*This post originally appeared on Hockey Graphs.*

## tl;dr

- We can measure a team’s power play structure using shot location data, creating a
*Power Play Structure Index*that quantifies their ability to establish and shoot from a structured formation. - A Team’s
*Power Play Structure Index*is a stronger predictor of future goal scoring than past goals, but weaker than shot attempt generation. - When examined together with shot attempt generation, power play structure is a significant predictor of future goals, although slightly less important than shot attempt generation.
- A team’s structure index can provide valuable additional insight into why certain power plays succeed or fail.

*Edit 2017-02-15: An earlier version of this piece had a small error in the regression coefficient for PP Structure Index. While the article previously indicated the coefficient was -0.19, it should in fact be -0.30. The text both above and below has now been corrected.*

## Introduction

The importance of structure in a team’s power play is something that’s really easy to see. We’ve all watched a power play executing at the top of its game: the puck flies from player to player, leaving defenders pivoting in place to try to keep up. Each shot looks exactly like it was diagramed by the coach, with attackers working to set up a specific shot from a specific player in a specific location.

A solid structure doesn’t just look good; it actually produces better results. Arik Parnass has written extensively on the importance of structure to power play success, showing that teams who get set up in a dangerous formation score more goals than those who don’t.

Perhaps the best example of the importance of structure is the Columbus Blue Jackets. In late December, hockey graphs alum and Visualisation Visionary Micah Blake McCurdy tweeted out these images showing the year-to-year change in shot locations for the Jackets power play:

On the left we see a power play which appears to have few well-defined roles; one where Jack Johnson roamed the entire right side of the ice and David Savard seemed to hang out at both the left point and far right corner. That group was the first unit of a power play that finished 19th in goals for per 60 last year.

On the right, however, we see a much more structured group, one where each player appears to have a specific location they’re aiming to shoot from. It shouldn’t be surprising to see that this improved structure has helped Columbus, as they currently sit first in the league with 8.8 goals for per 60 on the power play, despite being one of the lowest ranking teams in terms of shot attempt generation.

While these cases are of course anecdotal, they may offer some clues about what makes a good power play. Teams who are well-structured on the man advantage will see their players frequently creating opportunities from the same part of the ice, and will have shot location charts that look more like Columbus from this year than the Jackets from the previous campaign.

## PP Structure Index

The question then is how we go from shot location maps, which are easy to read on their own but difficult to compare across teams, to a statistic that allows us to easily summarize a team’s ability in one number.

One way to do this is to measure the size of each of those shapes on the shot location diagrams. We can do that by simply measuring how far each player on a team’s power play shoots from their average shot location. Players on well-structured teams will shoot closer to the same location most of the time, while players on poorly structured power plays will take more shots from locations that are further from their central point.

We’ll start by looking at the average distance of each player’s shots from their average shot location.

*Player Structure = (Σ Distance of Shot To Player’s Average Shot Location) / (# of Shots For Player)*

We then define a club’s power play *Structure Index**, by finding the average of these average distances and weighting by the number of shots each player contributes to a team’s power play.

*Team Structure Index = (Σ # of Shots for Player * Player Structure ) / (Σ # of Shots for Each Player)*

Lower values for a team’s *Structure Index *are good because they represent a stronger structure, meaning each player’s shots are closer to their average shot location, while higher values signal a weaker structure, meaning each player’s shots are more spread out over the ice.

## PP Structure Index: Example

A simple example illustrates how straightforward the metric is to calculate. First, let’s choose a random player (Nicklas Backstrom), and we’ll assume he took 3 shots on the power play from the following locations:

- X = 60, Y = 12
- X = 63, Y = 10
- X = 61, Y = 11

The average X location is 61.3, while the average Y location is 11. His 3 shots are 1.67, 1.94, and 0.33 feet from the average shot location, respectively. Therefore, Nicklas Backstrom’s average distance from his average location (what we’ve called Player Structure above) can be calculated as follows:

*(1.67 + 1.94 + 0.33) / 3 = 1.31*

The table below has (fake) data for the Caps power play, including the number of shots each player took and the average distance each player was from their average shot location for those shots.

Player |
Average Distance from Average Shot Location |
# of Shots |

Alex Ovechkin | 5.0 | 4 |

Nicklas Backstrom | 1.3 | 3 |

John Carlson | 3.0 | 3 |

TJ Oshie | 3.0 | 2 |

Marcus Johansson | 4.0 | 2 |

Totalling up all this data, Washington’s Structure Index becomes:

*Washington SI = (5.0*4 + 1.3*3 + 3.0*3 + 3.0*2 + 4.0*2)/(4+3+3+2+2) = 3.35*

While this fabricated data doesn’t accurately represent a reasonable structure index (3.35 would be the best number ever recorded by far, and an actual team will have many more than 5 players contributing to their structure index), it should give you a sense of what goes into each team’s total.

## Results

So which teams are well structured according to our metric?

The Washington Capitals have been the recent kings of our new stat. The Caps have topped the league in each of the last 4 years, and currently sit second this year, behind – you guessed it – the Columbus Blue Jackets. Columbus is actually more structured this season than any other club in the past 7 years, with the exception of the 2012-13 Capitals.

Interestingly enough, the Caps, along with the Philadelphia Flyers (currently 3^{rd} in structure this season), are two clubs that Arik flagged as being able to consistently establish dangerous formations last year, providing a nice bit of anecdotal support for our new metric.

At the bottom end of the rankings this year are the Florida Panthers, LA Kings, and San Jose Sharks, sitting 30^{th}, 29^{th} and 28^{th} in Structure Index respectively. All three clubs have also struggled to score on the power play, with each of them sitting in the bottom half of the league in Goals For per 60 despite being above average in terms of shot generation.

Full data from the past 7 years, including data up to this weekend’s games, are available here.

## Repeatability and Predictive Power

With any new statistic, we always want to check both its repeatability (is this statistic more a product of skill or luck) as well as its predictive power (how useful is that skill, if it exists). We measure the former by dividing the data into odd and even games and looking at how well our metric in one half predicts the same metric in the other half, which we call the split-half correlation. The table below lists the split-half correlation for our new power play structure index, as well as 5-on-4 Corsi For Per 60, and 5-on-4 Goals For Per 60, based on data from 2010-11 to 2015-16.

Metric |
Split-Half Correlation |

PP Structure Index | 0.64 |

5-on-4 CF60 | 0.70 |

5-on-4 GF60 | 0.09 |

While *PP Structure Index* is less repeatable than shot attempt generation, a split-half correlation of 0.64 is still quite high, especially given the smaller sample sizes involved in special teams play, indicating that there appears to be a repeatable skill in generating opportunities from a consistent location. It is also significantly more repeatable than raw goal scoring.

What about predictive power? We can perform a similar test, except instead of looking at how well our metric in one half predicts itself in the other half, we’ll look at how well it predicts goal scoring in the other half.

Metric |
Split-Half Correlation |

PP Structure Index | -0.17 |

5-on-4 CF60 | 0.20 |

5-on-4 GF60 | 0.09 |

There are two important things to take away from this table. First, *PP Structure Index *is negatively correlated with goal scoring, which we would expect given that a low Structure Index is good (and obviously a high goal scoring rate is good). The second is that **PP Structure Index is nearly as good at predicting goal scoring as shot attempts, and much better than past goal scoring**, confirming our original hypothesis about the importance of structure in creating a dangerous power play.

Perhaps even more interesting, however, is that the correlation between *PP Structure Index* and *5-on-4 CF60* is only 0.07, indicating that **shot attempt generation and PP structure are somewhat independent skills.**

We can then test the relative worth of each of these skills by building a simple model to predict goals in one half using both PP Structure and CF60 in the other half. We first normalize each of our variables to ensure that the coefficients produced by our model are comparable. When we run our model we see that shot generation is almost twice as important as PP structure in predicting out of sample goals (coefficient of 0.34 for CF60 vs -0.19 for Structure Index).

Variable |
Coefficient |
P-Value |

Intercept | 6.17 | < 2e-16 |

PP CF60 (Z) | 0.34 | 0.000039 |

PP Structure Index (Z) | -0.30 | 0.0002 |

What this is essentially saying is that a 10.75 increase in a team’s CF60 (basically going from league average to the top third of the league) would result in a 0.34 increase in their GF60. Similarly, a 0.77 improvement in a team’s Structure Index (once again going from league average to the top third of the league) would result in a 0.30 increase in their GF60. While shot generation is more important when both metrics are considered together, power play structure is still an important driver of on-ice results.

## Limitations and Conclusion

While our new statistic shows promising results, it is based on crude estimates of a team’s power play structure, and thus has several limitations and weaknesses that should be considered.

First, our model makes the implicit assumption that each team is trying intentionally to have every player shoot from a given location, which is obviously untrue. Our model therefore may underestimate the effectiveness of power plays where one or more player is designed to move freely throughout the ice.

In addition, rush shots may introduce additional noise into our estimates, and they likely skew our view of how teams get setup in formation. Excluding them going forward may improve both the consistency and predictive power of our metric.

Nevertheless, the predictive power of even our crude metric shows that power play structure is a key driver of team success, and that shot location data may provide important clues about how well teams are able to establish dangerous structures in their power play.

*It could have technically been called the *Weighted Average Average Distance From Average Shot Location*, but WAAFDASL seemed like a terrible acronym.

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