Saturday, October 25, 2008

Gambling Analyst Crunches Numbers To Cast Doubt On NBA Donaghy Claims

On October 2nd, NBA Commissioner David Stern had a press conference to discuss the Pedowitz Report, which supports the assertion from the NBA that referee Tim Donaghy was the only referee gambling on games, he did not affect the outcome of games and he acted alone.

Well, affecting the outcome of games, Mr. Stern was likely referring only to the official scoreboard outcome, not the gambling outcome. If a referee doesn't do anything that has one team win that shouldn't (e.g. the "Tuck Rule" NFL playoff game), but does do things that impact the point spread result, I suppose you could claim that the referee didn't affect the outcome as the actual winner of the game didn't change. Gamblers, however, may not see things the same way.

RJ Bell of did some analysis and found out some very interesting information. Here's a quote from his post:

"The first 15 games of the 2006-07 refereed by Tim Donaghy that had big enough betting to move the point spread by at least 1.5 points were UNDEFEATED against Las Vegas - meaning that the big-money gamblers won 15 of 15 times on his games. The odds of that happening randomly are 32,768 to 1."

For those not mathematically inclined, how did Mr. Bell come up with those odds? In spread betting, the theory is that the spread will be such that equal betting will occur on both teams. If that occurs, the assumption is that each team would have a 50% chance of prevailing, even if in real life one team may be much better than the other. The point spread tends to provide a positive handicap to the perceived weaker team. So, if each team has a 50% chance, then it is similar to a coin flip.

What are the odds of heads coming up on a single coin flip? 50% or 1/2. How about heads coming up on three straight coin flips? The probability is P = 1/2 * 1/2 * 1/2 or 1/8 or 1 out of 8. Another way to say this is that the odds of three straight heads is 8 to 1.

What Mr. Bell discovered is that for those 15 games refereed by Tim Donaghy that had such heavy betting on one of the teams, such that the spread actually had to be shifted by at least 1.5 points, the big-money gamblers were on the right side of the wager every single time. Think of it as you knowing heads will come up 15 straight times. What are the odds of that? P = 1/2 to the 15th power or 1/32,768. The odds of this are 32,768 to 1. The NBA Commissioner states that referees didn't impact the outcomes of games. That is not the same thing as not having an impact of any kind.

Tim Donaghy also made calls to another referee in this time period. RJ Bell looked into that and found 10 games refereed by that person had heavy betting on one of the teams such that the spread had to be shifted by at least 2 points. The big-money gamblers were on the right side of those wagers every time. The odds of that happening were P = 1/2 to the 10th power, or 1,024 to 1.

You really think that these gambling outcomes were random? What are the odds that 15 games by one referee went one way and 10 games by another referee went one way (in favor of the heavy betting action)? P = 1/32,768 * 1/1,024 or 33,554,432 to 1. What actually happened only had a 1 in 33 MILLION chance of happening randomly. know what I think? I don't think this was random chance. Do you?

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