More on luck

I noticed a discussion of luck and consistency on HoyaTalk tonight, and that thread pointed to an article by John Gasaway on Basketball Prospectus.

Gasaway provides a list of top lucky and unlucky teams, based on winning percentage compared to net efficiency. This is something that I set up to track a while ago, but just have been too busy to get around to posting. Now that I've been scooped, I thought I'd just dump what I've got.

First, to define terms:

• winning percentage is for conference play only, as are all following stats
  
• net efficiency is simply the difference between offensive efficiency (points scored / 100 possessions) and defensive efficiency (points allowed / 100 possessions)
• luck is the difference between actual winning percentage and expected winning percentage, based upon net efficiency

So how do we determine expected winning percentage? Well, there is a fairly strong correlation between net efficiency and actual winning percentage. Here are the actual winning percentage versus net efficiency numbers for the past five seasons (2005-2009) for the Big East:




I've colored the markers for this season (through 2/26) in blue, all previous seasons in red. The horizontal and vertical black lines represent the break-even points, either as net efficiency is zero or winning percentage is 50%.

The diagonal black line is the best linear fit to the data and the dashed blue lines are the 99% prediction bands - there is only a 1 in 100 chance that a team will lie outside of the prediction bands.

Teams that lay above and to the left of the fitted line are "lucky" in the sense that they have a better winning percentage than a team would expect to have based on net efficiency. And teams below and to the right of the fitted lines are unlucky.

The infamous 2006 Notre Dame team has been the unluckiest team in the five years I've run - they ended the year 6-11 (including a loss in the BET), but would have been expected to end up 10-7. Actually their expected won/loss record in the Big East was 9.7-7.3; I'm not a big fan of decimal wins and losses, but I'll use the extra significant digit to distinguish between teams (below).

That same year, the Syracuse Orangemen ran off four improbable wins in a row in the BET, which makes them the luckiest team in the last 5 years.

We can also glean a bit more from the graph:

• While the conference is normally thought of as the Big 5 (UConn, Pitt, Louiville, Marquette and Villanova), the net efficiency rankings indicate that 'Nova may be just a bit behind those other four, and at about the same level as West Virginia.
• It may not be apparant by winning percentage, but the efficiency stats indicate that there is a big jump between the top-12 teams in the conference and the bottom four (Rutgers, USF, St. John's, DePaul).
• While there are some lucky and unlucky teams, this year there are not gross outliers either way - at least not yet.
• It's always important to keep in mind that this analysis is for the conference season as a whole, and doesn't account well for injuries (D. James, J. Dyson, etc.).
  

Note: The actual method used by Ken Pomeroy (and probably John Gasaway) to calculate luck is based on Pythagorean winning percentage. The math is a bit more complicated, but the results are essentially the same as the graph presented above - the only big differences are for extremely good or bad teams, such as DePaul. For the table below, I'll use this more rigorous method.


Here's a table summarizing this year's teams, ranked by luck.

.                 Wins  Losses   Exp Win  Exp Loss   Luck
Cincinnati          8     7        5.6      9.4       2.4
Providence          9     7        7.1      8.9       1.9
St. John's          4    11        2.3     12.7       1.7
Villanova          11     4       10.4      4.6       0.6
South Florida       3    12        2.4     12.6       0.6
Louisville         13     2       12.7      2.3       0.3
Marquette          12     3       11.7      3.3       0.3
Seton Hall          6     9        5.7      9.3       0.3
Connecticut        14     2       14.1      1.9      -0.1
Pittsburgh         12     3       12.6      2.4      -0.6
Notre Dame          7     8        7.7      7.3      -0.7
DePaul              0    15        0.9     14.1      -0.9
Syracuse            8     7        9.1      5.9      -1.1
Georgetown          5    10        6.4      8.6      -1.4
Rutgers             1    14        2.5     12.5      -1.5
West Virginia       8     7       10.4      4.6      -2.4

As Gasaway says, Cincinnati, Providence and St. John's are the luckiest teams so far this season in the Big East, and Georgetown and West Virginia are amongst the unluckiest (for some reason, he left out Rutgers).