I found the stats article they reference posted on one of the original author's home pages -
http://www.rob-mcculloch.org/exec_da...ing/penpap.pdf
Interestingly, in the news article, they state that the shape does not change based on the score. However, this other journal article says differently.
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[goal differential] and [time between penalties] are important variables with intuitive effects. If the last penalized team was behind, you don’t want to call them again. The longer it has been since the last penalty, the smaller the tendency to reverse call
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A few other interesting bits out of this. Keep in mind what they call 'reverse call' is making the call on the team that was NOT penalized last.
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The results confirm that various game situations (score, time, time since last penalty, etc) and characteristics (home team, one versus two referees, etc) have extremely significant effects on the reverse-call probability.
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Quote:
The reverse call percentages under the one-referee system are higher overall as well as more disperse. ... suggest that referee behavior was changed by the addition of a partner. There are several possible explanations. One possibility is that with a partner, the psychological stress is diminished and so is the tendency to reverse call. Another possibility
is that two referees are able to more accurately detect actual offenses and, therefore, fewer reverse calls are needed in the name of fairness.
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Quote:
Our basic hypothesis is that the speed and physical nature of the NHL game, combined with the expectation that many infractions will go uncalled, put the referee in a very difficult situation. Since penalty calling can be largely subjective, it is easy for teams, coaches, and fans to view referees’ calls as unfair to their side. In order to keep control of the game and avoid being blamed for the outcome of the game by the loser, it would seem logical that referees would adopt the following strategies:
• make fewer calls later in the third period when the game is on the line
• avoid making repeated calls on the same team
• avoid penalizing the team that is behind
• avoid penalizing the home team
• avoid calls on the same team in quick succession
The empirical findings of this paper are consistent with each of these strategies.
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And finally... well... duhhhh... OBVIOUSLY.