An Introduction to Rate Stats
One traditional way of categorizing sports statistics is to divide them into counting stats and rate stats. A counting stat measures the accumulation of successes (or failures) in some area. Total points, field-goal makes and misses, free-throw makes and misses, assists, rebounds, turnovers, blocks, steals, and fouls are counting stats. A rate stat measures the rate or frequency of the accumulation of successes (or failures). Baseball-Reference has a good summary of the difference in the context of baseball here.
I think it can be useful to split rate stats into two subcategories - opportunity rates and time-period rates.
Opportunity Rates:
Opportunity rates measure successes per opportunity. The opportunities consist of those tries resulting in successes plus those resulting in the failures that correspond to those successes.
Opportunity rate = successes / opportunities
= successes / (successes + failures)When the player or team fails at every opportunity, successes = 0, and thus the opportunity rate = 0/(0 + failures) = 0. When they succeed at every opportunity, failures = 0, and thus the opportunity rate = successes/(successes + 0) = 1. So opportunity rates are on a scale from zero to one, which means they can easily be expressed as a percentage (by multiplying the rate by 100).
Another characteristic of opportunity rates is that the goal is to maximize them - a higher rate is better than a lower rate because it means more successes and less failures. This may seem trivial, but it turns out to have some important consequences.
Perhaps the most basic opportunity rate is field-goal percentage. Field-goals made are the successes, field-goals missed are the failures, and field-goals attempted are the opportunities. If a player misses all his shots (FGM = 0), his FG% = 0/(0 + FGmiss) = 0.00 (or 0%). If a player makes all his shots (FGmiss = 0), his FG% = FGM/(FGM + 0) = 1.00 (or 100%).
Other opportunity rates include three-point percentage, free-throw percentage, assist-to-turnover ratio (technically an opportunity ratio), and rebound rate.
Time-period Rates:
Time-period rates measure successes per some period of time. Here the denominator is not the successes plus their corresponding failures, but rather some set time span. A time-period rate can be per career, per season, per game, per minute, per possession, or per play.
Time-period rate = successes / time-period
Unlike opportunity rates, time-period rates are not on a scale from 0 to 1, and thus they can’t be easily expressed as percentages. Also, with time-period rates, it’s not as clear that the goal is always to maximize them. All else being equal, maybe you do want a player to have as many made free throws per team possession as possible, but not necessarily at the expense of made three-pointers. The basic idea is that for time-period stats you’re tallying the accumulation of one type of success in a limited time frame during which other types of successes could also be achieved, so trade-offs are involved.
Some examples of time-period rates include per game counting stats (e.g. assists per game), per minute counting stats (e.g. blocks per minute), pace (i.e. possessions per 48 minutes - note here that the numerator isn’t really a type of success or failure), and offensive and defensive rating/efficiency (i.e. points scored or allowed per 100 possessions).
In my next post, I’ll look at some advanced stats and try to see how they fit into these categories (and how we can evaluate those stats based on these classifications). In particular I’ll examine what kinds of passing-related rate stats one can construct from assists.
Great article, I think how you break down the different categories.
Just one thing. I think the there might be another category that takes into account the pace of the game (similar to time rates, but on a per-posession basis rather than per-minute) somewhat akin to time-period rates.
Stats like rebounds, assists and steals, which don’t lend themselves well to opportunity rates due to the lack of an easily quantifiable failure metric, can also be a little misleading when converted to time period stats.
For example, Shawn Marion has an inflated rebound total because phoenix typically has more posessions to play with. So measuring rebounds as a percentage of the total number of rebounds in the game or total number of posessions in the game seems better than the number of minutes.
Just an idea.
Cheers,
Mark
Comment by mark — November 30, 2007
That is an important distinction. I lumped per possession rates into the time-period rates because I think they share a lot of similarities to them. They may have the advantage of controlling for pace, but the basic idea is still successes per time-period (where the time-period is marked by when possession of the ball changes hands). Though sometimes per possession stats are more like opportunity rates than time-period rates - for instance, though I listed it under time-period rates, points scored per possession can be seen as the successes of points divided by the opportunity of a possession.
And you’re right to note that per possession stats are often more useful than per minute ones. In the case of rebounding, I agree that rebounds per minute can be misleading. Rebounds per possession is an improvement, and rebounds per rebound opportunities (total team and opponent rebounds while the player was in the game) is even better. My latest post has some more discussion of rebounding.
For steals, I like to use the opportunity rate of steals per opponent play while the player was on the court, where oppPlay = oppFGA + .44*oppFTA + oppTO (all scaled down by the percent of his team’s minutes that the player played).
Comment by Eli — November 30, 2007