If I understand the anarchy presentation correctly, I think it has some validity and application, but it fails to explain "The Ewing Theory".

First of all, and this may be besides the point, the Knicks very rarely did better without Ewing. By looking at the Knicks record in Ewing's BR splits, it is apparent that they win more frequently when he plays. I estimate that this methods shows he adds at least 7 wins per 82 games over his Knicks carer. I can expand on this conclusion if people want to see it. In fact, if I do this for other superstars, this usually ends up being a decent proxy for their expected value using statistics, etc. A similar method is used to approximate value in Basketball on Paper.

To me there appears to be mild usefulness for applying this to skill curves. The problem lies with how the team determines who shoots what shot. I feel teams should look for the easiest shot first and the bailout shot last. Thus, the last shot that should be passed up is an open layup then an open three (depending on the player of course), etc. If the team can set up a good strategy that basically looks for this progression, then you can clearly envision the effects of the "skill curve". In Ray Allen's example, the first shot would be successful at 75% (using the given .75 - .62x curve provided with x being usage%), the next would be less than that and his hardest shots when he is taking 60% of his team's shots would have virtually no chance of success. (Keep in mind that there is limited applicability to estimate success beyond the observed data points used to determine the yield curve. There are few observable situations where a player takes more than 60% of his team's shots.) By this method, which assumes a linear decrease in eFG%, the point in which Allen's next shot is expected to succeed at less than 50%, he has a 62.5% cumulative eFG%, which corresponds to the optimal eFG% quoted in the "Price of Anarchy" presentation. If I understand the assumption of traffic theory, it is assumed that when Ray Allen's eFG% is 50%, every shot he takes has a 50% success rate.

In reality, teams employ a combination of the two. A team will often look for a good shot type such as a close shot or open three and give the ball to their best shot creator, or bailout guy as the shot clock winds down. This is why eFG%'s decrease with the shot clock. However, teams will often have their best player shoot difficult shots to keep the defense honest and to suck the defense in and open things up on other possessions.

The best use for this study would be analyzing shot types. I always thought that being able to shoot a 15 footer was very valuable in keeping the defense honest, even though it is the poorest shot in terms of expected points produced. I always wondered what the optimal 2 point shooting usage would be in relation to its actual success. Shooting this more might suck the defense in and open up easier 3's and close shots for others. This could shed some light on the value of keeping defenses honest.

-at LEAST Cuban and Morey were in the room for the 'adj +/-' presentation. There was an entire row of experts, possibly a dozen of them, all clustered together in the middle of the audience. Afterwards, during the question-and-answer part of the program, Mr. Cuban made note of HOW his team uses adjusted +/-, and how extremely specific and situational the data needs to be in order for statistical analysis to TRULY have merit for predictive purposes. I didn't have time to get direct quotes, but he made general mention of the following points:

1) The data is only worth noting if you have a large enough sample (he mentioned pulling the trigger on the Evan Eschmeyer signing BECAUSE his metrics showed so much promise for the young NorthWestern Alumnus; and noted that they NEVER jump to conclusions based on paltry data samples because of it.

2) The data needs to be specific in order to be important. (Eg: Stats in the 2nd night of a back-to-back; stats in the 4th game in 5 days; stats on the last game of a road trip; stats in the 4th quarter, against a double-team, when down by 10 or more points; (he continued on for 7 or 8 more examples, which truly showed how ahead of the pack the Mavs' 'statistical war chest' has become). -how do you like the parenthetical-in-a-parenthetical? Thats how I ROLL!)

On that note, I have spoken too much.

-Dresch

http://gravityandlevity.wordpress.com/2009/05/28/braesss-paradox-and-the-ewing-theory/