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SRS Standard Errors, the Probability of Being the Best Team, and a Layup

Posted by Neil Paine on January 20, 2011

I finally got around to calculating the standard errors for our team Simple Ratings today:

Team Estimate Std. Error
SAS 7.97 2.62
MIA 6.90 2.60
BOS 6.67 2.63
LAL 5.78 2.59
CHI 4.81 2.61
ORL 4.61 2.61
DEN 3.48 2.63
DAL 3.30 2.62
NOH 2.40 2.60
OKC 2.05 2.61
ATL 1.75 2.60
UTA 1.73 2.61
HOU 0.86 2.60
POR 0.52 2.60
MEM 0.49 2.61
NYK 0.09 2.62
MIL -0.57 2.65
PHI -0.79 2.63
IND -0.87 2.65
LAC -1.51 2.63
PHO -1.91 2.64
GSW -2.92 2.62
CHA -3.74 2.64
DET -3.94 2.61
TOR -4.23 2.62
MIN -5.33 2.60
WAS -5.82 2.64
SAC -6.12 2.64
NJN -6.22 2.61
CLE -10.88 2.62

Then I set up a little Monte Carlo sim to estimate what is the probability of each team being the NBA's best (aka the team with the greatest "true" SRS skill). After 10,000 simulations using the estimates and standard errors above, here were the results:

Team Best Team p(Best)
SAS 3532 35.3%
MIA 2045 20.5%
BOS 1773 17.7%
LAL 984 9.8%
CHI 576 5.8%
ORL 476 4.8%
DEN 211 2.1%
DAL 152 1.5%
NOH 69 0.7%
OKC 56 0.6%
UTA 42 0.4%
ATL 33 0.3%
HOU 17 0.2%
POR 11 0.1%
MIL 6 0.1%
NYK 6 0.1%
MEM 5 0.1%
IND 2 0.0%
PHO 2 0.0%
LAC 1 0.0%
PHI 1 0.0%
CHA 0 0.0%
CLE 0 0.0%
DET 0 0.0%
GSW 0 0.0%
MIN 0 0.0%
NJN 0 0.0%
SAC 0 0.0%
TOR 0 0.0%
WAS 0 0.0%

According to this, we can be about 94% sure that the best team is either San Antonio, Miami, Boston, the Lakers, Chicago, or Orlando.

One interesting idea for a playoff system would be to eliminate all teams we were 95% sure weren't the best team and set the odds of winning the playoff to mirror the uncertainty we had regarding who was the best -- i.e., rig it so San Antonio had a substantially larger chance of winning the tournament than Chicago, etc. The NBA already does this to a degree via seedings and home-court, but you could even go as far as giving teams automatic 1-0 leads in a series to get the probabilities right.

For a great article that goes further with that idea, check out this Sky Andrecheck piece on the MLB playoffs, and the philosophy of why playoffs are necessary at all:

The Baseball Analysts: The Science of Playoffs

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8 Responses to “SRS Standard Errors, the Probability of Being the Best Team, and a Layup”

  1. Ben Says:

    This is really cool. Have you done this it all for previous seasons. I wonder what the highest level of certainty has been at the end of the the playoffs?

  2. Neil Paine Says:

    I only did it for this year, but then I plugged in 2007 (playoffs included) just as a test. Here were the errors:

    Tm Estimate Std. Error
    ATL -5.089 2.452
    BOS -3.919 2.452
    CHA -4.187 2.452
    CHI 4.141 2.421
    CLE 3.367 2.394
    DAL 6.192 2.433
    DEN 1.545 2.436
    DET 3.826 2.405
    GSW 0.599 2.418
    HOU 4.427 2.430
    IND -2.834 2.452
    LAC -0.279 2.452
    LAL -0.117 2.436
    MEM -4.656 2.452
    MIA -1.668 2.439
    MIL -4.658 2.452
    MIN -3.384 2.452
    NJN -0.641 2.415
    NOK -1.416 2.452
    NYK -3.282 2.452
    ORL -0.110 2.439
    PHI -3.472 2.452
    PHO 7.287 2.418
    POR -3.995 2.452
    SAC -1.566 2.452
    SAS 8.052 2.394
    SEA -2.660 2.452
    TOR -0.026 2.433
    UTA 3.281 2.403
    WAS -1.212 2.439
    HCA 3.079 0.321

    And here were the likelihoods of being the best:

    Tm Pct
    SAS 45%
    PHO 26%
    DAL 14%
    HOU 4%
    CHI 4%
    DET 3%
    UTA 2%
    CLE 1%
    All Others 1%
  3. Ben Says:

    Very cool. I bet 2006 would not be very decisive at all. 1996, probably pretty clear cut.

  4. Ben Says:

    Also would be interesting to see pre and post playoffs for different years.

  5. Ben Says:

    45% for Spurs. 6% chance for other Conference Finalists! And the best part is, that it really does make sense.

  6. Neil Paine Says:

    Here's 1996, post-playoffs:

    Team p(Best)
    CHI 87%
    UTA 5%
    SEA 5%
    SAS 2%
    ORL 1%

    I would imagine that's about as much certainty as you're going to get in a given season.

  7. Ben Says:

    Interesting - would've guessed they'd crack 90%, but from the first post you'd made I was a little surprised at how big the standard errors were so I shouldn't be surprised here. Thanks for doing that. Very fun to see.

  8. Ben Says:

    If you used this methodology for players (using adjusted plus minus), the very best would probably be lucky to hit 10%.