Absolute Risk vs. Relative Risk

Absolute risk and relative risk are two terms that are often confused. Though commonly used in the medical world, these terms also have use in sports gambling. Besides “correlation doesn’t equal causation”, absolute risk and relative risk are often used to deceive readers of the news or data studies.

For this exercise, we are going to discuss an endgame situation. The Knicks are down two points to the Warriors with five seconds left in the game. We want to figure out the risk of fouling Stephen Curry instead of Draymond Green (or another average shooter). If two free throws are made, then the game is essentially over. We will consider two made free throws to be our “risk”.

What is Absolute Risk?

Absolute risk is simply the probability of an event occurring. So, if Stephen Curry historically makes 93 out of 100 free throws, then the absolute risk of him making both free throws is .93*.93 = 86.5%. For the sake of comparison, Draymond Green is roughly a 71% career free throw shooter. His risk of making both is 50.4%.

Next, the term absolute risk reduction is simply the difference between the event control group and the event treatment group. So, what’s the absolute risk reduction of fouling Draymond instead of Steph? 86.5%-50.4% = 36.1% absolute risk reduction.

What is Relative Risk?

Relative risk is a descriptive statistic that tells you what % of change there is between events.

In our example, the relative risk of fouling Steph over Draymond is 50.4%/86.5% = 58.3%. Meanwhile, the relative risk reduction = (86.5%-50.4%)/86.5% = 41.7%.

There isn’t too much of a difference between 36.1% and 41.7%, but which is the correct number to use? Well, it depends…

That Doesn’t Seem Bad. What is Controversial?

Where the numbers can get misused are typically in very low probability events. Let’s say there is a drug trial for Virus X that is done with 1,000,000 participants that are split evenly between a control group and a treatment group. After twelve months, the trial finds that fifty people in the control group got sick with Virus X, and ten people in the treatment group got sick.

The marketing departments at the drug company will tout this new wonder drug reduces your risk by 80%! Not using this drug increases your risk of catching Virus X by 400%! At this point, it should be obvious that this is relative risk.

But what is the reality?

The risk of catching Virus X without the drug is 50 divided by 500,000 = 0.0001.
The risk of catching Virus X with the drug is 10 divided by 500,000 = 0.00002.
The absolute risk reduction is only 0.00008 (or 0.008%).

There is a pretty obvious difference between 0.008% (the absolute risk reduction) and 80% (the relative risk reduction). Can you see how easy it is to sway people one way or the other with these numbers? The best way to avoid being fooled is to really understand the data and not just read numbers in headlines.