## Friday, May 15, 2015

### Consequence of Morey's Law: Lucky vs Unlucky teams

In a previous post, I looked at a 1994 paper by Daryl Morey (current Houston Rockets GM) who investigated how a team's winning percentage was related to the number of points they scored and allowed, deriving the "modified Pythagorean theorem":

expected win percentage =
pts_scored ^ 13.91 / (pts_scored ^ 13.91 + pts_allowed ^ 13.91)

At the end of his paper, Daryl explores teams who had the biggest delta between their actual and predicted wins. In 1993-1994, the Chicago Bulls and Houston Rockets top the list and Daryl refers to them as lucky teams. But why is lucked involved?

The rationale is that if you have two teams A and B with almost identical points scored and points allowed, we would expect them to have very similar win percentages. The only way to create a discrepancy (without changing points scored and points allowed... too much), is by changing the outcome of the very close games. So for all the games team A won by a point, flip the scores so that they lose by 1, and reversely for team B who now wins all the games they previously lost by 1. With this hypothetical construction, we will have two teams still with very similar points scored and allowed but potentially different records. It would make common sense that for very close games the probability of each team winning is around 50%, so winning or losing amounts to "luck", whether a desperation buzzer-beater is made or bounces off the back of the rim. And so it would make sense that teams with high discrepancies between actual and predicted wins were either much better or much worse than 50% in close games. Let's confirm.

Here's the table of teams with discrepancies greater or equal to 6 between their actual and projected records, ranked by year:

 Team Year Scored Allowed Wins (proj) Wins (actual) Win % NJN 2000 98.0 99.0 38 31 37.8 DEN 2001 96.6 99.0 34 40 48.8 NJN 2003 95.4 90.1 56 49 59.8 CHA 2005 94.3 100.2 24 18 22.0 NJN 2005 91.4 92.9 36 42 51.2 IND 2006 93.9 92.0 47 41 50.0 TOR 2006 101.1 104.0 33 27 32.9 UTA 2006 92.4 95.0 33 41 50.0 BOS 2007 95.8 99.2 31 24 29.3 CHI 2007 98.8 93.8 55 49 59.8 DAL 2007 100.0 92.8 61 67 81.7 MIA 2007 94.6 95.5 38 44 53.7 SAS 2007 98.5 90.1 64 58 70.7 NJN 2008 95.8 100.9 27 34 41.5 TOR 2008 100.2 97.3 49 41 50.0 DAL 2010 102.0 99.3 49 55 67.1 GSW 2010 108.8 112.4 32 26 31.7 MIN 2011 101.1 107.7 24 17 20.7 PHI 2012 93.6 89.4 43 35 53.0 BRK 2014 98.5 99.5 38 44 53.7 MIN 2014 106.9 104.3 48 40 48.8

So how did these teams fare in close games? I've labelled a team/year as High if they won 6 or more games than expected (8 teams from the previous list), Low if they lost 6 or more  games than expected (13 teams from the previous list), and Normal otherwise. I then look for each group their win percentage in closely contested games (final scores within 1, 2 and 3 points).

Final scores within 1 point:

 Type # Wins # Games Win % Normal 721 1439 50.1 Low 8 21 38.1 High 2 2 100.0

Final scores within 2 points:

 Type # Wins # Games Win % Normal 1760 3515 50.1 Low 20 52 38.5 High 10 13 76.9

Final scores within 3 points:

 Type # Wins # Games Win % Normal 2820 5617 50.2 Low 24 80 30.0 High 14 19 73.7

Our intuition was correct and so were Daryl's closing comments: teams can indeed be qualified as lucky and unlucky, some winning almost 3 out of 4 close match-ups, others losing 2 out of 3 tight games. This intangible "luck" factor is sufficient to explain why certain teams have much better or worse records than their offense/defense would typically lead to. It doesn't take much for to flip the outcome of an entire game.

As a quick aside, much has been said about the San Antonio Spurs this year and their drop from a potential 2nd seed to 6th seed entering the Playoffs. Most articles focused on their loss on the final day of the regular season which led to that seeding free-fall, but was excessive focus placed on that last game? Had they been particularly lucky/unlucky during the season? It turns out their record is a couple games lower than what the modified Pythagorean theorem would have predicted, and that they weren't particularly lucky or unlucky in their close games, winning 2 of 5 games decided by 1 point, and 6 of 13 decided by 3 points or less.