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One aspect of sports analytics is the use of graphic arts to convey trends at a glance (see examples for various sports here and here). In the present posting, I apply to the recently concluded Kings-Rangers Stanley Cup finals a format I created a year ago for depicting all the goals and penalties in an entire playoff series within a single diagram. I've refined the style a little bit since last year, to make it easier to follow, in my judgment. For each game, there's a timeline for the Rangers (in light blue) and one for the Kings (in gray). Each little box in the timelines represents one minute of play. Goals are depicted by a goal judge's lamp (featuring the abbreviation of the scoring team) and by a red square in the scoring team's timeline. Penalties are illustrated by a referee's jersey (featuring the offending team's abbreviation) and by a yellow rectangle on the offending team's timeline. As described in the legend below, I've also created symbols for power-play and short-handed goals. A few major trends jump out to me upon viewing the diagram. • In none of the five games of the final series did the Rangers score in the third period (or overtime).
• The Rangers experienced a scoring drought of approximately 123 minutes, from 14:50 into the second period of Game 2 (which featured 30:26 of overtime play) until 7:25 into the first period of Game 4 (the only game the New Yorkers won).
• It was not as though the Rangers lacked scoring opportunities during their drought. During the same span of time, the Kings committed nine penalties. New York's power play during the finals was weak generally, producing only two goals in 22 attempts (Los Angeles recorded 24 penalties overall, but two were coincidental with New York penalties).
Statistician Andrew C. Thomas has done extensive research on the frequency of goal-scoring at different points in time during NHL games. We can thus compare the goal-distribution compiled by Thomas over four seasons (2003, 2004, 2006, and 2007) with the temporal distribution of the Kings-Rangers series. Putting aside the advanced mathematics Thomas uses in his analyses (e.g., exponential distribution, Poisson model, and Semi-Markov process), Thomas shows that equal-strength goals are equally likely to occur at any time in a game, with two exceptions. First, there is a lower-than-usual likelihood of goals being scored in the first minute of a period, presumably due to the opening center-ice face-off keeping the teams away from either team's net for a little while. The fastest goal in this year's finals, after the start of a period, was scored 1:46 into the second period of Game 2 by the Kings. Second, scoring goes way up in the final two minutes of a game, due to pulling of the goalie. There were neither any empty-net nor 6-on-5 equalizer goals scored in this year's finals. Thomas also states that power-play goals are most common in the second-period. Power-play goals were pretty rare in the Kings-Rangers finals, but of the five that were scored, four occurred in the second period. In order for power-play goals to be scored, one needs penalties, and the Kings and Rangers produced more of them in the second periods of their games (20 for all games combined) than in the first (11) and third (9) periods. Why might the second period be so conducive to penalties and thus power-play goals? Players may become extra cautious about committing penalties in the third period (especially in a close game), but I don't have a ready explanation for the relatively low penalty totals in first periods. Thomas also looked at the "inter-arrival times" or time-intervals between consecutive goals. I also examined the time-intervals between goals in the Kings-Rangers series (in seconds). Note that it didn't matter if both goals of a consecutive pair were scored by the Kings, both by the Rangers, or one by each team. I included all consecutive pairs in the same analysis. Also, all time-intervals were within the same game; I did not include the time between the last goal of one game and the first goal of the next. I found that consecutive goals in this year's Stanley Cup finals occurred an average of 774 seconds (almost 13 minutes) apart. The median time between goals, which removes the influence of outliers due to the overtime games, was 453 seconds (about 7:30). Short inter-arrival times were most common in this year's finals, with seven pairs of goals being separated by 240 seconds (4:00) or less (see the following plot). Thomas's plots generally exhibited the same patterns. Graphical analyses can be put to many purposes, and I hope I have illustrated some useful ones here.
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