This is a review of the NHL research conducted by Stephen Pettigrew, applying third-order polynomial regression.
Hockey statistics have come a long way over the years, yet they still lag behind other sports like baseball and football. To close this lag two new statistics are created, In-Game Win Probability and Added Goal Value. The Game Win Probability provides second-by-second probabilities that a team will the game. It takes into account the current score, penalty situation, and home-ice advantage. Added Goal Value looks at the contribution individual players make to the team’s probability of winning a game.
An algorithm is developed to deal with penalty situations, which looks at remaining time based on unexpired penalty time, goals that may erase penalty time, and league rules that dictate how penalties are handled. From there, win probabilities for each goal differential are determined. These probabilities are regressed with a third order polynomial for the time remaining in the game. The resulting coefficients are used to calculate expected win probabilities at each point in regulation time. The probabilities of short-handed and power play goals are determined using a Poisson distribution.
Not all goals have the same impact on a game or the same importance level. A goal that breaks a tie is more valuable than a goal that puts a team up 8-2. To deal with this the Added Goal Value statistic is created. Added Goal Value looks at the impact each goal has on the Game Win Probability to determine its value.
This information provides analysts with information regarding the importance of goals and killing penalties and the impact they have on win probabilities. It also provides analysts with a tool to watch for patterns throughout a game in order to determine what actions have the greatest impact on the ongoing win probability. From there player skills can be evaluated as to which add the most benefit to the win probability. It can also be used to predict who will win a playoff series by looking at the in-game win probabilities for each game.
Players can be compared and contrasted based on their Added Goal Value, especially useful when teams are deciding between two similar players in a trade situation. Players who score approximately the same number of goals in a season can be ranked based on the goal added value. This statistic is especially useful when looking at young players. Those with a higher goal added value will add greater value to a team and should be looked at closely in order to add more depth to a team.
A player’s Added Goal Value tends to remain fairly constant across seasons. This makes it an extremely useful statistic when making trades. Teams can be fairly assured that what a player contributes to their current team will be carried over to a new team.
It must be noted that the Added Goal Value is most useful when comparing players with similar goal scoring ability.
Analytics Used: In-Game Win Probability, Added Goal Value, Third-Order Polynomial Regression, Poisson Distribution
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