Math Evidence Backs Tim Donaghy’s Claim of Game Seven Bias

Statistical verdict: 44% MORE Game Sevens 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, with the help of my handicapping team at Pregame.com, 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 percent of the time. Since 2000, a surprisingly large, 26 percent of non-first round NBA Series have extended to the maximum of seven games. That’s 44 percent more often than expected. That’s 16 of 62 Series when only 11 would have been expected. The odds of this increase happening randomly are less than one percent, 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 percent?

Assume the average favorite has a 60 percent chance to win the series (sometimes the favorite will have a better chance than that, sometimes worse; 60 percent is a solid average estimate). The odds of a series extending to seven games are:

P (favorite winning at least four of seven games) + P (underdog winning at least four of seven games) – P (favorite sweeping four) – P (underdog sweeping four) – P (favorite winning exactly four of five) - P (underdog winning exactly four of five) - P (favorite winning exactly four of six) - P (underdog winning exactly four of six).

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