Sports Analytics 101 is a series of blog posts outlining the core concepts behind sports analytics in non-technical terms. You can find all available installments in the series here.
In an earlier post, I introduced a framework for thinking about an individual sports analytics metric. This framework is essentially mental “paperwork” to fill out whenever you use a new metric to ensure you understand what the metric is and what it isn’t.
In using the framework, we first establish the name of the metric and what it’s being used to quantify. Next, we establish whether the metric is a fact or a proxy, whether the metric is descriptive or predictive, and whether metric is a productivity metric or a style metric. Once all that’s done, we need to establish whether the metric is adjusted for opportunity.
Let’s start with an example. Isaiah is a soccer player who has scored 20 goals. Tobey has only scored 10. It might seem that Isaiah is the better player. However, it’s actually impossible to say for sure which of these two players is a more talented goal scorer without some critical context: opportunity. How many minutes have each of these two players played? If both players have played the same number of minutes, then you’re probably correct to guess that Isaiah is a more talented goalscorer. But let’s say that Isaiah has scored those goals over 2,700 minutes (about 30 games) of play, while Tobey has scored 10 goals over only 450 minutes (about five games). Suddenly the comparison looks a bit different. That’s why it’s critical to either account for opportunity within a metric itself, or factor opportunity into the contextual interpretation of the metric.
In the simplest of cases, adjusting for opportunity means dividing a measure of total output by a measure of the amount of opportunity the player or team had to achieve that total output:
Opportunity Adjusted Metric = Total Output / Opportunity
Returning to our example of the two soccer players, let’s say we wanted to compare the players’ goal-scoring while adjusting for opportunity. The natural inclination would probably be to start with a metric like Goals per Minute. The calculation here is obvious and easy: we divide Total Goals, the measure of total output, by Minutes Played, the opportunity each player had to score those goals:
Goals per Minute=Total Output / Opportunity = Total Goals Scored / Games Played
So while Isaiah has 20 total goals to Tobey’s 10 Total Goals, Isaiah has a lower Goals per Minute rate (0.007) than Tobey (0.022). And, in case you hadn’t connected the dots, adjusting for opportunity is synonymous with measuring efficiency. So, when we say that Tobey scores more Goals per Minute than Isaiah, we are effectively saying that Tobey is a more efficient goalscorer than Isaiah.
Get used to hearing the term efficiency and understanding the difference between volume and efficiency. Volume metrics, which are not adjusted for opportunity, are often misleadingly equated with strong performance. For example, you might hear an announcer discuss how many points a player scored or how many total yards a running back ran for. Total Points and Total Yards are volume metrics that give no context as to how much opportunity the player or team had to achieve the totals. A basketball player may have scored an impressive 30 points, but if they took 80% of their team’s shots to do so, we should be a little less impressed. Of course, players with high point totals generally are the better players (the coach probably would’ve benched them otherwise), but it’s still important to take into consideration the minutes it took to score that many points.
With this in mind, you’ll generally always want to make sure a metric is adjusted for opportunity. There is, however, a critical factor to consider as you do so: sample size. Sample size in this context equals the total opportunity a player has had, like the total number of minutes or games played. I’ll leave it up to the statistics textbooks to explain further, but in simple terms, larger sample sizes are better and smaller sample sizes can be misleading.
For example, let’s say Abby is a basketball player who generally rides the far side of the bench: she very rarely plays. However, at the end of a blowout game, the coach brings in Abby to play the final minute. The opponent isn’t exactly showing a lot of effort on defense and Abby hits an open three as the clock winds down, ending the game with three points. When we adjust Abby’s total points for opportunity by dividing her total points by minutes played, we see that Abby scored an incredible 3.0 Points per Minute, much higher than anyone else on the team, including the team’s star point guard, Carol, who scored 30 points in 40 minutes, which comes out to only 0.75 Points per Minute.
Did Abby have a “better” game than Carol? If you looked at Points per Minute without considering any additional context, you might believe she did. But it’s bad practice to put any stock into metrics adjusted for opportunity when the opportunity is very small. In the case of Abby, one minute of play just isn’t enough time to read into whether she had a good game or a bad game. The only reasonable answer when asked how good of a game Abby had is “she didn’t play enough minutes for us to know.”
Further, whenever possible, we should cite metrics that are adjusted for opportunity alongside the total units of opportunity over which the metric was calculated. For example, we shouldn’t say “Gavin averaged 6 Yards per Carry.” With that statement alone, we have no idea whether Gavin only had one carry or 1,000. If he had only one carry, we shouldn’t use this metric: there isn’t enough sample size. If he had 1,000 carries, this metric is much more useful.
So, instead of simply saying “Gavin averaged 6 Yards per Carry,” we should say something along the lines of “Gavin averaged 6 Yards per Carry over 1,000 carries.”
When we’re adjusting for opportunity, we also need to be cognizant of any potential biases in the measure of opportunity we’re using. One of the most common examples of bias in a measure of opportunity surfaces when using games played as a measure of opportunity. Because players play different portions of games, a single game for a starter might add up to a lot more opportunity than a single game for a player coming off the bench, because the starter naturally plays more minutes.
Let’s say we have two centers on a basketball team, Andrew and Noah. Andrew is a starter and usually plays about 30 minutes every game. Noah comes off the bench and only plays about 10 minutes every game. If we wanted to compare how efficiently these two players score points, we probably wouldn’t want to use Points per Game because Andrew gets three times as many minutes as Noah every game. Over the course of 50 games, Andrew could score 500 points to average 10.0 Points per Game, while Noah could score 300 points to average only 6.0 Points per Game. But if we instead used Points per Minute, we would find that Andrew averages 0.3 Points per Minute while Noah averages twice that, at 0.6 Points per Minute.
In this case, we might find it a little awkward to use a metric like Points per Minute because we rarely think about scoring in terms of the number of points scored in a minute. Typically, the solution for this type of issue would be to multiply Points per Minute by the minutes a starter might typically play in a game. An NBA game that doesn’t go into overtime is 48 minutes and a starter might typically play 36 of those minutes, so we could use a metric like Points per 36 Minutes. In our example, Andrew averages 12.0 Points per 36 Minutes and Noah averages 21.6 Points per 36 Minutes. Those numbers are much easier to digest 0.3 Points per Minute and 0.6 Points per Minute.
Thus far in this discussion of adjusting for opportunity, we’ve only looked at examples where opportunity was expressed in terms of playing time (e.g. minutes played). This is not always the case. Opportunity can come in a number of forms.
For example, metrics that are expressed as percentages are often opportunity-adjusted metrics. Take Free Throw % in basketball, calculated as:
Free Throw % = Total Output / Opportunity = Free Throws Made / Free Throw Attempts
In this case, a player’s free throw attempts represents the number of opportunities they had to make a free throw. So we simply divide their output, free throws made, by that opportunity, free throw attempts.
Many of the advanced and non-advanced metrics you see today are adjusted for opportunity in some way. However, even if a metric is adjusted for opportunity, be aware of how the opportunity measure might be biased. Analytics involves a constant inner dialogue along the lines of “how could this metric be biased or lacking context?” We’ll dive into that dialogue in the next post.