Multi-Tiered Playoffs and Their Impact on Professional Baseball

Article excerpt

1. INTRODUCTION

Professional baseball has recently witnessed a radical shift in fan support. This is due, in part, to the 1994 professional baseball strike and the inability of baseball management and the player's union to successfully negotiate a new collective bargaining agreement. The resulting loss of fan support has led to unprecedented reform in the hope that professional baseball may regain part of the market share lost to other competitive team sports.

One area of reform involves an expanded playoff structure, first introduced in 1995. The long standing policy of two divisional champions competing head to head in a best-of-seven playoff series, with the winner advancing to the World Series, has been replaced with a two-tiered wildcard playoff format. This format involves pairing off three divisional winners and one wildcard entrant in a best-of-five series, with the winners meeting in a best-of-seven playoff series; the survivor advances to the World Series.

This article investigates the statistical impact of the wildcard series. An allocation rule is developed for the distribution of a specified number of games between two tiers so as to maximize the likelihood that the team with the highest regular season winning percentage advances to the World Series. Results are not intuitive and indicate that the current best-of-five followed by a best-of-seven format used in professional baseball may not satisfy this objective, and increase the likelihood of an upset. Similar findings regarding statistical bias against better teams also applies to divisional play (Weiss 1986).

Other factors may also influence the likelihood of upsets. For example, between 1969-1995, professional baseball has produced only four teams that have won 65% of their regular season games, although the National Hockey league, National Basketball Association, and National Football League had three, six, and five .650 teams, respectively, during the 1994-1995 season alone. Perhaps the simple truth is that teams in professional baseball are not as dominant as in other sports, and what might be perceived as dominant in baseball might simply be considered above average elsewhere. The adage that "any team can win on a given day" may have more of a foundation in professional baseball than other sports, and partially explain why playoff upsets in baseball occur with some regularity: For the 25 regular seasons between 1969 to 1993 inclusive, the playoff team with the highest winning percentage has won the World Series only eight times (32%).

The study of pennants and playoffs was initially investigated by Mosteller (1951), who considers the probability that the better team wins a conventional seven-game world series. Gibbons, Olkin, and Sobel (1978) built on these results, concluding that a seven-game series is not sufficient to provide high levels of confidence that the winner is in fact the better team, a result supported by simulation findings (James, Albert, and Stern 1993). Hurley (1993) considered optimal pairings in tournaments and the home-field advantage in playoffs. This article extends these findings in considering how the inclusion of a wildcard round impacts on playoff results.

The format of the article is as follows: Section 2 considers a basic one-tier playoff format, the results of which are extended in Section 3 to a two-tiered playoff structure. Analysis of results and an allocation rule is developed in Section 4; Section V concludes the article.

2. THE ONE-TIER PLAYOFF SERIES

Consider a one-game playoff series, similar to the Super Bowl in professional football. Assume that the better team, defined as the team with the higher regular season winning percentage (team A), is expected to beat their opponent (team B) 60% of the time. Obviously, if a one-game series is played, there exists a 40% chance for an upset. To decrease this chance, a longer series may be considered. …