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What Can Basketball’s Pythagorean Theorem Tell Us About the 2009-10 NBA Season?


By Zachariah Blott

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 runs scored, squared 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 2009-10 season is only about 10 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, fall, and other pythagorean theorem tidbits after the break…

Kevin Garnett

Kevin Garnett Photo Credit: Icon SMI

Teams That Should Improve

These teams are at least 1.0 win below the expected amount, indicating they have probably lost most of their close contests and their luck will hopefully turn around at some point.

New Jersey Nets (1.7 expected wins, 0 actual): No crap; a team will win more than 0 games over an 82-game season, especially one that’s only had four players able to play in all 10 games so far. Star PG Devin Harris has missed eight games, and new SG Courtney Lee could only suit up for six. Additionally, they’ve lost four games by 3 points or less, including that Dwyane Wade heartbreaker on Saturday.

New York Knicks (2.2 expected wins, 1 actual): They’ve lost both of their overtime contests and had a valiant fourth-quarter effort denied in a 95-93 loss to Utah last week. If they can improve on their abysmal 30% shooting on a league high 28 three-point attempts per night, they’ll catch some breaks and win a few more.

Washington Wizards (3.0 expected wins, 2 actual): They’ve won big and have lost plenty of close ones: that’s a surefire sign that better days are ahead. That and bringing Antawn Jamison back from the IR.

Boston Celtics (9.0 expected wins, 8 actual): Uh-oh, everyone might be in trouble. Like the Lakers, this top team has lost two in a row, but KG is “resting” until the playoffs. He’s playing only 30 minutes per game compared to a career average of 38 so that he’s healthier and less likely to break down late in the year. I also see their four worst games (3 losses and a 2-point win at Minnesota) are to the four fastest teams they’ve faced. Just something to keep an eye on.

Teams That Should Drop

Magic Johnson and Andrew Bynum

Andrew Bynum & Magic Johnson Photo Credit: Icon SMI

You’ll notice that all three of these teams that are at least 1.0 win above expected fall into the category of large-market (three of the five largest U.S. cities) squads that the league showcases for their excitement. I’m not trying to pull a Tim Donaghy, but any trend is worth mentioning.

Phoenix Suns (6.9 expected wins, 9 actual): They have six wins by less than 10 points, and their two losses were absolute blowouts at the hands of last year’s Finals squads. That poor defense will come back to haunt them, and I’m curious if C Channing Frye will keep stroking 47% of his trifectas. The numbers say something has got to give.

Chicago Bulls (3.4 expected wins, 5 actual): Every Chicago win was close. Their biggest margin of victory was by 7 in a 92-85 opening night contest against the sluggish Spurs. Three of their four losses are by more than 7, so I highly doubt they can keep their heads above water forever. John Salmons and Kirk Hinrich have both been shooting much worse than expected (27% for both), but the team is still due for a dip.

Los Angeles Lakers (5.7 expected wins, 7 actual): The Lakers have looked terrible in their losses and have a mysteriously low amount of 4th-quarter fouls compared to their opponents in the close ones, including two OT wins. Granted they’re going without rugged PF/C Pau Gasol, but LA is still putting $75 million worth of talent out on the floor each night. Gasol is probably enough of a buffer to prevent any significant drop once he returns.

Other Random Pythagorean Theorem Tidbits

Two teams you’d expect to be better than their current records are the 4-4 Spurs and the 4-6 Jazz. They have 4.6 and 4.5 expected wins, respectively, so there should be some improvement over time for these two clubs.

The Sacramento Kings are 5-4. Now read that sentence again, but slower. Let it sink in. Their 4-game win streak came after 31 ppg SG Kevin Martin broke his wrist on November 6. They’re not really that good, right? Correct, their expected win total is 4.4, but that means they’re still a .500-ish team.

Was Hornets’ coach Byron Scott a victim of circumstances when he got canned after New Orleans started 2-7? They were expected to win 2.9 games during his 9, but that’s still only a .322 winning percentage. I’m guessing new Head Coach Jeff Bower will pick up one he shouldn’t during his tenure, but promptly getting blown out twice and losing Chris Paul won’t help the man much, however.

The Thunder’s young talent and new defensive-minded approach is paying off with a surprising 5-5 record in the top-heavy Western Conference. Not only that, their expected win total of 5.8 indicates the breaks haven’t gone their way so far (like absent-mindedly fouling the Lakers eight times in a close 4th quarter after only fouling them 13 times in the first three – how odd). On the flip side, the teams they’ve beaten always seem to be missing key stars; that can’t last forever.

Zachariah Blott is a dish best served cold.


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