Late-Game Reversals in Professional Basketball, Football, and Hockey

Article excerpt

Empirical evidence suggests that in basketball, football, and hockey, the leader at the beginning of the final period (quarter or period) wins the game about 80% of the time. We discuss modeling of late-game reversals in NBA, NFL, and NHL sports. The models are built around the assumptions that basketball scores and football scores are normally distributed and hockey scores vary according to a Poisson distribution. The models also accommodate the proverbial home field advantage. We use data from the 1997-1998 regular seasons of the leagues to estimate the parameters for the models. Predictions from the probabilistic models are in excellent agreement with the actual outcomes.

KEY WORDS: Goodness-of-fit; Normal distribution; Poisson distribution; Sports data.

1. INTRODUCTION

Most of us enjoy watching our favorite teams playing (and winning) in professional sports. Suppose you are watching on TV your favorite team playing a late night game. If your team is leading in the late part of the game, can you afford to switch the TV off to go to sleep? Mosteller (1997) suggested that one can do so unless the game is very close. Empirical evidence suggests that in basketball, football, and hockey, the leader at the beginning of the final period (quarter) wins the game about 80% of the time (Cooper, DeNeve, and Mosteller 1992). A late-game reversal occurs if the team trailing at the beginning of the final period recovers to win the game.

In this article we revisit the question of reversals using some recent and more extensive data from games played during the regular seasons of the National Basketball Association (NBA), the National Football League (NFL), and the National Hockey League (NHL). An NBA game consists of four quarters of 12 minutes each. If the scores at the end of regular time are tied, play is continued in five-minute overtime periods until the tie is broken. Similarly, an NFL game is played in four quarters of 15 minutes each, and a tied game is extended for a sudden-death period of 15 minutes. The game can end in a draw. Ice hockey in the NHL is played in three periods of 20 minutes each. In case of tied scores at the end of regular time, the game goes for a sudden-death tie breaker period of five minutes. About one in six of regular season NHL games ends in a tie.

The probabilistic modeling is built around the assumptions that basketball scores and football scores are normally distributed and hockey scores vary according to a Poisson distribution. The use of normal distribution for the American football (NFL and college) and basketball data has a long history (Stern 1991, 1998; Carlin 1996). Poisson distribution is an appropriate model for low scoring sports like ice hockey and soccer. Mullet (1977) suggested using Poisson modeling for NHL scores. Recently, Danehy and Lock (1995) developed the College Hockey Offensive/Defensive Ratings (CHODR) model based on Poisson distribution. Dixon and Coles (1997) and Lee (1997) used the Poisson model for the soccer scores in English leagues.

Almost all the league games are played at the "home arena" of one of the two teams. Thus, the two teams in a game are distinguished as "home" and "away" teams. It is well known that professional games exhibit some home-field advantage. We do not distinguish between the favorites and underdogs. As noted by Cooper, DeNeve, and Mosteller (1992), the present data also exhibit home-field advantage in reversals. Team scores at the beginning of the last period and the scores during the last period are modeled separately. As two referees pointed out, various teams in a given league differ in their ability to score and to produce late-game reversals. However, for the sake of simplicity and lack of sufficient data, we do not accommodate the differential ability of the teams.

We use data from the 1997-1998 regular seasons of the NBA, NFL, and NHL. This covered 1065 NHL games, 1,188 NBA games, and 240 NFL games. …