Math Evidence Backs Donaghys Claim of Game 7 Bias

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Math Evidence Backs Donaghys Claim of Game 7 Bias

Statistical verdict: 44% MORE Game 7s than expected!

Las Vegas, Nevada (6/11/08) Former NBA referee Tim Donaghy has accused the NBA of manipulation of game results in order to boost ticket sales and television ratings. Commissioner David Stern has called the allegations baseless. But statistical analysis by RJ Bell of supports the claim that an abnormal percentage of NBA playoff Series are extended to seven games.

Mathematics estimate (formula below) that a NBA Playoff series will go the full seven games approximately 18% of the time. Since 2000, a surprisingly large 26% of non-first round NBA Series have extended to the maximum seven games. Thats 44% more often than expected. Thats 16 of 62 Series when only 11 would have been expected. RJ Bell of said: The odds of this increase happening randomly are less than 1%, approximately 180 to 1.

Why consider non-first round Series only? Two reasons: A) First round Series were only five games before 2003. B) If the league did attempt to extend a Series for financial gain, the gain, and thus the temptation, would have been much less in the first round.

Math behind 18%? Assume the average favorite has a 60% chance to win the Series (sometimes the favorite will have a better chance than that, sometimes worse; 60% is a solid average estimate). The odds of a series extending to 7 games is: P(favorite winning at least 4 of 7 games) + P(underdog winning at least 4 of 7 games) P(favorite sweeping 4 ) P(underdog sweeping 4) P(favorite winning exactly 4 of 5) - P(underdog winning exactly 4 of 5) - P(favorite winning exactly 4 of 6) - P(underdog winning exactly 4 of 6).

44% more Game 7s than expected clearly supports Tim Donaghys claim that the NBA Playoffs are officiated with the agenda of extending Series as long as possible.

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About RJ Bell of

RJ Bell, president of, has been featured on CBS News with Katie Couric, ABC News with Charles Gibson, Nightline, Sportscenter, Outside the Lines (ESPN), First Take (ESPN2),, ESPN National Radio, Yahoo,, and in Wall Street Journal, USA Today, Associated Press, LA Times,, Maxim, and Forbes.

Read updated math that looks at this matter from a different perspective.


  • Dan, I think a valid case could be made for some of your comments. There are certainly other POSSIBLE factors to contribute to the numbers. But there are also rebuttals to your arguments such as a team faced with elimination has increased pressure which leads to nervous play; home/away factor wise, the case could be made that a minority of series have the home team winning each game on the way to a 7th game.

    I also question your seeming assumption that there is one factor contributing, whereas it could be many (some that you mention) plus others. The math is strong, and the standard answers do not seem sufficient to explain it.

    Also note that the word used is evidence and not proof . . . there can be multiple pieces of evidence, some of it contradictory  all of it combining to yield a conclusion. I'm not assuming a conclusion - but rather offering a piece of evidence.

  • There are many just as plausible explanations for an increase in the # of Game 7s: if teams play harder when facing elimination, this would result in more Game 7s.  If there is a home court advantage, that would favor more Game 7s because each team would be favored in some games.  If playoff-caliber teams tend to "come back" from bad losses.  So, even if the numbers were fine, this is barely evidence of game-fixing.

    Also, your assumption of average 60% favorites is very unsophisticated.  A good analysis would need to take into account both home-away variance, and the variance between different match-ups.   For example, if instead of assuming 60%, you assumed 50% in half, 70% in half,  that would increase the expected # of game 7s?  

  • good read! interesting, but not surprising

  • Excellent work...I have to say that when it comes to the Donaghy scandal, has really come up big by supplying such crucial information, that so few others have dug up. And its a real testament to what Pregame is all about because those findings are know being used by everyone and anyone discussing this topic...great work, VR

  • Very impressive info RJ - Donaghy has a great point.