Ten Thousand 2010s
Posted by Neil Paine on October 14, 2009
Quick question: What's the probability that the league's "best" team will win the championship this season? Okay, then what are the odds that a team outside the top 5 in talent will win it all? Outside the top 10? The top 15?
Well, with a Steve Nash-esque assist from S-R head honcho Sean Forman, I set up a Monte Carlo simulation of the 2009-10 NBA season and ran 10,000 trials in an attempt to answer questions like the ones posed above. Before we continue, though, you should read these posts at Pro-Football-Reference that my colleague Doug Drinen wrote 3 years ago:
How often does the best team win?
Ten thousand seasons
Ten thousand stories
Ten thousand seasons again
Ten thousand 2005s
Done? Good. By now, you probably get the idea -- every team is assigned a "true strength" number (in the form of SRS) at random, which determines their probability of winning any given game. Using those ratings, you can simulate every game in a season schedule, establish playoff seedings based on those standings, and simulate through the playoffs until you have a champion. Lather, rinse, repeat.
Here are some important notes about the 10,000-season sim:
- In "10,000 2005s", Doug used actual SRS scores from the 2005 season to establish team strengths. Obviously we don't know what teams' SRS scores are going to be in 2010 because the games haven't been played yet, so I'm using the following equation (based on a regression of every team-season in NBA history) to establish an expected SRS for 2010: 2010_SRS = (0.68194 * 2009_SRS) + (-0.08459 * 2007_SRS) + (0.0784 * 2006_SRS). (Yes, you read that correct -- 2008_SRS is not included in the equation, because a team's SRS from 2 seasons prior was not found to be statistically significant.)
- To represent the historical uncertainty surrounding this equation, team strengths were assigned using a random number from a normal distribution with a mean of 2010_SRS and a standard deviation of 3.082. That means that if the regression formula predicts Boston to have an SRS of 5.26 in 2010, what it really means is that there's roughly a 68% chance that their true strength in 2010 will fall between an SRS of 8.34 and 2.18, and a 95% chance that it will be between 11.43 and -0.90.
- The average SRS is not going to be zero for every season. As Doug put it, "Even though we can't observe it (at least not easily), there must surely be years when the league is stronger and years when it's weaker. And in any case, since we are primarily interested in questions like "how often does the best team in football (for that year) win the [Championship]," it doesn't matter much."
- Tiebreakers were determined by team strength, not the NBA's official tie-breaking rules... I don't think that will matter much. I also fudged on the playoff seedings, ranking teams within conference 1-8 instead of ensuring that all division winners are in the top 4. Again, I don't think it will make much of a difference.
- Home-court advantage was a constant 60% for all teams.
Make sense to everyone? Cool. First things first: How often did the team randomly assigned to be the NBA's most talented actually win the NBA Championship?
| TeamRank | Champs |
|---|---|
| 1 | 4801 |
| 2 | 1980 |
| 3 | 1058 |
| 4 | 708 |
| 5 | 424 |
| 6 | 298 |
| 7 | 224 |
| 8 | 135 |
| 9 | 107 |
| 10 | 82 |
| 11 | 48 |
| 12 | 36 |
| 13 | 33 |
| 14 | 18 |
| 15 | 15 |
| 16 | 12 |
| 17 | 8 |
| 18 | 5 |
| 19 | 5 |
| 20 | 2 |
| 21 | 1 |
| 22 | 0 |
| 23 | 0 |
| 24 | 0 |
| 25 | 0 |
| 26 | 0 |
| 27 | 0 |
| 28 | 0 |
| 29 | 0 |
| 30 | 0 |
Compare that to what Doug found for the NFL, and it speaks volumes about the differences in parity between the two leagues. In Doug's sim, the team that was morally the NFL's best only won the Super Bowl 23.99% of the time; in this NBA sim, the best team won the Championship 48.01% of the time. 7-game series vs. single-elimination playoff formats, 82-game regular seasons vs. 16-game ones, and a soft cap vs. a hard one all contribute to this rather sizable discrepancy, but the bottom line is that the elite group of NBA teams won a championship almost 90% of the time, and bottom-feeders had literally no shot at a ring. In Doug's sim, even the worst team won it all once in 10,000 trials, but the lowest-ranked NBA team to win a title was #21. What did that season look like, you ask?
| Sim #8400 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Rk | Eastern Conference | W | L | Str | Rk | Western Conference | W | L | Str | |
| 1 | Orlando | 58 | 24 | 6.96 | 1 | Houston | 59 | 23 | 4.52 | |
| 2 | Charlotte | 51 | 31 | 2.42 | 2 | SanAntonio | 52 | 30 | 4.74 | |
| 3 | NewJersey | 49 | 33 | 0.92 | 3 | Phoenix | 49 | 33 | 3.20 | |
| 4 | Toronto | 48 | 34 | 0.84 | 4 | L.A.Lakers | 46 | 36 | 3.84 | |
| 5 | Detroit | 43 | 39 | -0.92 | 5 | Dallas | 44 | 38 | 2.31 | |
| 6 | Cleveland | 41 | 41 | 2.53 | 6 | Utah | 43 | 39 | 3.81 | |
| 7 | Boston | 41 | 41 | -0.12 | 7 | NewOrleans | 43 | 39 | 1.29 | |
| 8 | Miami | 39 | 43 | 0.81 | 8 | Denver | 42 | 40 | 1.38 | |
| 9 | Indiana | 39 | 43 | -0.02 | 9 | GoldenState | 42 | 40 | -0.60 | |
| 10 | Atlanta | 36 | 46 | 0.45 | 10 | Memphis | 41 | 41 | -1.65 | |
| 11 | Washington | 36 | 46 | -4.45 | 11 | Portland | 39 | 43 | 0.42 | |
| 12 | Chicago | 34 | 48 | 1.79 | 12 | L.A.Clippers | 39 | 43 | -3.16 | |
| 13 | Milwaukee | 34 | 48 | -1.02 | 13 | Sacramento | 33 | 49 | -1.29 | |
| 14 | Philadelphia | 33 | 49 | -1.65 | 14 | OklahomaCity | 25 | 57 | -2.66 | |
| 15 | NewYork | 31 | 51 | -2.02 | 15 | Minnesota | 20 | 62 | -6.82 | |
| Conf. Quarters | Conf. Quarters | |||||||||
| ORL def. MIA | DEN def. HOU | |||||||||
| DET def. TOR | LAL def. DAL | |||||||||
| NJN def. CLE | PHO def. UTA | |||||||||
| BOS def. CHA | SAS def. NOR | |||||||||
| Conf. Semis | Conf. Semis | |||||||||
| DET def. ORL | DEN def. LAL | |||||||||
| NJN def. BOS | SAS def. PHO | |||||||||
| Conf. Finals | Conf. Finals | |||||||||
| DET def. NJN | SAS def. DEN | |||||||||
| NBA Finals | ||||||||||
| DET def. SAS |
Here Detroit, despite ranking 21st overall and being inferior to several teams who missed the playoffs entirely, got hot and won the NBA championship. As was mentioned previously, in 10,000 trials, this was the only one in which a team ranked so low managed that feat... It would be the equivalent of last year's Bucks lucking their way to 43 wins and then winning the championship! Trial #8,400 is truly where amazing happens.
Some other cool tidbits from the 10,000 2010s? 88 times, a team went 82-0 during the regular season. 64 of them occurred in the Eastern Conference. Check out Season #1,037:
| Sim #1037 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Rk | Eastern Conference | W | L | Str | Rk | Western Conference | W | L | Str | |
| 1 | Cleveland | 82 | 0 | 15.33 | 1 | Phoenix | 80 | 2 | 11.76 | |
| 2 | Boston | 61 | 21 | 7.03 | 2 | L.A.Lakers | 55 | 27 | 6.52 | |
| 3 | Orlando | 54 | 28 | 5.04 | 3 | Denver | 53 | 29 | 4.25 | |
| 4 | Milwaukee | 50 | 32 | 4.89 | 4 | OklahomaCity | 47 | 35 | 3.12 | |
| 5 | Charlotte | 47 | 35 | 2.72 | 5 | Utah | 47 | 35 | 0.33 | |
| 6 | Toronto | 41 | 41 | -0.92 | 6 | Houston | 45 | 37 | 2.22 | |
| 7 | Atlanta | 40 | 42 | -0.13 | 7 | Memphis | 42 | 40 | -2.54 | |
| 8 | Indiana | 39 | 43 | -0.18 | 8 | SanAntonio | 40 | 42 | 0.17 | |
| 9 | Washington | 39 | 43 | -0.55 | 9 | Dallas | 31 | 51 | 0.53 | |
| 10 | Detroit | 39 | 43 | -3.17 | 10 | Portland | 30 | 52 | 1.20 | |
| 11 | Chicago | 39 | 43 | -4.02 | 11 | NewOrleans | 29 | 53 | -4.69 | |
| 12 | Miami | 38 | 44 | -0.55 | 12 | Minnesota | 28 | 54 | -4.00 | |
| 13 | Philadelphia | 29 | 53 | -4.98 | 13 | L.A.Clippers | 20 | 62 | -6.86 | |
| 14 | NewJersey | 25 | 57 | -3.53 | 14 | GoldenState | 20 | 62 | -7.50 | |
| 15 | NewYork | 24 | 58 | -5.88 | 15 | Sacramento | 16 | 66 | -8.84 | |
| Conf. Quarters | Conf. Quarters | |||||||||
| CLE def. IND | PHO def. SAS | |||||||||
| MIL def. CHA | OKC def. UTA | |||||||||
| ORL def. TOR | HOU def. DEN | |||||||||
| BOS def. ATL | LAL def. MEM | |||||||||
| Conf. Semis | Conf. Semis | |||||||||
| CLE def. MIL | PHO def. OKC | |||||||||
| BOS def. ORL | HOU def. LAL | |||||||||
| Conf. Finals | Conf. Finals | |||||||||
| CLE def. BOS | PHO def. HOU | |||||||||
| NBA Finals | ||||||||||
| PHO def. CLE |
Wow. Imagine for a second, what did that season look like? How did the Cavs go 82-0, and even more shockingly, how did the Suns go 80-2? Did Steve Nash get a new running mate in the desert? Phoenix and Cleveland played twice in December -- what were those games like? Did LeBron and the Cavs get off to a hot start and hold on desperately to their undefeated record late in the season, like a real-life undefeated team I know? And what were the Finals like? Shades of Super Bowl XLII? Every season tells a story, and I can only imagine the stories that would have come from this alternate-reality version of 2010.
Meanwhile, at the other end of the spectrum, at least one team went winless 92 times in 10,000 seasons -- but only 6 of those 0-fers took place in the Eastern Conference. In Season #4,720, the Kings went 0-82 and the Clippers went 6-76! And the Clipps actually had the lower SRS, -14.60 to -12.18! How ugly would those matchups have been?
Finally, here are the average results over all 10,000 seasons:
| Team | W | L | Str | Champs |
|---|---|---|---|---|
| Atlanta | 43.7 | 38.3 | 1.21 | 229 |
| Boston | 54.6 | 27.4 | 5.30 | 1564 |
| Charlotte | 38.7 | 43.3 | -0.78 | 79 |
| Chicago | 39.2 | 42.8 | -0.51 | 95 |
| Cleveland | 55.8 | 26.2 | 5.81 | 1997 |
| Dallas | 43.9 | 38.1 | 0.98 | 232 |
| Denver | 46.2 | 35.8 | 1.98 | 388 |
| Detroit | 40.4 | 41.6 | -0.11 | 102 |
| GoldenState | 34.8 | 47.2 | -2.62 | 29 |
| Houston | 46.4 | 35.6 | 2.03 | 395 |
| Indiana | 40.4 | 41.6 | -0.18 | 109 |
| L.A.Clippers | 26.7 | 55.3 | -5.59 | 6 |
| L.A.Lakers | 54.4 | 27.6 | 5.00 | 1499 |
| Memphis | 33.7 | 48.3 | -2.90 | 24 |
| Miami | 42.7 | 39.3 | 0.68 | 186 |
| Milwaukee | 39.8 | 42.2 | -0.30 | 82 |
| Minnesota | 33.6 | 48.4 | -3.07 | 24 |
| NewJersey | 37.0 | 45.0 | -1.44 | 45 |
| NewOrleans | 43.5 | 38.5 | 0.83 | 197 |
| NewYork | 36.2 | 45.8 | -1.83 | 36 |
| OklahomaCity | 30.2 | 51.8 | -4.19 | 9 |
| Orlando | 51.8 | 30.2 | 4.32 | 1025 |
| Philadelphia | 41.4 | 40.6 | 0.23 | 132 |
| Phoenix | 43.9 | 38.1 | 0.93 | 214 |
| Portland | 49.5 | 32.5 | 3.03 | 649 |
| Sacramento | 26.6 | 55.4 | -5.66 | 3 |
| SanAntonio | 46.7 | 35.3 | 2.10 | 412 |
| Toronto | 35.2 | 46.8 | -2.03 | 23 |
| Utah | 44.0 | 38.0 | 1.14 | 213 |
| Washington | 28.8 | 53.2 | -4.58 | 2 |
What's the larger point of all this? To paraphrase what Doug said in one of his posts, if people like me (and, I would imagine, a large number of you, too) can find these randomly-generated make-believe seasons interesting, then the present-day NBA is incapable of producing an uninteresting season. There may be a 48% chance that the best team will win, but there is a 100% chance that we'll enjoy the NBA this year.
October 14th, 2009 at 11:48 pm
Nitpicking here, but just because 2008 SRS wasn't statistically significant doesn't necessarily mean it should be thrown out. Statistical significance is important, but I think if you throw out 2008 SRS, you should have a theory as to why your intuition might be wrong. I'm guessing it doesn't make a big impact on the regression though.
Anyways, it's funny how there are so many 82-0 and 0-82 seasons in the simulations! Perhaps the sims can't properly take into account teams not giving it their all every time out?
October 15th, 2009 at 11:42 am
Yeah, that's my guess too, Jeremiah. This is really interesting.
October 16th, 2009 at 3:10 am
Look at Phoenix. They lost their 2 games to the Cavs in the regular season (only 2 losses), then beat them in the Finals!
Really interesting stuff here. I think that besides the 180 anomalies in 10,000 seasons (the undefeated and the fully defeated), the numbers work out like one might expect. It's strange, though, that there are so many zeros in the rank-order draws. In fact, double-digit champs were divided at the 16-mark, the number of teams in the playoffs per year, and the triple-digit champs were divided at the 9-mark, pretty close to the number of higher seeds in the playoffs each year (8).
October 20th, 2009 at 5:36 am
If a team knows that their seeded at the top before the regular season ends, the tendency of teams and coaches/staff is to rest their starters to be ready for the playoffs. So an 82-0 team is really unlikely to happen. It would be nice if it did though.
October 22nd, 2009 at 5:51 pm
"Anyways, it's funny how there are so many 82-0 and 0-82 seasons in the simulations! Perhaps the sims can't properly take into account teams not giving it their all every time out?"
It's because real life SRS does not follow a normal distribution. When they used "a mean of 2010_SRS and a standard deviation of 3.082", that was inaccurate--the standard deviation is correct, but the distribution should be unsymmetrical. There should be a much longer and thicker tail toward the mean of NBA teams, and a steeper decline toward the other side... in other words, a distribution skewed towards the mean....