In order to avoid too many tied games after playing the five-minute overtime period, the National Hockey League (NHL) introduced two rule changes in the 1999-2000 season. First, a team that loses in overtime receives one point instead of zero points. Second, the number of skaters in overtime is reduced from five to four. The theoretical literature analyzing these rule changes predicted that they would also produce the unintended side-effect that more games would reach overtime and recommended that a team that wins in regulation should receive three points (instead of two) in order to counterbalance the converse effect. We are the first to empirically support this theoretical prediction using NHL data and data from Swiss ice hockey, in which the rule changes of the NHL were copied in the 2006-2007 season and in which the three-point rule was also introduced.