Posted by Neil Paine on April 19, 2011
ESPN had an interesting news story today about Danny Crawford's history with the Dallas Mavericks in the playoffs:
The gist is this:
"The Mavs have a 2-16 record in playoff games officiated by Crawford, including 16 losses in the last 17 games. Dallas is 48-41 in the rest of their playoff games during the ownership tenure of Mark Cuban, who has been fined millions of dollars in the last 11 years for publicly complaining about officiating."
At the risk of running afoul of the Wyatt Earp Effect again, what is the probability that this has happened due to chance alone?
In his book Mathletics, Wayne Winston finds that the final margin of victory in an NBA game can be approximated by a normal random variable with a mean of the point spread and a standard deviation of 12. Using that knowledge and the handy chart ESPN provided at the bottom of their story on Crawford, we can calculate the probability of Dallas winning each of their Crawford-officiated games since 2001:
|Round||Year||Date||Team||Site||Opp||Result||DAL PTS||OPP PTS||DAL Pt Diff||DAL Line||p(DAL W)|
So let's simulate that set of games 10,000 times and see how often Dallas has each possible record.
Yep, out of 10,000 simulations, Dallas ended up with a 2-16 record or worse...
That's 0.05% of the time. Now, maybe the zombie corpse of Wyatt Earp is going to eat my brain for saying this... but given their point spreads, it seems like there's very little chance that Dallas' poor performance in Crawford-officiated games has happened due to random variation alone.