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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.

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5 Responses to “Ten Thousand 2010s”

  1. Jeremiah Says:

    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?

  2. Tsunami Says:

    Yeah, that's my guess too, Jeremiah. This is really interesting.

  3. Jared Ras Says:

    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).

  4. Carl Says:

    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.

  5. DSMok1 Says:

    "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....