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Scoring Trends in the Third Period in the Nhl

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Scoring Trends in the NHL

Scoring Trends in the Third Period in the NHL
Jack Davis
Simon Fraser University

Joint work with Dr. Paramjit Gill, University of British Columbia - Okanagan

Scoring Trends in the NHL Outline

Background Questions and Hypotheses Modelling Scoring Rate Rolling Truncated Exponential Model Effect of Scoring Trends on Ties. Proportion of games tied GLM Poisson model Diagonally Inflated Double Poisson

Scoring Trends in the NHL Background

Three eras based on regular season payoff structure:

Scoring Trends in the NHL Background

Three eras based on regular season payoff structure: Zero-Sum Era (Up to 1998-99) 5 minute OT 2pts for a win, 1pt for a tie. 0 for a loss

Scoring Trends in the NHL Background

Three eras based on regular season payoff structure: Zero-Sum Era (Up to 1998-99) 5 minute OT 2pts for a win, 1pt for a tie. 0 for a loss OT Loss Era (Up 1999-2000 to 2003-04) 5 minute OT 2pts for a win, 1pt for a tie, 1pt for an OT loss.

Scoring Trends in the NHL Background

Three eras based on regular season payoff structure: Zero-Sum Era (Up to 1998-99) 5 minute OT 2pts for a win, 1pt for a tie. 0 for a loss OT Loss Era (Up 1999-2000 to 2003-04) 5 minute OT 2pts for a win, 1pt for a tie, 1pt for an OT loss. Shootout Era (2005-06 until now) 5 minute OT followed by a shootout 2pts for a win, 1pt for an OT or shootout loss.

Scoring Trends in the NHL Questions and Hypotheses

We ask two questions: 1. Has the scoring rate in the 3rd period conditional on situation changed?

Scoring Trends in the NHL Questions and Hypotheses

We ask two questions: 1. Has the scoring rate in the 3rd period conditional on situation changed? 2. Has the probability of a game going to overtime changed?

Scoring Trends in the NHL Modelling Scoring Rate Rolling Truncated Exponential Model

N = Number of intervals sampled. Truncation at t ∗ = 300. m = Times out of N an interval ends early because of a goal. ti = Length (seconds) of i th short interval, i=1,...,m ˆ θ = MLE estimate of time to goal (Bartholomew 1957)

ˆ θ=

ti + (N − m)t ∗ m

ˆ Scoring intensity = 3600/θ = Goals per hour

Scoring Trends in the NHL Modelling Scoring Rate Rolling Truncated Exponential Model

Truncated exponential model applied to find the goal rate at each minute of regulation play. Each situation (ahead by 1, tied, behind by 1, etc.) is considered seperately and measured at the beginning of the interval.

Scoring Trends in the NHL Modelling Scoring Rate Rolling Truncated Exponential Model

Rolling truncated example.

Scoring Trends in the NHL Modelling Scoring Rate Rolling Truncated Exponential Model

Rolling truncated example.

Scoring Trends in the NHL Modelling Scoring Rate Rolling Truncated Exponential Model

Rolling truncated example.

Scoring Trends in the NHL Modelling Scoring Rate Rolling Truncated Exponential Model

Rolling truncated example.

Scoring Trends in the NHL Modelling Scoring Rate Rolling Truncated Exponential Model

Scoring Intensity for 1997-98 and 1998-99 seasons (Zero-sum era)

Scoring Trends in the NHL Modelling Scoring Rate Rolling Truncated Exponential Model

Scoring Intensity for 2002-3 and 2003-4 seasons (OT-Loss era)

Scoring Trends in the NHL Modelling Scoring Rate Rolling Truncated Exponential Model

Scoring Intensity for 2007-08 and 2008-09 seasons (Shootout era)

Scoring Trends in the NHL Modelling Scoring Rate Rolling Truncated Exponential Model

All eras have a spike in goal intensity in the last five-minute block, especially in the leading intensity. (Empty net?) After the OT Loss rule, a divergence appears between the tied situation and other situations. The divergence is less pronounced but starts near the same time in the Shootout Era.

Scoring Trends in the NHL Effect of Scoring Trends on Ties. Proportion of games tied

Proportion of games in OT by season

Scoring Trends in the NHL Effect of Scoring Trends on Ties. Proportion of games tied

Proportion of games tied after X minutes

Scoring Trends in the NHL Effect of Scoring Trends on Ties. Proportion of games tied

Scoring Trends in the NHL Effect of Scoring Trends on Ties. Proportion of games tied

Scoring Trends in the NHL Effect of Scoring Trends on Ties. Proportion of games tied

Scoring Trends in the NHL Effect of Scoring Trends on Ties. GLM Poisson model

A Poisson family generalized linear model (GLM) is fit to the number of goals scored in regulation play by a team. The scoring team’s overall offensive ability (average goals scored), the opposing team’s defensive ability, and an indicator of that the scoring team is at home were used as predictors. λijk is the expected number of goals scored during regulation play of a game by team i against team j during home-game situation k.

log(λijk ) = α + Offi + Defj + HomeTeamk φ

Scoring Trends in the NHL Effect of Scoring Trends on Ties. GLM Poisson model

log(λijk ) = α + Offi + Defj + HomeTeamk φ α is the baseline scoring rate Offi is the offensive skill of the team were modeling. Defj is the defensive skill of the team opposing the one were modeling. φ is the league home team advantage, which is only included for the home team.

Scoring Trends in the NHL Effect of Scoring Trends on Ties. Diagonally Inflated Double Poisson

Karlis & Ntzoufras (2003) mixture model x = Home team score; y = Away team score, where Pr (x, y ) = (1 − p) × Pois(x, λH ) × Pois(y , λA ) when x = y (1 − p) × Pois(x, λH ) × Pois(y , λA ) + pD(x, θ) when x = y Diagonal (tie) inflation proportion= p D(x, q) = Poisson(q)

Scoring Trends in the NHL Effect of Scoring Trends on Ties. Diagonally Inflated Double Poisson

Pr (x, y ) = (1 − p) × Pois(x, λH ) × Pois(y , λA ) when x = y (1 − p) × Pois(x, λH ) × Pois(y , λA ) + pD(x, θ) when x = y When modelling both of the scores in a game, the standard Poisson model is the inflated model when p = 0. A likelihood ratio test indicates that the diagonally inflated model explains the data better.

Scoring Trends in the NHL Effect of Scoring Trends on Ties. Diagonally Inflated Double Poisson

In OT loss; shootout eras, diagonal inflation improves the model. The structural diagonal proportion p in DIDP model) is larger in OT loss; shootout eras. Season 1996-7 1997-8 1998-9 2001-2 2002-3 2003-4 2007-8 2008-9 2009-0 DIDP mixture p .005 .005

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