Learning From Point Differential

By Kevin Pelton
For Hoopsworld.com
Sep. 19, 2002

If you're a baseball fan and you spend a lot of time on the internet -- and if you're reading this, I'm going to guess the latter is true -- you're probably familiar with the term 'Pythagorean winning percentage'. No, geometry-phobes, don't go running and screaming, this has nothing to do with triangles, though there is a formula.

Pythagorean winning percentage in baseball, derived like most everything else by stat guru Bill James, uses a team's runs scored and runs allowed to project its winning percentage. "Why", you ask, "not just use the actual winning percentage?" Like it or not, luck has a tendency to play a role in sports. Teams that outscore their opponents by a lot but don't have the expected wins to follow are likely the victims of bad luck, though it should be noted that close-game ability, if there is such a thing, also is a major factor. (For example, it didn't surprise me that for much of the season the Washington Wizards were outperforming their point differential; MJ is the ultimate close game advantage.)

We can tell that most of the variance between Pythagorean winning percentage and actual winning percentage in baseball is luck because for the most part it does not hold up from year to year. While you wouldn't expect Greg Maddux's ERA or Shaquille O'Neal's points per game to fluctuate wildly from year to year, that is typically the case with this difference.

If a team way overperforms relative to its run differential, then, odds are that team is going to come back to earth the next season. In baseball, that's called "The Johnson Effect", though I have no idea why.

Dean Oliver of the Journal of Basketball Statistics has done some work on translating Pythagorean winning percentage to basketball (because the point totals are much different than in baseball, there is a different relationship). Though he's now switched to a more complicated and accurate model, I don't have the time to go through the work necessary to do that for all 29 teams, so we'll stick with what he came up with for basketball Pythagorean winning percentage:

points scored^16.5 / ((points scored^16.5)+(points allowed^16.5))

Calculating this for each of the NBA's teams last season yields pretty similar results to what actually happened; using point differential would only change one playoff team. Here, for reference, would be the playoff seedings in each conference using point differential:

1. Sacramento (actually 1)
2. San Antonio (2, but like in real life, they would not have second-round homecourt)
3. L.A. Lakers (3)
4. Dallas (4)
5. Minnesota (5)
6. Seattle (7)
7. Portland (6)
8. Utah (8)

1. New Jersey (1)
2. Detroit (2)
3. Boston (3)
4. Philadelphia (6)
5. Orlando (5)
6. Charlotte (4)
7. Indiana (8)
8. Milwaukee (NS)

As you can see, there are a few slight changes. Milwaukee replaced Toronto as a playoff team in the East, and there was some shuffling of the seeds elsewhere. By how much did the teams' projected wins differ from their actual wins? I'll rank them from the biggest underachievers (more projected wins than actual wins) to the biggest overachievers:

1. Seattle (+6)
2. L.A. Lakers (+5)
3. Philadelphia (+4)
4(t). San Antonio (+3)
New Jersey
Golden State
9(t). Minnesota (+2)
12. Cleveland (+1)
13(t). Charlotte (0)
L.A. Clippers
18(t). Milwaukee (-1)
22(t). Dallas (-3)
New York
26. Denver (-5)
27(t). Memphis (-6)

As you notice, for the most part teams that underacheived were top teams and overachievers were bottom-feeders, which is an admitted bias of the formula. As a result, it's probably smart to focus on the teams who show up where they seemingly shouldn't.

Seattle SuperSonics
Projected record: 51-31
Actual record: 45-37

The Sonics only move up one seed -- in the context of last year, a bad thing, since nobody really wanted to play the Lakers -- but that understates how much different things would look for the Sonics using point differential, as they would go from a distant five games behind Minnesota for the fifth seed to just one out.

The Sonics definitely did struggle in close games last year, something that was not the case during the 2000-01 season. (I had the numbers on this once, but they're lost with the inadequate search function at SonicsCentral). In addition, they were better in the second half of the season, which is something else I weigh heavily when projecting what a team will do next year. If Gary Payton is in camp and giving 100%, I don't think 50 wins is unrealistic for the Sonics even in the Western Conference.

Philadelphia 76ers
Projected record: 47-35
Actual record 43-39

Think of the difference between having to go on the road to face Boston and playing a beat-up Orlando team with homecourt, and you've got the Philly picture. The question, then, is whether that positive effect is outweighed by the changes that the team has undergone this summer, which I'm not sure are a positive, at least for next season. In this case, I wouldn't be as optimistic.

Golden State Warriors
Projected record: 24-58
Actual record: 21-61

Again, three games don't seem like much, but the Warriors and the Cleveland Cavaliers were the only two teams with less than 36 wins to 'underachieve', and going from wins to point differential vaults the Warriors over Memphis and Denver from the cellar of the West (for lottery teams, it's better to underperform so your draft pick is better, as I've found out in an online baseball league I'm currently rebuilding in).

With the additions of rookies Mike Dunleavy, Jiri Welsch, and Steve Logan, the subtraction of miserable Danny Fortson from the starting lineup, and Gilbert Arenas at the point for a full season, the Warriors could be ready to distance themselves from the Grizzlies and Nuggets of the world. Unfortunately, I still have a hard time seeing them not finish in the Pacific cellar unless Payton holds out; the division is just that strong 1-7.

Detroit Pistons
Projected record: 49-33
Actual record: 50-32

The Pistons and a team I'm about to discuss, the Dallas Mavericks, were the only two teams in the NBA to outscore their opponents yet still 'overachieve'. That's strike one. Strike two is the fact that the Pistons had several players have career years. (By my rating system, four Pistons veteran regulars -- Chucky Atkins, Jon Barry, Ben Wallace, and Corliss Williamson -- had the best seasons of their career. Wallace is likely to continue the effort, but I doubt the bench will be nearly as effective next year.) Strike three was the recent Jerry Stackhouse-Richard Hamilton trade. Tell me all you want about the economics of the deal; on the court, the Pistons are worse for it. As a result, they may be out -- of the playoffs.

Dallas Mavericks
Projected record: 54-28
Actual record: 57-25

If the Mavericks had pulled the coup of signing Rashard Lewis, I might not be so pessimistic but much as I like Popeye Jones, I'm not sure how much of a help he'll be in Dallas (assuming he's their guy). For one thing, Jones is a far better offensive rebounder -- where the Mavs don't need much help -- than a defensive rebounder. For another, he's not that great defensively. I don't think Jones for Greg Buckner (and probably Wang ZhiZhi) is really going to help Dallas much, and they might not have been as good as billed last season. Not that I think anything dire will happen to them, but I'm starting to lean towards San Antonio as the favorite to repeat in the Midwest.

Atlanta Hawks
Projected record: 27-55
Actual record: 33-49

As noted, teams at the bottom of the standings tended to be counted as overachieving, but the Hawks were not nearly as bad record-wise as the teams they shared the title of biggest overachievers with (Memphis, Chicago). Again, this is a case where off-season moves clash with what this tells me about the Hawks’ performance next season. Obviously, adding Glenn Robinson and Dan Dickau should make Atlanta much better, as should getting back a healthy Theo Ratliff in the middle. This and DerMarr Johnson’s unfortunate injury temper my hopes for the Hawks a bit, but I still see them as a playoff team that has the chance to do some real damage in the East.

When he's not writing about the Sonics for Hoopsworld.com and SonicsCentral.com, Kevin Pelton usually has Excel open to check out NBA statistics. He can be reached via e-mail at kpelton@sonicscentral.com.