Before we begin, please note that our answer below is only one of an infinite number of correct answers. Furthermore, metrics are not constrained only to athletes and sports, and could be applied in countless contexts.

To begin, let's consider ice hockey as the sport whose metrics we will compare, then assess the quality of some players.

Find and Evaluate A Metric

Ice hockey is a game-type sport. As such, the metric that defines which team wins a match is the score — whichever team has more points at the end of the game wins. Therefore, one metric that could be used to compare players to one another is the average number of points each one scores per game. Let's look at some players from a certain local team.

Player Name	Position	Points Per Game
Timmy	Right wing	$5.1$
A.J.	Goalie	$0.1$
Chester	Center	$1.7$

It looks like Timmy is a high-scoring player, while A.J. barely contributes to the team's score at all. Is points-per-game an effective metric for assessing the performance of these players?

Timmy is in an offensive position, well-suited for scoring many points.
A.J. is in a defensive position, and is unlikely to score very often.

Points-per-game would not be an effective metric for assessing player performance.

Comparing Other Metrics

Consider that the opposing team's objective is also to score as many points as possible. Timmy might score a lot of points, but maybe A.J. and Chester contribute defensively as well. Let's look at a few more statistics.

Player Name	Position	Points Per Game	Assists Per Game	Shots Blocked Per Game
Timmy	Right wing	$5.1$	$1.9$	$0.2$
A.J.	Goalie	$0.1$	$0.3$	$14.7$
Chester	Center	$1.7$	$4.8$	$6.0$

An ice hockey team generally has $6$ players on the ice at any given time during a game, each playing an equally important role.

Timmy scores the most points per game
A.J.'s defensive contributions prevent opposing teams from accumulating too many points.
Chester supports both Timmy on offense and A.J. on defense.

Defining A New Metric

As we saw above, a single metric on its own is insufficient for an effective model. In such situations, it is helpful to combine several metrics into one new metric. Let's combine Points scored, Assists made, and shots Blocked into a new metric called P/A/B.

Player Name	Position	Points Per Game	Assists Per Game	Shots Blocked Per Game	P/A/B
Timmy	Right wing	$5.1$	$1.9$	$0.2$	$7.2$
A.J.	Goalie	$0.1$	$0.3$	$14.7$	$15.1$
Chester	Center	$1.7$	$4.8$	$6.0$	$12.5$

Combining metrics often paints a more accurate picture of a scenario than observing individual metrics. However, there are many other possible metrics to compare player performance, so even the P/A/B is not necessarily a totally effective metric.

Exercise

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