was.

What is interesting about the table above is that Dirk comes in ahead of Bird, Jordan, and so many others. Does this mean Dirk is a better player than Jordan or Bird? Of course not. But it does mean that he is as efficient a scorer as those two were, if not better. Scoring efficiency only tells one part of the story on one side of the floor, which is why PPM can only be considered a small piece of the puzzle when comparing players, but it is a good way to give one of the most unique scoring talents in NBA history is due.

Mavericks coach Rick Carlisle said last week that Dirk was one of the ten best players of all-time. Most people disagree with this assessment, and I do to. However, had Carlisle instead said that Dirk is one of the ten most efficient offensive players of all-time, I don’t think anyone could argue.

Something else I also found interesting is that the only player of those I analyzed that is above Dirk is Kareem Abdul-Jabbar (Update: and Magic), the NBA’s all-time leading scorer. This is interesting to me because while Dirk and Kareem are different in so many obvious ways, there is one way in which they are very much alike, and it is the reason why they both have such highly efficient offensive games: their go-to shot could not/cannot be guarded.

Dirk Nowitzki’s step-back jump shot is simply unguardable; heck, in many ways any Dirk shot is unguaradable because of his size, high release, and ability to make shots at weird angles. The turnaround or step-back shot is especially tough because Dirk becomes even more unguardable by creating additional space. And he is such a good shooter that he rarely misses. The same was true of Kareem and his sky hook. There was no way to defend it.

Few players in NBA history have go-to moves that literally could not be stopped. This is why Kareem is always someone I think of when trying to compare Dirk’s game to someone else in the NBA history. The truth is that there isn’t anyone in NBA history that I consider to be a lot like Dirk (no, not even Bird), and we should all appreciate his unique greatness now while it is at its peak.

Final Thought on PPM

To wrap up this relatively brief but hopefully fun look at this Bill Simmons-suggested stat, my final thought is that I like PPM, I think it’s fun, and it seems to do a good job of organizing players in terms of their abilities in this specific area, but it faces that same limitations that most single statistics do. It only tells us one aspect of one part of the story, so no argument should begin or end with PPM.

Mostly though, it illustrates just how incredible Dirk Nowitzki’s performance last night was. The guy renowned by almost everyone as the greatest basketball player ever, Michael Jordan, had a career PPM of 2.342. Last night, in one of the biggest games he’s ever played in, Dirk Nowitzki’s was 16.

As I said in my tweet last night: un-fucking-believable.

What do you think of Points Per Miss as a stat? Is it useful? Can it be improved? What does it suggest to you about a player’s abilities?

Chime in below.

(Also, if anyone wants to take Simmons up on researching the top single-game, 40-point PPMs in NBA history, go right ahead. Email me and we’ll post it. I didn’t have enough time so I made my analysis more general.)

Update: Andy Bailey tackled Simmons’ specific question. Not surprisingly, Dirk’s game is head and shoulders above any other high scoring game in playoff history. (Though I think MJ’s 63 against the Celtics is missing.)

About Jerod Morris

I love words. I write for Copyblogger and founded MSF, The Assembly Call, & Primility. I practice yoga, eat well, & strive for balance. I love life. Namaste. Say hi on Twitter, Facebook, & G+.


  1. Kind of messes up the lede when a typo happens to inflate his missed field goals.

  2. As of the time that I’m posting this comment, your article shows his FG numbers as 12-25, not 12-15, which I think is the whole point of this article, no? Still though, fantastic article.

  3. Rusty Shakelford says:

    yea man u messed up. u wrote an entire article with th wrong stats.

  4. I sent you a tweet, but how do you leave off Magic Johnson? 2.67 PPM all while averaging 11 assists and 7 boards a game

    • Great point. Honestly, I was not trying to make a complete list of the all-time greats. Did not have time. Might be a good way to expand the post though. I'm sure there are others who are up there. When I get a little more time this afternoon or tomorrow I'll try to add that.

      • Since you brought up the fact of unstoppable shots, how does Hakeem rank? His dream shake was unblockable and therefore should have a high number. He was also a decent FT shooter.
        And to add to that, consider adding Steve Nash. His 50/40/90 numbers have to make for an interesting comparison. While his overall point production isnt league leading his efficiency should make for an interesting test case.

  5. I think these lists would be best served broken down into position by position as well. Mostly because 4s and 5s are at an overall disadvantage like your argument about an efficient scorer like Shaq getting skewed overall number to the lower side with horrendous FTs and no 3 point chances. And in career breakdowns because I agree when people say its too hard to compare different eras, positions, in best player ever arguments. It IS a fun way to break efficiency down.

    Your 1st Team 2011 NBA All-Efficiency !!! Pretty awesome lineup

    PG- Derek Rose
    SG- Kevin Martin
    SF- Paul Pierce
    PF- Dirk Nowitski
    C- Dwight Howard

  6. The points per miss stat would be more meaningful if it weighted to account for the fact that FTs are worth 1 point while FGs are worth 2 or 3 points.

  7. I'd be interested in seeing what Tim Duncan's PPM is

  8. I really enjoyed this read. I think PPM is definitely an interesting concept that can tell us a lot about a player. I’ve always made sure to look at field goal percentage when I see a high scoring performance. Something like this simplifies it.

    When you were talking about an unblockable go-to shot, I couldn’t help but thinking about KG’s turnaround jumper. It clearly can’t be blocked, and when he’s hot, he rarely misses it. I know it’s not as reliable as Dirk’s step back or Kareem’s sky hook, but it was the one shot I’ve seen a lot that simply cannot be stopped when he’s on.

    Good work.

  9. Absolutely fantastic post – Ii had always thought of efficiency as limited to points divided by FG attempts (meaning Dirk was 3.2(!) last night). This is truly informative and puts Dirk (and Kareem) in the proper context.

  10. To clarify, I when I said "the one shot I've seen a lot that simply cannot be stopped when he's on," I meant that in addition to the others mentioned.

  11. willyum says:

    Maybe weighting the missed shots like .5 for FT, 1 for FG, 1.5 for 3 pt shots? The 3 point extra .5 miss seems ok because of how some players get killed for taking numerous bad 3 pt shots or just throwing it up because they can't make a play

  12. willyum says:

    Maybe weighting the missed shots like .5 for FT, 1 for FG, 1.5 for 3 pt shots? The 3 point extra .5 miss seems ok because of how some players get killed for taking numerous bad 3 pt shots or just throwing it up because they can’t make a play

  13. birbilgi says:

    Jordan in Game 1 of 1992 NBA Finals (the Shrug Game): 16/27 FG/FGA; 6/10 3PM/ 3PA; 1/1 FT, for 39 Pts = 3.54 PPM.
    Even discounting the second half (four points, on 2/4 FG shooting (I think?)): 14/23 FG/FGA, for 35 Pts = 5 PPM. PPM is a weird stat, or D. Nowitzki shot the lights out. Or both.

  14. You could be onto something good with this stat if you weighted 2 point shots as 1, 3 point shots as 1.5, and free throws as .5. That would give a relative value to each shot.

  15. FulhamPete says:

    Phil Simms was at a 6.00 (22-25, 3 TDs 18 pts.) in his superbowl.

    Oh, wait…BASKETBALL? I don't think Phil was that good.

  16. Did you weight missed free throws and missed field goals differently? It seems to me that a missed free throw should only be worth half as much (possibly less). For instance, making one FT and missing one FT still yields a point on the possession. What about missing a FT on a potential three point play?

    Also, you spelled Michael Jordan incorrectly.

    • Did you not take the time to actually read the article? He discusses the need for a weighting system. And a free throw missed is a missed opportunity, regardless of whether you made the preceeding or the next free throw

  17. Would be fun to do a comparison for all-time greats’ all-time great games, and then we’d have true perspective on Dirk’s performance. e.g. Jordan’s 63 against Boston, Wilt’s 100, Kobe’s 81, etc.

  18. Making Tim Duncan right below Shaq's 2.127 and above Wilt's 1.890, on Jerod's All-time Greats List.

  19. i like that FTs count the same as FGs. a 50% FT shooter will yield a PPM of 1 (1 make, 1 miss= 1. Just as a 33% 2 pt FG shooter would(1 make, 2 misses= 2/2=1), as well as a 25% 3 pt shooter (1 make, 3 misses=3/3=1). To me, a 50% FT shooter is about equivalent to a 33% 2 pt FG shooter, which is about equivalent to a 25% 3 pt shooter; all 3 are pretty bad.

  20. I like the idea of weighting shots by their value (1,2, or 3). I wonder if you could also add in a loose representation of other stats i the "points total" part of this. For example, you could make a case that each rebound, assist, steal, block roughly equates to 1 point earned for the player's team, so if those were added to the total, you'd have an even better representation of the team's points the player helped produce per missed basket. I suppose you could even include things like turnovers or fouls as negative towards the total . . .

  21. Another way to improve the stat, would be to factor in how many PPG they scored. Magic Johnson, for instance, scored less per game than anyone on that list — about 4 PPG less than Dirk. So you could split it into things like PPM for people averaging over 25 or more PPG, PPM for people averaging more than 20 PPG, and so on.

    So the above list would be reformatted…

    PPM for 25+ PPG: Jordan, Robertson, Malone, Bryant, Wilt, Iverson
    PPM for 20+ PPG: Kareem, Dirk, Bird, and Shaq

  22. Don't forget Jerry West. He'd rank ahead of Kobe as well.

  23. In terms of calculating ppm, I agree that a free throw miss should only be worth .5, but there is no reason that a 3-pointer miss should be worth more than a 2-pointer miss, as both cost the team 1 scoring opportunity.

  24. Nice Article. I think you could have noted that forwards/centers tend to be on the top of the PPM rankings, probably due to being closer to the basket.

  25. John Stockton–2.977

  26. Here’s a version of this that weights 2-pointers and 3-pointers; I’m calling it Point Ratio, which is a terrible name. The formula is:

    Point Ratio = (total points)/[ (3*missed3pters) + (2*missed2pters) + missedFT ]

    So you’re dividing a players total points by the points he attempted to get but did not due to a missed shot.

    How should we interpret this stat? Well, for starters, notice that if a player’s Point Ratio is higher than 1, this means the number of points he scored is higher than the number of points he failed to score, due to a miss; in other words, he is getting more than half of the points he had an opportunity to get, had 100% of his shots fallen.

    Here are your Point Ratio leaders, among the top 30 scorers in the league, for the 2010 – 2011 season:

    1. Dwight Howard – 1.45
    2. Paul Gasol (!) – 1.36
    3. Dirk Nowitzki – 1.31
    4. Chris Bosh (!!!!!) – 1.23
    5. Amare Stoudemire – 1.22
    6. Tony Parker – 1.2
    7. Paul Pierce – 1.18
    8. LeBron James – 1.17
    9. Brook Lopez – 1.17
    10. LaMarcus Aldridge – 1.16

    Notice how it seems to favor big men who don’t take a lot of threes. Gasol and Bosh ranking so high, despite neither being in the top 15 in scoring, indicates that while they may not put up 30 a night, they score a lot of the points they try for.

    Thoughts? I could really use a better name…

  27. "Specifically, because a missed shot equates to a missed scoring opportunity that could have perhaps been capitalized on by another player, PPM should give us some measure how efficient a player turns the shooting opportunities he takes for his team into points."

    Based on this comment I'm wondering if we need to add Offensive Rebounds and Turnovers to the mix somehow. The offensive rebound equates to an additional scoring opportunity while the turnover equates to a missed scoring opportunity. If what we're looking for with PPM is the player's effect on scoring opportunities, I think these other attributes probably need to get involved.

    PS Your site or its ads are trying to install a virus on my PC. FYI.

  28. how would you calculate it if someone were perfect, you can't divide by zero. For instance, a relatively ok performance such as 5-5 from the field and 6-7 from the FT line would also 'match' Dirk's performance. You'd have to factor in a "with a minimal shot attempts of x" type of qualifier, otherwise the who "missed" per game stat becomes meaningless.

    • I dunno, somebody with that line would have a really efficient game. Which this stat is all about efficiency.

  29. Great article. Small nitpick: you mention Ray Allen's PPM of 2.521 which makes him 5th, but I don't see him in the chart.

    • because the person who wrote this article only included the top 23 scorers in the game for the regular season. Ray was not in the top 23

    • He said that the table was the PPM of the TOP 23 scorers in the league, of which Ray Allen was not (hence the mention and not the inclusion).

  30. Steve Nash – 2.62

    Kobe 81 pt game – 2.7 (81/30)

    Wilt 100 pt game – 2.5 (100/40)

    Jordan 63 pt game – 2.625 (63/24)

  31. i'm curious about Simmons' original question – what are some of the best performances in NBA playoff history, vis-a-vis PPM? perhaps a minimum of 15 points scored, or 10 FGA, would have to be the minimum criteria.

  32. I was hoping to see which individual games by players had the best PPM. Might be hard. But I’d love to know which was Jordan’s best, which was Lebron’s best, etc. and how they stack up…

  33. Agreed. The scale should be standardized in some fashion if we want to truly use it on a large scale.

  34. So I changed it so that a missed free throw only counted as half (with 2's and 3's weighted the same as they both take up an opportunity).

    Here's the regular season:
    Dwight Howard2.92
    Dirk Nowitzki2.83
    LeBron James2.62
    Dwayne Wade2.52
    Kevin Durant2.49
    Kobe Bryant2.19
    Derrick Rose2.19
    Russell Westbrook2.17

    And the post season:
    Dwight Howard3.68
    Dirk Nowitzki3.16
    Kevin Durant2.6
    Dwayne Wade2.42
    LeBron James2.27
    Kobe Bryant2.1
    Derrick Rose2.03
    Russell Westbrook1.87

    Gut instinct is that it weight big men too much, but Dwight did have some killer games in his series. These are not the top points per weighted miss, just a selection of top scorers.

    • Good stuff. On the other hand, if we think of how few teams win titles without great big men, this stat really sheds light on something necessary for NBA success.

  35. If the idea is to assess points per missed opportunities, it might be simplest to take 2 points as the baseline. In this case, missed FGs are -2, and missed FT are worth -2 / number of free throws, with missed and-1s not counting against the stat. Points scored are then totaled as usual. So, if a player is fouled on a missed two-point shot, each miss counts -1. If he's fouled on a missed 3, then each miss count -2/3. FT after a made shot can only count as positive.

  36. I think this is cool, but we cannot really compare PPMs of current players to PPMs of players in eras where the defensive rules were different or- even worse to players that played when the 3 point shot wasn't even invented. Both these factors really affect the shot selection, FG% and therefore PPM of a player

    • That is true a simple equation cannot truly compare eras, but more true if FTs or 3 pointers are weighted more or less based on stats which people are discussing to even out the overall position differences. Point being no matter the 3 point line's existence, shot selection and accuracy on opportunity is here. Good discussion here.

      NBA GMs may want to look at this as a stat during the offseason to see if their moves are improving their overall team efficiency, if that is what the direction or coach of the team wants to put emphasis on during change.

  37. So I ran the numbers for single games. Regular Season only goes back to 1985-86 on Basketball Reference and playoff games only back to 1991.

    Regular Season top ten:
    Cedric Ceballos 40.00
    Chris Bosh 20.00
    Dominique Wilkins 14.67
    Mitch Richmond 13.33
    Amare Stoudemire 11.00
    Alex English 10.75
    Amare Stoudemire 10.25
    Jeff Hornacek 10.00
    Wayman Tisdale 10.00
    Karl Malone 8.80

    Playoff Top 5:
    Dirk Nowitzki 16
    Terry Porter 10.25
    Charles Barkley 7.166666667
    Chris Mullin 6.833333333
    Elton Brand 6.666666667

    • Ben – awesome breakdown. Would you mind letting us know what games were used, and the players statlines for those games?

      Also, that 40 PPM be Cedric Ceballos makes me wonder if that was an actual NBA game, or if he was playing Rock N Jock on MTV being guarded by Dan Cortese or something.

  38. Sorry, forgot to post dates on those.

    Reg Season:
    3/9/1993 PHO @ SAC
    2/20/2008 TOR VS ORL
    3/2/1990 ATL VSMIL
    3/19/1991 GSW VS POR
    3/19/2010 PHO VS UTA
    3/5/1987 DEN VS SAS
    2/6/2011 NYK VS PHI
    11/23/1994 UTA VS SEA
    3/6/1990 SAC @ DET

    5/17/2011 DAL VS OKC
    5/19/1992 POR VS UTA
    6/1/1993 PHO VSSEA
    5/8/1991 GSW @ LAL
    5/8/2006 LAC @ PHO

  39. mmm, not really, penalizing 3 point misses with a 1.5 would hurt efficient 3 point shooters (like Ray Allen) undeservedly, since a 3 point miss and a 2 point miss have the same net effect, however, the free throw misses should be weighted by 0.5. By that measure, for example, Shaq would improve a lot.

  40. Here's a first version of what I'd call Points Per Opportunity (Points / (FGA+0.5*FTA+TO-ORB)). This counts a turnover to be just as bad as a missed basket and an offensive rebound as making up for a missed basket.

    Regular Season:
    Dwight Howard – 1.21
    Dirk Nowitzki – 1.13
    Dwayne Wade – 1.06
    Kevin Durant – 1.06
    LeBron James – 1.04
    Kobe Bryant – 0.99
    Derrick Rose – 0.98
    Russell Westbrook – 0.94

    Dwight Howard – 1.24
    Dirk Nowitzki – 1.15
    Kevin Durant – 1.13
    LeBron James – 1.07
    Dwayne Wade – 1.07
    Derrick Rose – 0.95
    Kobe Bryant – 0.93
    Russell Westbrook – 0.89

  41. Agree that you need to divide the number of FT misses by 2. Good FT shooters come up too high. I wouldn't however distinguish between two pointers and three. A 3pt miss shouldn't be punished more than a 2pt miss, that makes no sense.

  42. I tried the revised weighting methods and the top 23 get's pretty shaken up. I think weighting FT, FG, and 3FG as 0.5, 1, and 1.5, respectively, is flawed since the new top 10 are all PF or C positions, and only 1 person (Dirk) had more than 35 3's. It appears as though this weighting unfairly hurts shooters. Using a scale of 0.5 for FT and 1 for all FGs results in what I see as a more balanced and "what-you'd-expect-watching-these-games" result.

  43. Just edited. I can't believe I did that. MSF's first post ever tweeted by Bill Simmons and the greatest basketball player of all-time's name is misspelled. I'm a dunce.

  44. If you want to weight the PPM statistic, I would multiply the misses by the league shooting average for each type of shot. Say the league average for free throws is 75%, FGs is 40%, and 3PT is 30%. Multiply each factor, and then your weightings don't skew towards big men that shoot atrocious FT% and don't shoot 3 point shots.

    Or even weight it by expected point per shot (FG% x point value, so .76×1 for FT, .4×2 for FG, and .30*3 for 3PT)

    2010-2011 Expected-PPS-Weighted PPM
    Kevin Durant: 3.41
    Dirk 3.35
    Dwight Howard 2.87

  45. Bryan Tisinger says:

    The first person that came to mind (who Bill Simmons probably thought of as well) is Kevin McHale, who had both a great FG% and FT% for a big man. I ran the numbers, and his PPM comes out to 2.699, or 2.70 to round up to 2 digits. That beats Magic, and is the best of anyone calculated so far. Another guy that came to mind is John Stockton. His PPM turns out to be great as well, at 2.58.

  46. Cedric Ceballos had a 40-point, 1 miss game:

  47. Whoever wrote this article failed to include missed three pointers as part of the stat. Therefore, it is not valid and should be changed based on all missed shots…. including missed 3pt shots! (not just missed FT's and FG's)

  48. Greg Rubin says:

    Lots of comments, so not sure if this is covered, but there are a couple of interesting things, most notably:

    1) Salary does not correlate to PPM
    2) If you weight the PPM by "expected points missed" salary does correlate

    The Details:

    Let's take the top 100 Guards from a "Points Scored" 2010-2011 standpoint. If we run a least squares regression fitting the Log of 2010-2011 Salary & 2010-2011 Salary to PPM we get:

    LogSalary T-Value = -1.64
    PER T-Values = 5.96
    R-Sq = 27%

    In other words, PPM is closely related to PER (which we expect to some degree) but not to salary. I don't think this is breaking news since it is so hard to accurately value production.

    So, if we revse PPM and weight the type of shot so that Weighted PPM = ((Made 2PTs*2)+(Made 3PTs*3)+(Made FT))/ ((Missed 2PTs*2)+(Missed 3PTs*3)+(Missed FTs)) things change dramatically. For example, James Harden is 14th among Guards for PPM (2.07) but only 28th for Weighted PPM (0.96).

    Now, if we run the regression fitting PER & Log Salary to Weighted PPM we get:

    Log Salary T-value = -2.07
    PER T-Value = 7.92
    R-Sq = 40%

    So, going forward, I suggest using a Weighted PPM since it clearly improves the predictive power. What is alos fairly interesting is that even though many of the 2010-2011 salary values were negotiated years in advance, when using a Weighted PPM there does seem to be some relationship between 2010-2011 Salaries & PPM.

    • Since it's been quite some time since I've done stats… A high T-Value or R-Sq means that they are correlated?

      Couldn't you use Total Points instead of ((Made 2PTs*2)+(Made 3PTs*3)+(Made FT))?

      How does it look if you weighted 2PTs and 3Pts the same (no weight, but missed FT has a 0.5 weight)?

  49. I like this formula, the best variation of PPM I have seen commented so far. Using Hollinger logic is a great start and the best use of this might be post 3 point line players and future seasons. Older sharp shooters like Jerry West (and others not mentioned) during eras without a 3 point line get shoved a little too far down the list in my opinion, with less opportunity for more Total Points. But whatever

    Great modern stat that could be just as good a single indicator as +/- has recently become.

  50. Very interesting, but it seems the results are very sensitive to how you combine FTs, FGs and 3Ps. One option would be to calculate three stats: PPM1 for FTs, PPM2 for FGs and PPM3 for 3Ps. Then you could try different combinations such as adding them, taking the simple mean or a weighted mean (where you weight each by the share of the players' overall shot attempts) to see which one makes the most sense. It makes it a little less concise, but it would be more transparent as to which part of a player's shooting is driving the results (e.g., Shaq looks really efficient if you weight up FGs but much less if you combine it with FTs).

    That said, I enjoyed the article and thought it was really fun to read.

  51. All in all, this shows that the reliance on misses rather than makes generates a 1/(1-x) dependence rather than simply an x dependence, which is completely counterproductive to the meaning that we're trying to generate through these stats, and also demonstrates why Steve Nash and Reggie Miller rank a lot more highly than Ray Allen – They both had a significantly higher FTA/3PA % for their careers – Nash is 3102/3644 (.851), Miller is 7026/6486 (1.083), and Allen is 4240/6554 (.646) – an absurd discrepancy that fully explains how Miller could rate so far ahead of Allen despite being significantly worse by any other efficiency rating. The natural conclusion is not to attempt to correct these misgivings, for any correction will simply steer it back to PPP – but rather to simply accept that this stat is relatively worthless in the presence of other more natural and meaningful such as PPP.

  52. All in all, this shows that the reliance on misses rather than makes generates a 1/(1-x) dependence rather than simply an x dependence, which is completely counterproductive to the meaning that we’re trying to generate through these stats, and also demonstrates why Steve Nash and Reggie Miller rank a lot more highly than Ray Allen – They both had a significantly higher FTA/3PA % for their careers – Nash is 3102/3644 (.851), Miller is 7026/6486 (1.083), and Allen is 4240/6554 (.646) – an absurd discrepancy that fully explains how Miller could rate so far ahead of Allen despite being significantly worse by any other efficiency rating. The natural conclusion is not to attempt to correct these misgivings, for any correction will simply steer it back to PPP – but rather to simply accept that this stat is relatively worthless in the presence of other more natural and meaningful such as PPP.

  53. Tristan says:

    I think the original PPM calculation which gives no weight to the various types of shots is the most accurate. The reason for this is because the number of points earned for each of these types of shots already takes into account the relative difficulty of hitting them. In Hollinger's calculation 3pt shots and 2pt shots count the same because they are each one shot. But there is less of a penalty for missing a free throw, even though this is also one shot. In reality, the free throw is the easiest shot to make, and a player who consistently misses free throws should be penalized accordingly.

  54. I'll have to ask my dad who thinks Larry Bird is the all time best what he thinks of all of this.

  55. Is there any way to factor time in? Missing a free throw isn't as big of a deal because the clock is stopped. Misses during the game, when the clock is running, are lost opportunities to make up a deficit, expand a lead, etc.

  56. Jerod: Walter Davis, 2/25/83: 15-16; 6-6. Or a PPM for the game of 36. Was 15-15 and 6-6 before he missed his final FGA with less than a minute left in the game (so 34 consecutive points without a miss).

  57. Jerod: One more. Adrian Dantley = 23177/6952+1519=2.736

  58. Auch haben Sie beim Online Shopping nicht nur den Vorteil, bequem vom Sofa aus zu bestellen, sondern auch die Wahl zwischen mehreren Zahlungsarten.

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