# Sports Analytics: A Science — Ch. 2: Percentages, Rates, and Interpreting Metrics

## Percentages and Rates

The next two most basic categories of metrics both utilize the three fundamental types of metrics in their calculations: percentages and rates. These are perhaps both the most common, but also often the most tricky, types of metrics. A percentage metric refers to one that shows the success rate for performing a certain action, like 3P% in basketball. “Success” in this context is relative and refers to the success of satisfying a certain condition, not necessarily success in a sports sense. For example, a missed shot in basketball successfully satisfies the condition of being a shot that did not go in. The formula for these metrics will be No. of SuccessesNo. of Attempts and mathematically, these are also called ratios. These metrics are presented more often than not as a percentage, meaning 4 made 3PT10 3PT Attempts=0.4  and  0.4*100=40%. Percentages will be presented in a variety of ways though. While 3P% in basketball can be shown as 40%, a batting average in baseball can be shown as .400 and spoken as “four hundred”. But as long as the metric’s calculation follows that equation, it should be treated as a percentage.

A rate metric is one that shows the frequency of completing a certain action or satisfying some condition of the rules over the course of a designated measure of time, like goals per game or per minute in hockey. In that case, the action would be a goal and the measure of time would be a game or a minute. The formula for these metrics is No. of SuccessesTotal Measure of Time. The most common rate metrics you’ll see are per-game averages that show the average number of times an action has been completed per game.

Both percentages and rates offer more information about a player’s success in performing an action. A fundamental difference between them is that percentages must involve metrics regarding a single action, while rates can involve metrics regarding two actions. As an example, one can look at the metrics 3-point percentage (3P%) and 3-pointers made per game (3P/G) in basketball. The equation for 3P% is 3PT Made3PT Attempts and the equation for 3P/G is 3PT MadeGames Played. You’ll notice that for 3P%, the only action referenced is a player shooting a 3-pointer. But in 3P/G, the action of shooting a 3PT shot and the action of playing a game is referenced.

The presence of a second metric in the equation brings with it a second set of context needed to fully understand the resulting metric. This understanding is also required to be able to use the new metric to gain insight into a player’s performance. To start exploring the context surrounding sports analytics metrics, an understanding of the concepts of interpretation and interpretive value is necessary.

In this context, interpretation refers to how a given metric translates conceptually to the game being played. For example, the interpretation of a football/soccer goalie’s save-percentage is that it is how successful the player was at keeping shots from going into the goal. Interpretive value, on the other hand, refers to the contextualized numerical value of the metric that is presented. So, instead of how successful the player was at preventing goals, a save-percentage’s interpretive value would be that the metric represents the ratio of shots that the player prevented from going into the goal.

Interpretation refers to the way you would look at a metric and draw conclusions, while interpretive value refers more to the actual numbers and what they refer to in the game being played. A logically sound metric will have a solid interpretation and interpretive value.

Two common metrics to look at as a case study in this concept are On-Base Percentage (OBP) and On-Base-Plus-Slugging (OPS) in baseball. OBP is the percentage of times that a batter steps up to the plate that they get on base. The interpretation of this metric would be that it is the success rate of getting on base when coming up to bat and the interpretive value would be the ratio of having gotten on base when coming up to bat. It’s fair to say that those two statements are sufficiently in-line with each other.

OPS is the sum of a player’s OBP and their Slugging Percentage (SLG). SLG is the batter’s total bases per at-bat. The interpretation of SLG would be that the metric is a measure of the player’s ability to hit for power and the interpretive value would be the number of bases acquired per at bat. Let’s extend this exercise to OPS. The interpretation of the sum of a player’s OBP and SLG would be a blend of the context of those two metrics. The resulting metric is a measure of both a player’s ability to get on base and their ability to hit for power while doing it.

But what is the interpretive value? OBP is the ratio of having gotten on base and SLG is the number of bases per at bat, but a single data point of the resulting metric cannot be both of those at the same time. There must be a new, singular interpretive value that incorporates the calculation of those two metrics, while also considering the calculation of the metric itself.

So, OBP is a decimal presentation of the ratio of a player’s plate appearances in which they got on base (ex: reaching base 30 times in 100 plate appearances would yield an OBP of 0.300). SLG is a decimal presentation of the number of bases acquired per at bat (ex: 1 single [1 total base], 2 doubles [4 total bases], and 1 home run [4 total bases], in 25 at-bats would yield a SLG of 9/25 = 0.360). And OBP would be the sum of those two decimal presentations (ex: 0.300 + 0.360 = 0.660).

But herein lies the problem: what is the interpretive value of that 0.660 in the previous example? OBP clearly represents the success rate of plate appearances and SLG clearly represents the average number of bases per at-bat, but what does their sum represent? The answer, unfortunately, is that it doesn’t represent anything. This isn’t to say that it has no potential of being a useful tool, value, metric, etc., but the number itself doesn’t actually mean anything in a sports context. It can be interpreted in a sports context and given value, but it doesn’t actually have any direct value on its own.

Situations like this are why distinguishing between interpretation and interpretive value is so important. There could potentially be many more pages dedicated to the mathematical operations behind OBP and the issues with them, but the important fact for the sports analyst is that the number itself has no interpretive value.

##### Rob Weber
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Co-founder of First Line Sports Analytics