Bill James, the godfather of Sabermetrics (the field that uses advanced math to analyze baseball), found a useful formula about 25 years ago. He discovered that a baseball team’s winning percentage could be estimated quite accurately by dividing the square of runs scored by the sum of runs scored squared and runs allowed squared. That is RS^2/(RS^2 + RA^2). This is called baseball’s Pythagorean Theorem.
Because points in basketball come about much differently than runs in baseball—what is the basketball version of a 6-1 blowout?—a formula to calculate winning percentage based on points scored and surrendered will be different.
Many mathematicians much smarter than me have looked at this over the years, and the exponent they found to work the best for hoops teams is 14 instead of 2. This means a basketball team’s expected winning percentage can be calculated with this formula: Points^14/(Points^14 + Opponents’ Points^14). Football’s exponent, by the way, is 2.4. These formulas with different exponents are still referred to as the Pythagorean Theorems of these sports.
The value of a formula that calculates expected winning percentage, when real winning percentage is already known, is in predicting future success. Teams that are doing much better than expected tend to fall down a bit after a while. Teams that aren’t winning as much as expected tend to improve.
The 2006-07 NBA season–regular and playoffs–provides some great examples of how this can work. The Heat were scoring 94.6 ppg, but giving up 95.5. Their expected winning percentage was 47%, but they actually won 54% (44-38). The returning champs got unexpectedly swept 4-0 in the first round of the playoffs.
Similarly, Dallas was scoring 100 ppg and surrendering 92.8 for an expected winning percentage of 74%. They actually won 82% (67-15), and also faced a shocking first round exit. On the other hand, the Spurs won 71% (58-24), but were expected to win 78% (98.5, 90.1). They of course cruised through the playoffs to win the championship.
Although the 2010-11 season is only about 20 games old, we can still look at which teams are winning at a clip above or below the expected rate, which might result in a dip or bump down the road.
Teams That Should Improve
These teams are at least 2.0 wins below the expected amount through Monday, indicating they have probably lost most of their close contests and their luck will hopefully turn around sometime soon.
Miami Heat (17.0 expected wins, 14 actual, +3.0): As has been well publicized by this point, the Heat are leading the league in scoring margin, outscoring opponents by an average margin of 8.4 ppg, which is unbelievable considering they’ve lost 8 games. How have they done it? First of all, they are obliterating a slew of teams, with their recent 5-game winning streak coming with victory margins of 10, 12, 28, 25, and 11 points. They won some of their earlier games by 27, 32, 23, and 26 points. Second, they’re staying close in their losses. They have an OT loss by 2, a trio by 5 or less, and only two by double-digits.
Philadelphia 76ers (8.9 expected wins, 6 actual, +2.9): They Sixers just might be pushing the panic button too quickly with the whole shopping-AI thing. If they had won their expected amount of games and were sitting with a 9-11 record today, Philly would be firmly in control of the #8 spot in the East; even so, they’re still only one game back of Charlotte right now. The reason their luck is expected to change shortly according to the Pythagorean Theorem is that so many of their losses came in close contests. They just lost in Atlanta by 5 last Friday. Before that by 9 to Miami. Two Tuesdays ago, they lost by a deuce in OT in Washington. Throw in every single win coming by 9 points or more (18, 9, 16, 11, 10, 26 – they might be the only team to have done this), and Philly should be able to pull some close ones out soon.
Houston Rockets (9.2 expected wins, 7 actual, +2.2): The Rockets started with a MFer of a schedule, facing LAL, Denver, NO, and the Spurs in their first five games, all of which were losses, coming by 2 points, 4 points, 13 points, 8 points, and 3 points in overtime. Since then, they’ve had multiple close L’s, including by 7, 3, 7, and by 3 in OT. They’re bound to pick it up and look better soon (or at least when Aaron Brooks returns).
Teams That Should Drop
These teams have at least 1.9 wins above the expected amount, so expect their luck to turn around at some point.
Oklahoma City Thunder (10.7 expected wins, 14 actual, -3.3): The NBA’s newest darling is squeaking by all sorts of contests. Their first six wins came by 11, 1, 1 (in OT), 6, and 2 points. Their last seven wins have been by 5, 3 (in triple-OT), 6, 4 (in OT), 10, 1, and 5 points. They already have four losses by 10 or more, so really they’ve just been hanging on up to this point. Heaven forbid one of the Thunder actually sustains a real injury at some point.
Cleveland Cavaliers (4.8 expected wins, 7 actual, -2.2): Remember their embarrassing 28-point beatdown in LeBron’s homecoming on Thursday? The Cavs also have recent losses by 34, 24, 19, 11, 11, and 10 since November 19. None of their wins are anything special (the biggest was by 8), so expect some more misery in the coming month.
Dallas Mavericks (14.1 expected wins, 16 actual, -1.9): Cuban’s Mavericks are on a 10-game tear right now, a tear that includes 0 wins by 15 points or more (the designation of a “blowout” in the recent study that shows the link between blowouts and post-season success). In fact, Dallas’ largest win of the season was by 16 over the lowly Clippers back in October.
Other Pythagorean Theorem Tidbits
Some people might think Indiana’s 10-9 mark is a fluke, but the formula has them at 11.5 wins as a result of a ton of big wins so far. If anything, they’re only going to get better as the little things even out over time.
Dallas isn’t the only top team that should brace itself for some bad luck. The Spurs, Jazz, and Nuggets have all won nearly 2 more games than they were expected to through Monday. The Spurs were expected to win 15.5 (17 actual), the Jazz were expected to win 14.4 (16), and the Nuggets were expected to win 11.3 (13). Does that mean LA will have an easier go of it out West soon?
A lot of fans are surprised the Lakers have lost 6 games at this point. The formula is also surprised; it has the Lakers pegged for 15.3 wins through Monday, not 14. Considering how many teams they’ve blown out on their JV schedule up to this point, look for a better run of things in the future.
For as bad as John Wall’s Wizards have been looking with their 6-13 record, their expected win total is only 4.9. Ugh.