MT241 Unit 2 Metric Definition Exercise Example

Twelve Feet in the Slot and Sixty at the Point: A Unit 2 Metric Definition Exercise for Expected Goals

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Purdue University Global

MT241: Sport Analytics

Unit 2 Metric Definition Exercise

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[Date]

The club, its season figures and the winger are composite and illustrative; the sample probabilities are typical of published public models, not drawn from any one model; the sources cited are real.

Why Define the Measure at All

Our composite club's coaches already use the phrase expected goals in meetings, and the club's analytics staff report it every week. But the people using the number do not all mean the same thing. Some think it measures how well a player shoots. Others think it measures how many goals a team deserved. Different public websites also report different expected-goals totals for the same player in the same season, which makes the term look less precise than it is. Alamar (2013) argues that an analytics group earns trust when it can state plainly what each of its numbers measures and what decision it is meant to support. This exercise writes that statement for expected goals so that everyone at the club means the same thing when they use it.

The Definition, Row by Row

The definition is set out in seven parts.

Population. The measure scores every unblocked shot attempt at 5-on-5: shots on goal, shots that miss the net, and goals. Blocked shots are left out because the league records a blocked shot's location as the place where it was blocked, not the place it was taken, so its distance and angle would be wrong.

Unit of measure. The unit is goals. Each attempt receives a probability between zero and one that it becomes a goal, and the probabilities are added up. A player with 8.9 expected goals took shots that, on average, would produce about nine goals.

Inputs. The probability for each attempt is set by distance from the net, angle to the net, shot type (wrist, slap, snap, backhand, deflection, wraparound), and two flags: whether the shot is a rebound, meaning it came within a few seconds of a previous attempt, and whether it came off the rush, meaning shortly after the puck was in another zone.

Output. The model produces a probability for each attempt. Summed for a player, it describes the quality and number of chances he took. Summed for everyone on the ice, for and against, it gives an expected-goals share.

What it adjusts for. Expected goals adjusts for where and how a shot was taken, which raw shot counts do not. A typical public model might score a twelve-foot wrist shot from the slot near 0.16 and a slap shot from the point near 0.02, so one good chance can be worth eight long ones.

What it leaves out. The measure does not see passing before the shot, the goaltender's position, screens, or how hard the shot was. It also depends on the league's recorded shot locations, which vary by arena.

The decision it serves. Expected goals helps the club judge whether its players and lines are creating and allowing good chances, separately from whether those chances happened to go in.

A Worked Example

The club's second-line winger scored 14 goals at 5-on-5 last season on 8.9 expected goals. His raw shot total was average for a forward, and his shooting percentage was well above his career mark.

There are two readings. One is that he is a skilled shooter who beats goaltenders more often than the model expects. The other is that he had a lucky season. Expected goals cannot settle which reading is right from one season. What it can do is set the question up properly: he outscored his chances by about five goals, and the club should look at several seasons before deciding how much of that gap is skill. Published analyses of shooting talent suggest that a forward's shooting percentage needs several hundred shots before it settles near its true level, so one season of about 120 attempts is not enough.

Expected goals does not say whether he will keep scoring; it says how much of last season he would have to repeat.

Comparison With Other Counts

To show what the measure adds, the club's season can be described three ways. By raw attempts at 5-on-5, the club took 49.2 percent of all attempts in its games, slightly below even. By actual goals at 5-on-5, it scored 51.6 percent. By expected goals, it took 50.8 percent of the chance quality.

Each count tells a slightly different story. Attempts say the club was outshot. Goals say it won its games at even strength. Expected goals sits between them and suggests the club created slightly better chances than it allowed, even though it took fewer shots. Macdonald (2012) showed that adjusting for shot quality and other factors improves how well a measure predicts future results, which is why the club should give expected goals more weight than either raw count when planning.

What the Measure Cannot Credit

The gap between shooters and passers deserves its own note, because it is where coaches most often misread the number. Expected goals assigns every bit of a chance's value to the player who shot the puck. A center who carries the puck across the blue line, draws two defenders and slides it to an open winger for a one-timer gets nothing from the measure, while the winger's total rises by the full value of the chance. Over a season, that pattern can make a playmaking center look ordinary and his linemates look excellent. Researchers have tried to solve the problem by estimating each skater's share of everything that happens while he is on the ice; Gramacy et al. (2013), for example, used regularized regression on goals to estimate each player's contribution after accounting for teammates and opponents. Those approaches answer a different question from expected goals, and the club should not expect one number to do both jobs. For the club's purposes, the definition should say plainly that expected goals measures the chances a player took or was on the ice for, not his part in creating them.

Where the Measure Can Mislead

Three cautions belong in the definition. First, expected goals from different providers are not interchangeable. Each provider fits its model differently, and some include extra inputs, so totals for the same player can differ by a goal or more. The club should pick one model and use it consistently. Second, the measure is weakest for players whose value comes before the shot: a center who makes the pass that creates a chance gets no credit unless he takes the shot himself. Third, shot locations recorded in some arenas run systematically closer or farther than in others, which can shift a team's home figures.

What the Club Can Settle With It

Used carefully, expected goals can settle several of the club's questions: whether a line is creating chances, whether a slump is real or a cold streak, and whether a defensive system is keeping shots to the outside. It cannot settle who made the play that created a chance, and it cannot by itself say whether a player's finishing is skill.

References

Alamar, B. C. (2013). Sports analytics: A guide for coaches, managers, and other decision makers. Columbia University Press.

Gramacy, R. B., Jensen, S. T., & Taddy, M. (2013). Estimating player contribution in hockey with regularized logistic regression. Journal of Quantitative Analysis in Sports, 9(1), 97-111. https://doi.org/10.1515/jqas-2012-0001

Macdonald, B. (2012). An expected goals model for evaluating NHL teams and players. In Proceedings of the 2012 MIT Sloan Sports Analytics Conference. MIT Sloan School of Management.