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NBA Ref Scandal: Reviewing My Over/Under Theory

Tim Donaghy
AP
Tim Donaghy

Now that the NBA hasn't told us anything about whether former NBA ref Tim Donaghy bet on games or not, it's time to take a look back at my over/under analysis. I believed that Donaghy was clearly betting the over throughout the last two years because of the fact that his games his the over 57 percent of the time compared to 44 percent in the two years before.

Many in the media, including ESPN.com and the AP, picked up this stat from our guy R.J. Bell at Pregame.com. I was waiting for some good skepticism to come in from a reader or two. This morning, I found a great e-mail in my box from a reader named Brian Sisk.

Darren,
Read your article on Donaghy with interest. I'm a scientist by trade and get to play a lot with statistics -- not to mention a big sports fan. Naturally, this story has me extremely interested. I'll preface this by saying that I know nothing of Donaghy's guilt or innocence. However, pregame.com's interpretation of their statistics is quite inaccurate.

Let's examine their clincher. They state "Assuming 44 percent "over" is Donaghy's natural tendency, the odds of being "over" 57 percent for two full seasons are about 1000-1 against!" In reaching that conclusion, they make two fatally flawed assumptions.

First, the assumption they make -- that 44 percent is Donaghy's natural tendency -- simply isn't true. They only go back two years, which given the season-to-season variation (see below) isn't enough to characterize a ref's tendencies. I analyzed the data using Covers.com's online data. From 1997-2005, Donaghy's average "Over" percentage is 51.7 percent, a good bit higher than the 44 percent over the two-year span before Donaghy got turned by the gamblers. Still, that's lower than his 57 percent in the last two years. The question is, is that different enough for us to be able to make a determination?

That brings me to the second flaw: their analysis doesn't take into account the natural variation in year-to-year tendencies for other, presumably non-crooked refs. Many other refs show somewhat similar fluctuations -- a 10% swing isn't as rare as the 1000-1 odds would make it seem, and nearly every ref in the league shows similar swings at some point (most of whom, I hope, are clean). Let's consider a generally well reputed referee, Steve Javie. Between 2001/02 -2004/05, Javie's "Over" percentages were 49 percent, 51 percent, 43 percent and 49 percent.If pregame.com is right, and a 10 percent swing is evidence of a significant difference, then Javie must be dirty too, right? Problem is, every ref shows these sorts of swings.

In the end, Donaghy's behavior on Over/Unders, like every refs, shows significant swings over the years that is probably due to many factors, including the crew they work with, changes in rule emphasis, and luck. In the end, there is not sufficient evidence in the gross statistics collected to make a determination that Donaghy shows aberrant behavior recently. I've not given up on finding some more subtle effects than pregame.com considered, which may yet yield something. Problem is, we don't know yet how many games he altered, nor -- most importantly -- whether he always tried to push the over/under high, or whether he mixed it up. If he did, it may be hard to find a result.

I thought that Brian was very reasonable here. The only other thing I have is what I first found yesterday on Henry Abbott's True Hoop blog on ESPN.com. It's the fact that Donaghy apparently led all refs in technical fouls calls and free throw attempts per game. That I thought was another score for the over/under.

Questions? Comments? SportsBiz@cnbc.com

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