Strategic Snapshot: Isolating QREAM
This is a great start. The next step in confirming the validity of a statistic is looking how it holds up over time. Is goalie B consistently weak on powerplay shots from the left side? Is something that can be exploited by looking at the data? Predictivity is important to validate a metric, showing that it can be acted up and some sort of result can be expected. Unfortunately, year over year trends by goalie don’t hold up in an actionable way. There might be a few persistent trends below, but nothing systemic we can that would be more prevalent than just luck. Why?
Game Theory (time for some)
In the QREAM example, predictivity is elusive because hockey is not static and all players and coaches in question are optimizers trying their best to generate or prevent goals at any time. Both teams are constantly making adjustments, sometimes strategically and unconsciously. As a data scientist, when I analyse 750,000 shots over 10 seasons, I only see what happened, not what didn’t happen. If in one season, goalie A underperformed the average on shots from the left shooters from the left side of the ice that would show up in the data, but it would be noticed by players and coaches quicker and in a much more meaningful and actionable way (maybe it was the result of hand placement, lack of squareness, cheating to the middle, defenders who let up cross-ice passes from right to left more often than expected, etc.) The goalie and defensive team would also pick up on these trends and understandably compensate, maybe even slightly over-compensate, which would open up other options attempting to score, which the goalie would adjust to, and so on until the game reaches some sort of multi-dimensional equilibrium (actual game theory). If a systemic trend did continue then there’s a good chance that that goalie will be out of the league. Either way, trying to capture a meaningful actionable insight from the analysis is much like trying to capture lightning in a bottle. In both cases, finding a reliable pattern in a game where both sides and constantly adjusting and counter-adjusting is very difficult.
This isn’t to say the analysis can’t be improved. My expected goal model has weaknesses and will always have limitations due to data and user error. That said, I would expect the insights of even a perfect model to be arbitraged away. More shockingly (since I haven’t looked at this in-depth, at all), I would expected the recent trend of NBA teams fading the use of mid-range shots to reverse in time as more teams counter that with personnel and tactics, then a smart team could probably exploit that set-up by employing slightly more mid-range shots, and so on, until a new equilibrium is reached. See you all at Sloan 2020.
Data On Ice
Game Theory (revisited & evolved)
A More Robust (& Strategic) Approach
The primary role of analytics in sport and business is to deliver actionable insights using the tools are their disposal, whether is statistics, math, logic, or whatever. With current data, it is easier for analysts to observe results than to formulate superior on-ice strategies. Instead of struggling to capture the effect of strategy in biased data, they should be using this to their advantage and look at these opportunities through the prism of game theory: testing and measuring and let the best strategies bubble to the top. Even the best analysis might fail to pick up on some second order effect, but thousands of shifts are less likely to be fooled. The data is too limited in many ways to create paint the complete picture. A great analogy came from football (soccer) analyst Marek Kwiatkowski:
Almost the entire conceptual arsenal that we use today to describe and study football consists of on-the-ball event types, that is to say it maps directly to raw data. We speak of “tackles” and “aerial duels” and “big chances” without pausing to consider whether they are the appropriate unit of analysis. I believe that they are not. That is not to say that the events are not real; but they are merely side effects of a complex and fluid process that is football, and in isolation carry little information about its true nature. To focus on them then is to watch the train passing by looking at the sparks it sets off on the rails.
Hopefully, there will soon be a time where every event is recorded, and in-depth analysis can capture everything necessary to isolate things like specific goalie weaknesses, optimal powerplay strategy, or best practices on the forecheck. Until then there are underlying forces at work that will escape the detection. But it’s not all bad news, the best strategy is to innovate and measure. This may not be groundbreaking to the many innovative hockey coaches out there but can help focus the smart analyst, delivering something actionable.
 Is hockey a simple or complex system? When I think about hockey and how to best measure it, this is a troubling question I keep coming back to. A simple system has a modest amount of interacting components and they have clear relationships to other components: say, when you are trailing in a game, you are more likely to out-shoot the other team than you would otherwise. A complex system has a large number of interacting pieces that may combine to make these relationships non-linear and difficult to model or quantify. Say, when you are trailing the pressure you generate will be a function of time left in the game, respective coaching strategies, respective talent gaps, whether the home team is line matching (presumably to their favor), in-game injuries or penalties (permanent or temporary), whether one or both teams are playing on short rest, cumulative impact of physical play against each team, ice conditions, and so on.
Fortunately, statistics are such a powerful tool because a lot of these micro-variables even out over the course of the season, or possibly the game to become net neutral. Students learning about gravitational force don’t need to worry about molecular forces within an object, the system (e.g. block sliding on an incline slope) can separate from the complex and be simplified. Making the right simplifying assumptions we can do the same in hockey, but do so at the risk of losing important information. More convincingly, we can also attempt to build out the entire state-space (e.g different combinations of players on the ice) and using machine learning to find patterns within the features and winning hockey games. This is likely being leveraged internally by teams (who can generate additional data) and/or professional gamblers. However, with machine learning techniques applied there appeared to be a theoretical upper bound of single game prediction, only about 62%. The rest, presumably, is luck. Even if this upper-bound softens with more data, such as biometrics and player tracking, prediction in hockey will still be difficult.
It seems to me that hockey is suspended somewhere between the simple and the complex. On the surface, there’s a veneer of simplicity and familiarity, but perhaps there’s much going on underneath the surface that is important but can’t be quantified properly. On a scale from simple to complex, I think hockey is closer to complex than simple, but not as complex as the stock market, for example, where upside and downside are theoretically unlimited and not bound by the rules of a game or a set amount of time. A hockey game may be 60 on a scale of 0 (simple) to 100 (complex).
 Spoiler alert: if you performing the same thought experiment with rock-paper-scissors you arrive at the right answer – randomise between all 3, each 1/3 of the time – unless you are a master of psychology and can read those around you. This obviously has a closed form solution, but I like visuals better:
 This likely speaks more to personnel than tactical, Fedorov could be been peerless. However, I think to football where position changes are more common, i.e. a forgettable college receiver at Stanford switched to defence halfway through his college career and became a top player in the NFL league, Richard Sherman. Julian Edelman was a college quarterback and now a top receiver on the Super Bowl champions. Test and measure.