Are chance and probability the same thing?

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No! — and the difference matters. Both terms appear constantly in scientific articles, often as synonyms. They are not. A surgical example makes it clear: out of every 100 esophagectomies, 7 patients die postoperatively.

30-second summary
  • Probability = event ÷ all; odds = event ÷ non-event.
  • Risk belongs to cohorts; the odds ratio is the measure of case-control studies.
  • For rare events, risk and odds nearly coincide.

Probability (= risk)

The event divided by all possibilities: 7 deaths among 100 patients.

7 / 100 = 7%
7 deaths · 100 patients — ranges from 0 to 1 (or 0 to 100%)

Odds

The event divided by its non-occurrence: 7 deaths for 93 survivors.

7 : 93 = 0.075
7 deaths : 93 alive — the basis of the odds ratio (OR) in case-control studies

In a coin toss: the probability of heads is ½ (50%); the odds are 1:1. Measures such as postoperative mortality, complication rate and risk of dehiscence are probabilities; the odds ratio of case-control studies is odds.

Fun fact: for rare events, odds and probability nearly coincide. Risk of death in cholecystectomy: 1/1000 = 0.001. Odds: 1/999 ≈ 0.001.

Frequently asked questions

Why can't I speak of risk in a case-control study?

Because the sample is assembled from the outcome: disease frequencies do not reflect the population, and only the odds ratio remains valid.

When does the odds ratio approximate the relative risk?

When the outcome is rare (rule of thumb: prevalence below ~10%), OR and RR are numerically close.

What does OR = 2 mean?

The odds of the event in the exposed group are twice the odds in the unexposed group — odds, not probability.

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Written by Francisco Tustumi, digestive system surgeon (FMUSP), associate editor of ABCD.


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ABCD – BRAZILIAN ARCHIVES OF DIGESTIVE SURGERY is a periodic with a single annual volume in continuous publication, official organ of the Brazilian College of Digestive Surgery - CBCD. Technical manager: Dr. Francisco Tustumi | CRM: 157311 | RQE: 77151 - Cirurgia do Aparelho Digestivo

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