# Math major uncovers constant in pro hockey

Courtesy of Samantha Key
Samantha Key of Freeport, who attends Penn State Behrend, analyzed 10 years of hockey game box score to determined the importance of scoring the first goal.

It's commonly held in hockey circles that the team that scores the first goal of the game has the best chance to win.

But exactly how great of an advantage is that first goal?

Samantha Key, a Penn State Behrend (Erie) mathematics major and 2010 Burrell High School graduate, decided to quantify it.

Key, 22, studied more than 12,000 National Hockey League regular season hockey games from the past decade and was surprised by what she found.

“Anytime you score in the first two periods, you have a 67 percent chance to win the game,” Key said. “When the first goal is scored in the third period, you have a 79 percent chance of winning the game.”

Key said what shocked her about the data was that a team's chance of winning did not increase if it scored the first goal later in the first two periods.

“It's mind-blowing that it's a constant in the first two periods,” she said enthusiastically. “You'd think it would steadily increase.

“I was blown away when I saw the percentage stay the same.”

Maybe Key, whose family now lives in Freeport, should not have been so surprised. The mathematical term “a hockey stick regression” is used to describe a sharp increase late in a sample, after a flat period.

The recent Penguin-Blue Jackets playoff series seems to be an outlier in Key's data.

The team that scored first won only once in the six-game series.

“I assume (the playoffs) would follow a similar pattern,” Key said. “It would be different, though, because the pool would be reduced to only the better teams in the league. You eliminate the lesser teams.”

Key said those lesser teams make a big difference.

In the decade of hockey she studied, Key said, the Buffalo Sabres had the worst winning percentage of games won when scoring first — 46 percent — while the Detroit Red Wings had the best winning percentage — 89 percent.

It shouldn't come as a surprise that the Red Wings won two Stanley Cups and played for another during the years studied by Key.

Mike Rutter, a statistics professor at Penn State Behrend and Key's research adviser, said he was surprised by the trend the data showed.

“I would have expected it to slowly increase toward 100 percent,” said Rutter, who has published multiple papers on hockey statistics. “I expected it to grow gradually from the first minute (of the game). I was stunned when we showed that's not the case.

“That's what makes this fun: when you find something you weren't expecting.”

Rutter said Key's research goes along with a new way teams are looking for an advantage.

“There's an increasing trend in professional sports for using statistics and data,” he said. “Anytime a student can come up with what pro sports teams are doing, it's great.”

So what about the Pittsburgh Penguins?

According to Key's data, the Black and Gold won 80 percent of the games in which it scored the first goal.

“There's a distinct advantage to scoring first at home,” she said. “At home, the average team has a 76 percent chance of winning after scoring the first goal.

“That falls to 30 percent on the road.”

Key said the Penguins fell in the middle of the league at home but won a well-above-average 56 percent of the time when scoring first on the road.

9-month endeavor

Coming up with the data was no easy task for Key.

“It took me about eight or nine months,” she said. “I wrote a (computer) code that loops through every (NHL.com box score) and mines data.”

The NHL eliminated ties in 2005, so Key had to remove games that ended that way. She also discovered something about the league: It's bilingual.

“All the box scores from Montreal were in French,” she said with a chuckle. “So I had to go in and make changes for that.”

Key started her investigation out of personal benefit, but it's produced quite the opportunity for her post-college life.

The young numbers guru has been invited to present her findings in August at the prestigious Joint Statistical Meeting in Boston.

“I'd love to work with sports statistics,” Key said. “That would be a dream job.”

R.A. Monti is a freelance writer.

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