I Beg To Differential

Rob L. —  January 24, 2007

Rankings, Rankings, Rankings The NBA is far enough into the season that rankings such as Stein, Hollinger, Sagarin and FOTS (Friend of the Site) Knickerblogger generate heated debate. We the fans often go with our gut in response to outsiders ranking our team.

“Come on, Hollinger! The Lakers aren’t even in the top ten. They’re totally a top ten team.”

As we yell at the top of our lungs, the Staterati attempt to explain the why and how of their systems. There are real differences among the rankings, but one thing you’ll hear just about everyone mention is point differential.

A Win Is A Win, Right? The concept is simple. How much has a team outscored its’ opponents by? This idea migrated to basketball via Bill James. James found a strong correlation between runs scored/allowed and winning percentage in baseball. You can find the formula James used, as well as Dean Oliver’s basketball version here. Because this formula predicts team success fairly accurately, many use it to state what a team’s expected win % is.

And the short hand version of that is, “What’s that team’s point differential?”

Best In The West Which brings us to the debate raging over which team is currently tops in the Western Conference. The three teams in contention are the Mavs, Suns and Spurs. For whatever reason, most people (myself included) think of the Spurs as a little too old. This leaves the Mavs and Suns. Some go with record and pick the Mavs. But there are those out there that look at the point differential and pick the Suns.

All statistics compiled through Monday January 22, 2007

Mavs 34-8, +7.1
Suns 32-8, +8.9

The Mavs had played two more games than the Suns, but their records were comparable. Yet the Suns, on average, beat their opponents by 8.9 points per game. The Mavs, only by 7.1. In fact, the Suns sported the the biggest point differential in the NBA. And that’s just points per game. If we break it down into offensive and defensive ratings (points per 100 possessions) the Suns sport a +10.4 differential and the Mavs +7.7. The Suns are even further out ahead.

Here’s why I think that doesn’t tell the real story in this case.

Strength of Schedule Phoenix has had a much weaker schedule than Dallas to this point. Here’s how it breaks down.

Mavs vs Top 10 Teams 12-6, vs Top 16 18-6
Suns vs Top 10 Teams 4-7, vs Top 16 12-7

Sagarin’s Top 10 Teams are, in order: Dallas, Phoenix, San Antonio, Utah, Houston, LA Lakers, Chicago, Washington, Denver and Detroit. The Top 16 include: Cleveland, Orlando, Minnesota, Indiana, Toronto and New Jersey. If you look only at win-loss record, everything would stay the same except that the Bulls and Cavs change places in the 10/16 breakdown.

The first thing you’ll notice is that Dallas has played 18 games out of 42 against Top 10 teams. 24 out of 42 against Top 16 teams. That’s slightly more than half against the top half of the NBA. Phoenix has played only 11 games out of 40 against the Top 10. They played 19 of 40 against the Top 16, which is much more comparable to Dallas’ schedule. But it is clear that Dallas has faced more elite competition. My thought then, is that the Suns point differential is in part so high because they have beaten up on lowly teams.

The Test What I did was look at the Mavs first 42 games and the Suns first 40. (I know, the sample isn’t identical, but I’m just looking for close estimates.) I compiled point differentials for both teams against Top 10 teams and Top 16 teams. I further compiled two sets of Top 10 numbers: One where the Bulls were in it, the other had the Cavs instead. My hope was to see how the two teams played against similar opponents. Here’s what I found:

Mavs Top 10(Bulls) +2.11, Top 10(Cavs) +1.53, Top 16 +3.83 points per game
Suns Top 10(Bulls) -0.27, Top 10(Cavs) +1.36, Top 16 +5 point per game

And if we switch to offensive rating:

Mavs Top 10(Bulls) +2.39, Top 10 (Cavs) +1.73, Top 16 +4.33
Suns Top 10(Bulls) -0.29, Top 10(Cavs) +1.43, Top 16 +5.25

In both examples the Suns still hold the edge in point differential against the Top 16. But if we look at the Top 10 the Mavs hold the advantage. So at the moment, I’d have to say they are the better team. After Phoenix plays some more Top 10 teams I might come to a different conclusion. But I reserve judgment for now.

[Neither team has that many outlier games. The Suns had one win by 19 and another by 30. But most were closer to ten or less. The same is true of the Mavs who had wins of 27, 19 and 19 along with offsetting losses of 31 and 22 (the first was early season).]

Wrap It Up, Man! Point differential makes sense. It is a useful tool that has proven itself over time. But we must be careful not to use it without thinking. The current Mavs-Suns case is an example of how other factors can corrupt point differential.

Oh yeah. The Lakers are 9-7 against the Top 10, 17-7 against the Top 16. But their point differential is only…

“Whatever. The Lake Show’s going all the way, baby!


Rob L.


to I Beg To Differential

  1. From Hollinger’s ESPN chat yesterday:

    Brent (Sacramento): Ok John, you’re calculator must be broken. The Lakers are behind the Nets who are just a .500 team, have a point differential in the negative, play in the East, etc,. C’mon man, the problem is that you can’t take into consideration the Lakers missing Mihm, Brown and Odom and still doing what they are doing.

    SportsNation John Hollinger: I’m getting a variety of comments like this on the Hollinger power rankings. It’s designed to weight recent play fairly heavily (the team’s most recent 25% of games, specifically), and the Nets are 9-2 in their past 11 games. Obviously we should expect that to drop now that RJ is out, and as you point out the Lakers low rating is likely to improve once Odom gets back. But injuries aside, it’s hard to argue that L.A. has looked better than Jersey of late, and that’s what the power ranks are designed to reflect.


  2. Hey guys great news about Lamar. Yeah, we been doing okay without him (13-9), but these last few games you can tell we need him back ASAP. Our bigs have stepped in nicely to fill the void for a little while (Cook, Vlad, Turiaf) but they seem to be tiring a little.Theres a reason that they are role players and not all stars. Lamar’s versatility will be a huge boost, I wouldn’t be surprised if we see a little bit of the ballin’ we saw from the Lakers to start the season. Luke will probably improve the most with Lamar back out there.
    As for Kwame, he can take his time. Not to sound like I dont want him back, but theres no need to rush him. Bynum is doing fine. I think hes been averaging like 11 and 9 since Kwame got hurt. Those numbers are better than Kwame’s, and I know all of us Laker fans don’t mind seeing Turiaf get minutes. We love that guy.


  3. With Lamar’s return the David West’s and Al Harrington’s of the world won’t have such an easy time. Lamar will make other teams expend energy guarding him in a way that thos guys (Vlad, Cookie ,Ronny) can’t.


  4. Hey guys check it out… a little love for Joel.


  5. Wouldn’t a pythag-like record work better than point-differential when comparing the Mavs and Suns, considering the Suns play at a much faster pace, they should ‘outscore’ their opponents more. Or something like point-differential/100 pos.?

    In baseball, it is a matter of debate as too whether some teams are able to win close games consistently more than others. Statistically (for baseball, I don’t know if it also holds true in the association) there is no convincing evidence that this is true (other than maybe the ‘secret-sauce’ ratings at BP, which bring up some interesting questions).

    In regards to the Suns, they seem to blow their opponents away early (especially the weaker ones), which causes the game to get out of hand. Their opposition takes their starters out early in the 4th, as do the Suns. So really, we’re seeing a lot more bench minutes in Suns games than in all other games. I’m not sure if this would have any significance to point-differential, and I don’t know how to check to see if it’s in fact true.

    Personally, I’m sick of all the Nash/Suns glorification. How is he not the Payton Manning of the NBA (Simmons needs to write this article, and will when the Lakers bounce Pheonix from the playoffs :)?

    Two things always get overlooked when people fawn over the Suns that are HUGELY important when it comes to winning championships. 1, they have a hard time beating the top teams in the NBA. 2, they have a rep of loosing close games going back at least to last season (remember all the overtime games they lost). I think these facts derive from their game plan: they’re faster and more athletic and try to run you off the court (kinda familiar to the Colts?). As any NBA fan knows, close games slow to a crawl in the final 2 minutes (you know, kinda like football games). The Suns effectiveness collapses when the pace slows and they have to play defense.

    They key thing for us is … how can the Lakers become the Patriots (Brady : Kobe? PJ >Belichek). If the Lakers can come up with a killer DLine and a vetern secondary, the next few years can be really, really fun.


  6. I did run point differential for both points/gm and offensive rating. It seemed to narrow the gap for Dallas vs. Top 16 teams, but didn’t affect how much they were ahead of the Suns for Top 10 opponents.


  7. “Personally, I’m sick of all the Nash/Suns glorification. How is he not the Payton Manning of the NBA (Simmons needs to write this article, and will when the Lakers bounce Pheonix from the playoffs 🙂 ?”

    I’ve tried to make this argument with people with little luck. Not so much that I think either of them are chokers, but I wondered where all the “Nash can’t win the big one” articles were. The ones about Manning were all over the place, but somehow Nash has avoided them.


  8. Raw point differential is especially inaccurate when ignoring the total points in those games. I believe most stat gurus call this a team’s “pace.”


  9. Good argument for the Colts vs. Phoenix….one glaring problem: the Colts just made it to the Super Bowl!!!! the Suns have way too much talent to not keep them in that short list of contenders. 2 straight years of being in the Western Conf. Finals is also a terrific feat. I’m with you, I don’t care about the Suns and I always root against them, but it is quite hard to write them off as a one trick pony. This is also the first year they really have a refined and healthy roster as well. Imagine Amare in that series last year against us! The one thing i will say is that their numbers are misleading in point differential, and the Mavs do have more QUALITY wins. The Mavs also beat the Suns twice, which cannot be forgotten in this statistical debate.


  10. Like the “computers” in college football rankings, the NBA rankings become more and more circular as more and more assumptions are being made. For example, the standings of all of the teams fluctuate. When the Lakers defeated the Suns early in the season, the Sun were NOT one of the top teams. When the Lakers defeated Utah early in the season, they may have been #1. When the Lakers lost to Memphis at Memphis, the team had been changed and was on a winning streak–likewise the Hornets.

    By using cumulative rankings to retroactively rate whether a top or bottom team was played, teams are gradually leveraged into more and more static possibly questionable evaluations as the season goes on.

    We “know” that the Hornets will win more games when two more starters return, but will that be true? We “knew” that the Lakers would lose without Kobe and win when he came back–except it didn’t always happen that way.

    With such small sample sizes made into similar proportions and differences, we can’t reject the hypothesis that the differences and fluctuations are within the range of chance. Your statistician says that Dallas is SIGNIFICANTLY better than the Lakers, and the Riverboat Gambler (who makes prediction s with no knowledge based on chance and always says that there is no REAL difference) says the measured proportional differences from a sample of games could be chance fluctuations from a binomial 50/50.

    If one calculates the 90% confidence limits for Dallas proportions, it will overlap with many other presumably “lesser” teams that it cannot statistically separate itself from.

    The apparent superiority of certain teams (which may be real) are statistically close enough so that (with a small sample size with a mean proportion that fluctuates substantially by chance alone) may not be statistically REAL.

    It sort of agrees with the common sense of the fan. If the Lakers make it to the playoffs with similar proportions and proportional differences compared to the other teams, they will have very similar likelihoods statistically of winning it all!

    We can dream, can’t we?


  11. DrRayEye – You are correct that the ratings of NBA teams fluctuate during the season. While technically, the Suns were not a top 10 team when the Lakers beat them, they’re still the same team. Does it make more sense to count that win against the Suns as a vs top 10 win, or as a vs sub-16 win? Record rankings from early season are quite volatile. I think it makes more sense to go with the longer term ranking. The ranking that comes from about a half-season’s worth of play at this point. It is my feeling that, no matter the Suns relative standing when the Lakers played them on the first day of the season, the Suns should count as a top ten team. This is an attempt to counteract the small sample size problem you cite.


  12. With two developing big men, LO, and the best player in the game I think the Lakers have a chance. Oh, and that doesn’t even count the coach.

    Mostly statistics are only used to boost the fans view of their particular team. They really don’t say too much about injuries or player development (a big deal for younger teams) or system vs free-flowing situations.

    Me, I just look at each game as it’s played and notice what I said in the 1st sentence + we are a young team and inconsistent. Trying to figure out whether we are .5pts better or worse than Dallas/Phx/S.A. seems like too much work for me.


  13. No mention of head-to-head? Any rankings formula needs a head-to-head component. Right now every thing is pretty close between the Suns & Mavs–basicallly the same records, point differ., & both teams are equally hot. Well, then let’s go to the ultimate tiebreaker–head-to-head. Mavs are 2-0, one road win, one home. In the Suns’ current hot streak of the last 33 games where they have beaten all comers home or away, I find it interesting that one of their 2 losses came vs. the Mavs.


  14. Jay – You’re right. Head-to-Head should be a component of any ranking system. In this article, I was merely trying to “point out” that the point differential argument for placing the Suns #1 in the West had some holes in it.


  15. Rob L,

    I see nothing wrong with the logic of making progressive probabalistic rankings based on cumulative performance comparisons. I was merely trying to point out the simplifications necessary to make such comparisons–and the somewhat solipsistic consequences.

    When the Mavs keep in their regulars against the Lakers until the last two minutes (when they appear to have already won the game early in the 4th), it strongly suggests that they want to get home court advantage in the playoffs over resting thier veterans. It also pads their point spread.

    Other teams may want to rest their veterans as much as possible so that they have another gear available for the playoffs.

    Even though virtually any “statmaster” who plays games with outcomes as the season progresses will be forced to rate a team like the Mavs very highly–right now #1, the playoffs might be another story.

    Nobody on the Lakers has been overplayed. Lamar has had a month off, Kwame comes and goes–even Kobe has missed games. Against some opponents, the Lakers use two “teams” interchangeably.

    Experienced teams like San Antonio, Miami, and even Detroit may have an extra gear for the playoffs.

    The high flying Mavs and Suns may find that their playoff gear boxes are stripped and that they need a new tranny.


  16. I’m so sick of hearing about the Suns and the Mavericks dominance. Since the 1999-2000 season only two teams have had the best record and won the championship (the 00 Lakers and the 03 Spurs). As well, only two teams with the best record have even made the Finals (same two mentioned above). And have we forgotten that the Pistons were 32-5 at this time last year and that most people had them pegged as a sure fire NBA champ? No one expected them to get into the playoffs and fall apart, yet that is exactly what they did. Basically what I am saying is that the Phoenix streak means nothing. If they want to waste their energy upholding regular season streaks, then by all means do it. I think they would be better served winning 10-15 straight going into the playoffs like the Spurs and Lakers championship teams earlier in the decade did.