28 VOL. 22, NO. 1, 2009 L ate in the second period of a game between the Dallas Stars and Edmonton Oilers during the 2005–2006 National Hockey League (NHL) season, Jussi Jokinen, a rookie with the Stars, was awarded a penalty shot. For such shots, the goaltender has a sizable advantage, as NHL players score on roughly one in three penalty shots. Jokinen scored and, in the process, continued a rather remarkable streak. He scored on his three penalty shots during the NHL pre- season and on nine straight penalty shots during the regular season up to the Oiler game. So, all in, he was successful on his first 13 penalty shots, an unofficial NHL record not likely to be broken any time soon. Jokinen’s performance, and those of some lesser known players, led media commentators to assert that there were players with exceptional ability on penalty shots and that NHL teams were actively looking for these penalty shot specialists. Jokinen has since cooled off. Throughout the complete 2005–2006 regular season, he went 10 for 13, and over the 2006–2007 season, five of 12, a frequency more in line with the league-wide rate. Jokinen’s streak, his subsequent cool- ing off, and the media discussions at the time the streak was maturing raise some interesting questions. The first is an assessment of the role of chance in explaining Jokinen’s rookie season performance. Based on a standard order statistics argument, one would expect the highest relative scoring frequency (defined as the fraction of penalty shots that result in a goal) to be fairly high. The question is whether Jokinen’s frequency, 10 for 13, is suf- ficiently high to warrant the conclusion that something other than chance is part of the explanation. The second question is whether the media prognosticators were correct that taking a penalty shot is a special skill, that some otherwise gifted NHL scorers did not possess this skill, and that it was important for teams to identify their shootout specialists. For example, Joe Sakic, the Colorado Avalanche captain and future Hall of Famer, is a prolific scorer, but did not score a single goal in his seven penalty shots over the 2005–2006 season. There is significant experimental evidence that people are quick to find a pattern in a random sequence where there isn’t one, especially when the sequence is relatively short. Amos Tversky and Daniel Kahneman, in a 1971 article pub- lished in Psychological Bulletin, termed this bias the “law of small numbers.” In sum, does the evidence support the existence of a subclass of players with shootout ability superior to proven NHL stars? Finally, the shootout data set covers two NHL seasons. This affords an opportunity to study the phenomenon of regres- sion to the mean. Were players who exhibited high scoring rates on penalty shots throughout the 2005–2006 season able to maintain those rates over the 2006–2007 season? Did the worst players over the 2005–2006 season improve over the 2006–2007 season? Given the increasing competitiveness of the NHL, teams must do well in shootouts. Every point counts. For instance, during the 2005–2006 season of the Eastern Conference, Tampa Bay finished in the last playoff spot with two more points than Toronto. During the season, Tampa Bay won six of Jussi Jokinen, Regression to the Mean, and the Assessment of Exceptional Performance W. J. Hurley Dallas Stars forward Jussi Jokinen, of Finland, works the puck in a hockey game against the Montreal Canadiens on December 23, 2007, in Dallas, Texas. (AP Photo/Matt Slocum)