Bayesian Space-Time Models for Expected Possession added Value – Part 1 of 2

Cowritten by Brendan Kumagai, Mikael Nahabedian, Thibaud Châtel, and Tyrel Stokes


This is part one of a two part series introducing our bayesian space-time model for evaluating offensive sequences and player actions. In this part we describe the model and the key metrics derived from it. In part 2 we will show how the model can inform and integrate with player and team evaluations.

Hockey is a game of making the best possible decision in the shortest amount of time. Players need to react quickly to form a chain of plays to create valuable scoring chances. Our goal is to quantify the value of player actions as a function primarily of space and time in the offensive zone. This is to recognize that the puck location and the threat-level it poses to the opposition is a key driver of what options will be available to the puck carrier and – as a result – what is likely to happen next. Ultimately, we want to credit players that are able to make high quality decisions and difficult plays which advance the puck into more valuable locations on the ice.

To this end, we primarily build off of 3 previous papers. First, we use the conceptual framework of understanding play sequences in hockey (Châtel, 2020) from our team member Thibaud Châtel. Second, we adapt the multi-resolutional Expected Possession Value modelling framework pioneered by Cervone et al. (2016) in basketball to work with the detailed play-by-play data generously provided by Stathletes as part of the Big Data Cup hackathon. Finally, using this infrastructure we propose a metric called the Possession Added Value (PAV) based on Karun Singh’s Expected Threat Model in soccer (Singh, 2018) which has previously been adapted to hockey (Yu et al., 2020).

Due to the timeframe of the competition and the complexity of our proposed model, we decided to narrow our scope down to offensive even strength sequences that begin with an entry and end with either a shot or a whistle. By only considering offensive sequences the model as it stands can only properly evaluate the actions of the offensive team.

Before we dig into our methodology, here is an example of what our end product will look like in Figure 1 below. We assign each event in this entry-to-exit/whistle sequence with our Possession Added Value (PAV) metric, which can be thought of as the increase in probability that we score in the sequence by performing the observed action. For example, the pass by Landon McCallum from the top of the left circle into the slot adds 0.0677 goals to the expected value of the possession.

Figure 1: An offensive zone sequence with our Possession Added Value (PAV) metric

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Using Sequences for Analysis: Expected Goals Contribution and more

In a previous article, I presented a way to cut and slice a hockey game into Sequences. A Sequence extends from the moment a team gets control of the puck and starts moving forward, to the moment the team loses it for good. The objective was to measure the importance of every event happening between the beginning of a Sequence and its end, from a zone exit to any shot attempts, to a zone entry or any high-danger passes in between. If a Sequence includes one or several shot attempts, its value is the sum of the Expected Goals of all those attempts.

The natural follow-up was the creation of an Expected Goals Contribution metric for players.

The thinking behind it was to answer one of the two main questions we face in the daily use of analytics with coaches: What is the real contribution of each player? Overall, there are the well-known GAR or WAR type of metrics, but these are beyond the comprehension of many staffs as they are not tangible enough for a daily use.

Now, if we use Sequences where the team has possession of the puck, it means Expected Goals Contribution would only look at the offensive side of the game. Still, instead of looking separately at transition or shooting stats to evaluate a player, the objective is to sum all offensive efforts into one metric, weighting those efforts (zone exit, entry, etc.) according to their contribution to the Sequence. It also makes playmaking more apparent statistically.

In other words, it means sharing the total value of the Sequence (in terms of Expected Goals), between the players responsible. This is what we called Expected Goals Contribution.

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