Likelihood of Recent Winning Streaks
Posted by Neil Paine on December 14, 2010
Although we're only a month and a half into the season, the 2010-11 campaign has already seen its share of impressive winning streaks. The Spurs rattled off 12 straight across almost the entire month of November (a streak matched by the Mavericks last week), the Lakers & Hornets each won 8 consecutive to start the year, and the Celtics, Heat, & Knicks are currently in the midst of 8+ game win streaks themselves. How probable have these runs of victories been?
To answer this question, I'm turning to SPM in much the same way I did in this post. In a nutshell, I ran SPM for every player this season, but forced the team weighted sum to equal an efficiency differential that had been regressed to the mean with 908 possessions of league-average play. This allows us to use a full-season logistic win probability model to predict the outcome of any game:
p(home W) ~ 1 / (1 + exp(-0.525 - 0.15*Diff))
Where "Diff" is the home team's efficiency differential minus the road team's efficiency differential. Using this formula, each team's 2010-11 regressed SPM scores, and the distribution of minutes to each player in the game, I was able to generate the probability of each team winning each game this season, which in turn allowed me to calculate the likelihood of each winning streak.
Here are the probabilities, from most likely to least likely:
LA Lakers - 8 straight from 10/26 to 11/09 (20.6%)
| Date | Tm | Opp | tmRtg | opRtg | ishome | p(W) |
|---|---|---|---|---|---|---|
| 10/26/2010 | LAL | HOU | 6.11 | 3.04 | 1 | 72.8% |
| 10/29/2010 | LAL | PHO | 7.20 | -2.72 | 0 | 72.4% |
| 10/31/2010 | LAL | GSW | 2.69 | -13.39 | 1 | 95.0% |
| 11/2/2010 | LAL | MEM | 2.73 | -5.48 | 1 | 85.3% |
| 11/3/2010 | LAL | SAC | 7.50 | -4.45 | 0 | 78.0% |
| 11/5/2010 | LAL | TOR | 7.37 | -2.07 | 1 | 87.4% |
| 11/7/2010 | LAL | POR | 1.70 | -4.04 | 1 | 80.0% |
| 11/9/2010 | LAL | MIN | 3.43 | -6.58 | 1 | 88.4% |
| 8-gm W streak | 20.6% |
Miami - 9 straight from 11/29 to 12/13 (11.2%)
| Date | Tm | Opp | tmRtg | opRtg | ishome | p(W) |
|---|---|---|---|---|---|---|
| 11/29/2010 | MIA | WAS | 7.48 | -6.53 | 1 | 93.2% |
| 12/1/2010 | MIA | DET | 3.73 | -6.92 | 1 | 89.3% |
| 12/2/2010 | MIA | CLE | 5.00 | -8.56 | 0 | 81.9% |
| 12/4/2010 | MIA | ATL | 8.71 | 0.67 | 1 | 84.9% |
| 12/6/2010 | MIA | MIL | 8.15 | -1.86 | 0 | 72.7% |
| 12/8/2010 | MIA | UTA | 9.82 | 6.22 | 0 | 50.4% |
| 12/10/2010 | MIA | GSW | 7.00 | -12.46 | 0 | 91.6% |
| 12/11/2010 | MIA | SAC | 8.11 | -2.85 | 0 | 75.4% |
| 12/13/2010 | MIA | NOH | 9.11 | 4.65 | 1 | 76.7% |
| 9-gm W streak | 11.2% |
New York - 8 straight from 11/28 to 12/12 (6.8%)
| Date | Tm | Opp | tmRtg | opRtg | ishome | p(W) |
|---|---|---|---|---|---|---|
| 11/28/2010 | NYK | DET | 1.24 | -4.02 | 0 | 56.6% |
| 11/30/2010 | NYK | NJN | 2.93 | -5.79 | 1 | 86.2% |
| 12/3/2010 | NYK | NOH | 5.06 | -5.61 | 0 | 74.5% |
| 12/5/2010 | NYK | TOR | 4.41 | 1.04 | 0 | 49.5% |
| 12/6/2010 | NYK | MIN | 4.81 | -2.04 | 1 | 82.5% |
| 12/8/2010 | NYK | TOR | 6.71 | -3.15 | 1 | 88.1% |
| 12/10/2010 | NYK | WAS | 5.90 | -3.14 | 0 | 69.7% |
| 12/12/2010 | NYK | DEN | 6.29 | 2.64 | 1 | 74.5% |
| 8-gm W streak | 6.8% |
Boston - 10 straight from 11/22 to 12/11 (3.4%)
| Date | Tm | Opp | tmRtg | opRtg | ishome | p(W) |
|---|---|---|---|---|---|---|
| 11/22/2010 | BOS | ATL | -0.34 | -4.02 | 0 | 50.7% |
| 11/24/2010 | BOS | NJN | 6.79 | -1.22 | 1 | 84.9% |
| 11/26/2010 | BOS | TOR | 10.97 | 3.07 | 1 | 84.7% |
| 11/30/2010 | BOS | CLE | 7.74 | -6.71 | 0 | 83.8% |
| 12/1/2010 | BOS | POR | 12.50 | 0.68 | 1 | 90.9% |
| 12/3/2010 | BOS | CHI | 8.68 | 4.51 | 1 | 76.0% |
| 12/5/2010 | BOS | NJN | -3.92 | -9.07 | 0 | 56.1% |
| 12/8/2010 | BOS | DEN | 7.75 | 0.52 | 1 | 83.3% |
| 12/9/2010 | BOS | PHI | 8.88 | 4.58 | 0 | 53.0% |
| 12/11/2010 | BOS | CHA | 1.00 | -6.60 | 0 | 64.9% |
| 10-gm W streak | 3.4% |
San Antonio - 12 straight from 11/1 to 11/24 (2.8%)
| Date | Tm | Opp | tmRtg | opRtg | ishome | p(W) |
|---|---|---|---|---|---|---|
| 11/1/2010 | SAS | LAC | 2.46 | -5.64 | 0 | 66.6% |
| 11/3/2010 | SAS | PHO | 3.46 | -1.01 | 0 | 53.6% |
| 11/6/2010 | SAS | HOU | 8.71 | -4.47 | 1 | 92.4% |
| 11/8/2010 | SAS | CHA | 8.44 | -4.42 | 0 | 80.3% |
| 11/10/2010 | SAS | LAC | 8.42 | -8.35 | 1 | 95.4% |
| 11/13/2010 | SAS | PHI | 0.73 | -4.12 | 1 | 77.7% |
| 11/14/2010 | SAS | OKC | 7.62 | 1.84 | 0 | 58.5% |
| 11/17/2010 | SAS | CHI | 9.67 | 2.03 | 1 | 84.2% |
| 11/19/2010 | SAS | UTA | 10.15 | 4.77 | 0 | 57.0% |
| 11/20/2010 | SAS | CLE | 7.08 | -6.52 | 1 | 92.9% |
| 11/22/2010 | SAS | ORL | 9.10 | 4.94 | 1 | 75.9% |
| 11/24/2010 | SAS | MIN | 7.95 | -1.77 | 0 | 71.7% |
| 12-gm W streak | 2.8% |
Dallas - 12 straight from 11/20 to 12/11 (0.3%)
| Date | Tm | Opp | tmRtg | opRtg | ishome | p(W) |
|---|---|---|---|---|---|---|
| 11/20/2010 | DAL | ATL | 5.56 | 3.65 | 0 | 44.1% |
| 11/23/2010 | DAL | DET | 6.49 | -5.76 | 1 | 91.4% |
| 11/24/2010 | DAL | OKC | 7.35 | 1.98 | 0 | 57.0% |
| 11/26/2010 | DAL | SAS | 8.13 | 9.35 | 0 | 33.0% |
| 11/27/2010 | DAL | MIA | 6.99 | 7.90 | 1 | 59.6% |
| 11/29/2010 | DAL | HOU | -0.18 | -2.71 | 1 | 71.2% |
| 12/1/2010 | DAL | MIN | 1.71 | -4.64 | 1 | 81.4% |
| 12/3/2010 | DAL | UTA | 2.71 | 3.55 | 0 | 34.3% |
| 12/4/2010 | DAL | SAC | 4.32 | -3.81 | 0 | 66.7% |
| 12/7/2010 | DAL | GSW | 3.38 | -2.47 | 1 | 80.3% |
| 12/9/2010 | DAL | NJN | 3.47 | -6.89 | 1 | 88.9% |
| 12/11/2010 | DAL | UTA | 5.62 | 4.41 | 1 | 67.0% |
| 12-gm W streak | 0.3% |
New Orleans - 8 straight from 10/27 to 11/13 (0.1%)
| Date | Tm | Opp | tmRtg | opRtg | ishome | p(W) |
|---|---|---|---|---|---|---|
| 10/27/2010 | NOH | MIL | 2.95 | 2.60 | 1 | 64.1% |
| 10/29/2010 | NOH | DEN | 3.03 | 2.48 | 1 | 64.7% |
| 10/30/2010 | NOH | SAS | -3.58 | 9.43 | 0 | 7.8% |
| 11/3/2010 | NOH | HOU | -0.41 | -0.27 | 0 | 36.7% |
| 11/5/2010 | NOH | MIA | 1.62 | 10.35 | 1 | 31.3% |
| 11/6/2010 | NOH | MIL | 1.02 | -0.37 | 0 | 42.1% |
| 11/9/2010 | NOH | LAC | -2.57 | -9.90 | 1 | 83.5% |
| 11/13/2010 | NOH | POR | 0.91 | -2.92 | 1 | 75.0% |
| 8-gm W streak | 0.1% |
Here were the distributions of minutes from that Hornets-Spurs game where New Orleans had less than an 8% chance of winning:
| Date | Player | Tm | Opp | GS | MP | SPM | tmRtg | ishome | p(W) |
|---|---|---|---|---|---|---|---|---|---|
| 10/30/2010 | Chris Paul | NOH | SAS | 1 | 31.1 | 12.84 | -3.58 | 0 | 7.8% |
| 10/30/2010 | Trevor Ariza | NOH | SAS | 1 | 31.1 | 0.52 | -3.58 | 0 | 7.8% |
| 10/30/2010 | Marcus Thornton | NOH | SAS | 0 | 30.5 | -6.28 | -3.58 | 0 | 7.8% |
| 10/30/2010 | David West | NOH | SAS | 1 | 25.7 | 3.51 | -3.58 | 0 | 7.8% |
| 10/30/2010 | Willie Green | NOH | SAS | 0 | 23.4 | -5.22 | -3.58 | 0 | 7.8% |
| 10/30/2010 | Marco Belinelli | NOH | SAS | 1 | 22.8 | -2.33 | -3.58 | 0 | 7.8% |
| 10/30/2010 | Jason Smith | NOH | SAS | 0 | 20.8 | -4.03 | -3.58 | 0 | 7.8% |
| 10/30/2010 | Emeka Okafor | NOH | SAS | 1 | 18.6 | -1.31 | -3.58 | 0 | 7.8% |
| 10/30/2010 | Didier Ilunga-Mbenga | NOH | SAS | 0 | 15.3 | -4.79 | -3.58 | 0 | 7.8% |
| 10/30/2010 | Jerryd Bayless | NOH | SAS | 0 | 11.3 | -7.61 | -3.58 | 0 | 7.8% |
| 10/30/2010 | Pops Mensah-Bonsu | NOH | SAS | 0 | 9.6 | -4.58 | -3.58 | 0 | 7.8% |
| 10/30/2010 | DeJuan Blair | SAS | NOH | 1 | 38.3 | 1.83 | 9.43 | 1 | 92.2% |
| 10/30/2010 | Manu Ginobili | SAS | NOH | 1 | 36.9 | 7.73 | 9.43 | 1 | 92.2% |
| 10/30/2010 | Richard Jefferson | SAS | NOH | 1 | 33.4 | 1.25 | 9.43 | 1 | 92.2% |
| 10/30/2010 | Tim Duncan | SAS | NOH | 1 | 27.5 | 1.53 | 9.43 | 1 | 92.2% |
| 10/30/2010 | Tony Parker | SAS | NOH | 1 | 26.9 | 3.20 | 9.43 | 1 | 92.2% |
| 10/30/2010 | George Hill | SAS | NOH | 0 | 26.5 | 1.81 | 9.43 | 1 | 92.2% |
| 10/30/2010 | Antonio McDyess | SAS | NOH | 0 | 21.2 | -3.50 | 9.43 | 1 | 92.2% |
| 10/30/2010 | Gary Neal | SAS | NOH | 0 | 18.8 | -1.54 | 9.43 | 1 | 92.2% |
| 10/30/2010 | James Anderson | SAS | NOH | 0 | 10.6 | -1.62 | 9.43 | 1 | 92.2% |
If we regressed to preseason projections instead of the league average, New Orleans' expected win % would probably be higher... but still, they went into San Antonio, played Chris Paul & David West less than their usual MPG, gave significant minutes to Marcus Thornton, Willie Green, & Jason Smith (all of whom have been varying degrees of terrible this season) and still came away with the victory, paving the way for the most unlikely long winning streak of the season so far.
December 14th, 2010 at 1:21 pm
Neil,
This is very interesting stuff! What software do you use to make logistic regression?
-Nathan
December 14th, 2010 at 1:27 pm
I use R, which is free and (for my purposes) can do pretty much anything a high-priced package does.
http://www.r-project.org/
December 14th, 2010 at 1:34 pm
Q:What do pirates use for statistical computing?
A: ARRRRRR
December 14th, 2010 at 1:37 pm
Nice. That one definitely couldn't wait until September 19.
December 14th, 2010 at 2:43 pm
Notes on the distribution of minutes in that NO-SAS game: of course, the reason West and Paul played so little is that they were way ahead. The distribution would have been different had the game been closer.
I'm not sure how to account for that.
December 14th, 2010 at 2:48 pm
I don't think you can. But theoretically, playing Marcus Thornton, Willie Green, & Jason Smith so much could have made it a close game again (and in fact, San Antonio outscored them 30-23 in the 4th).