Betting on NBA Playoffs

King Yao is the author of Weighing the Odds in Hold‘em Poker, and Weighing the Odds in Sports Betting. He uses his experience from making millions in financial derivative markets and translates it into gambling. Since he left his trading position in 2000, he has been playing poker and betting on sports. He travels to Las Vegas frequently, especially during football season.

A Sports Riddle

Two teams play in a best-of-seven series in which each team has exactly 50% chance of winning each game. There is no home field advantage and there is no memory of previous games (results in previous games do not affect later games). Which is more likely to occur: the series ends in six games or the series ends in seven games?

Try to answer this question without doing any math. Try to use logic only. Do not read further until you have given it some thought.

Most people’s gut-feel answer is that the series is more likely to end in seven games than six games. Since the teams are equally matched, it feels like the series will be closely played. There is no closer series than a 4-3 series.

The correct answer is that the series is equally likely to end in six or seven games. Brute force can be used to crank out all the possibilities and come up with that answer. But a logical answer with no math involved is more elegant and interesting.

Two questions will help to get the logical answer: How can a series end in seven games? How can a series get to 3-3?

• How can a series end in seven games? Answer: the series must be tied 3-3 in order for the seventh game to be played.
• How can a series get to 3-3? Answer: the series can get to a 3-3 tie only when one team is ahead 3-2.

Putting these two together, you see that if a team that is ahead 3-2 wins the sixth game, then it wins the series. If the team that is ahead 3-2 loses the sixth game, then the series will go to the seventh game. If each team has a 50% chance of winning each game,the team ahead 3-2 in the series has a 50% chance of winning game 6 and ending the series in 6 games. Conversely, the team ahead 3-2 in the series has a 50% chance of losing game 6, which means a seventh game will be played.

In real life this may not be directly applicable, because teams and players do have memories and there is usually an advantage to playing at home. The NBA home-court advantage is large, so it often matters which team is at home and what the series results are going into Game 6. NBA teams have the tendency to play better and win more often after a bad game in the playoffs. The informally named zigzag theory explains this effect.

Zigzag Theory

The simplest form of the zigzag theory in the NBA playoffs is: The team that lost a game is likely to cover the spread in the next game. For example, if the Lakers lost to the Suns in game 1 of a playoff series, the zigzag theory suggests betting on the Lakers to cover in game 2.

From a database of NBA playoff games over several years, the zigzag theory’s record is 231-211 for a winning percentage of 52.3%, basically break-even for -110 lines.

A refinement to the zigzag theory is to add in the qualification that the losing team did not cover the point spread in the previous game. With that refinement, the zigzag theory’s record was 190-163 for a winning percentage of 53.8%. Data miners can get better winning percentages with more refinements, but testing them runs into the problem of small sample sizes.

I do not recommend you bet the zigzag theory based on this discussion alone. Line makers learn from history and sportsbooks adjust to action. Because the zigzag theory is well known, line makers probably have a good handle on its historical performance. Lines in the NBA playoffs may already have the zigzag factor embedded in them. Thus blindly betting the zigzag theory may be negative EV in future games.

Future articles will present historical against-the-spread (ATS) records and line changes from game to game, which are more important. Bigger line changes than in the past suggest that the zigzag theory is embedded in the line.

This is part of an occasional series of articles.

Excerpted with permission from the e-book version of Weighing the Odds in Sports Betting by King Yao, edited for this format.