In an effort to stimulate a more exciting and entertaining style of play, the National Hockey Association (NHL) changed the rewards associated with the results of overtime games. Under the new rules, teams tied at the end of regulation both receive a single point regardless of the outcome in overtime. A team scoring in the sudden-death 5-minute overtime period would earn an additional point. Prior to the rule change in the 1999-2000 season, the team losing in overtime would receive no points while the winning team earned 2 points. This paper presents a theoretical model to explain the effect of the rule change on the strategy of play during both the overtime period and the regulation time game. The results suggest that under the new overtime format equally powerful teams will play more offensively in overtime resulting in more games decided by a sudden-death goal. The results also suggest that while increasing the likelihood of attacking in overtime, the rule change would have a perverse effect on the style of play during regulation by causing them to play conservatively for the tie. Empirical data confirm the theoretical results. The paper also show that increasing the rewards to a win in regulation time would not prevent teams from playing defensively during regular time.