Compare two groups on a binary outcome — see the difference as people, then measure it with Risk Ratios and Odds Ratios.
When a logistic regression or A/B test reports an Odds Ratio of 3.0, marketers routinely tell executives that Group A is "3 times as likely to buy" as Group B. Whenever the outcome is common, that statement is flatly wrong: if conversion jumps from 50% to 75%, the Risk Ratio is only 1.5× while the Odds Ratio balloons to 3.0×! Odds-O-Matic translates 2×2 counts and rates into side-by-side Probabilities, Part-to-Part Odds, Risk Ratios (RR), and Odds Ratios (OR) so you never misstate an effect size again.
a, b, c, d) for Group A and Group BP_A and P_B directly via sliders1 − p ≈ 1, so the Odds Ratio (2.04) closely matches the Risk Ratio (2.00). Above 15% conversion, OR diverges sharply upward.P_B, you can recover the exact Risk Ratio via RR = OR / [(1 − P_B) + (P_B × OR)].💬 Read it in plain English: Probability divides events (a) by everyone in the group (a + b), whereas Odds divide events (a) by non-events (b) in the same group.
💬 Read it in plain English: The Risk Ratio divides Group A's probability by Group B's probability ("times as likely"), while the Odds Ratio divides Group A's odds by Group B's odds (and always exceeds RR when RR > 1).
Select a marketing use case above to auto-fill realistic values, or set your own segment names and counts below.
Every comparison starts here: count how many people in each group experienced the outcome — and how many didn’t.
Enter the raw count data from your study. Probabilities and all downstream metrics will be derived automatically.
| Outcome | No Outcome | Total | |
|---|---|---|---|
| Group A | 1000 | ||
| Group B | 1000 |
Quicker when you already know the conversion rates or want to explore “what if” scenarios.
Now let’s see what these numbers look like as people. ↓
If we scale each group to exactly 100 people, here’s what you’d see…
The groups clearly differ — but by how much? That’s where ratios come in. ↓
Two ways to quantify the gap: the Risk Ratio compares probabilities, the Odds Ratio compares odds. When the outcome is rare they agree; when it’s common they diverge.
“How many times more likely is Group A to experience the outcome?”
“How many times higher are the odds for Group A?”
The OR is the natural output of logistic regression — every coefficient in a logistic model is a log-odds ratio. It’s also the only valid measure in case–control studies where you can’t estimate absolute risk. When the outcome is rare (< 10%), OR ≈ RR.
The rare-event assumption dictates when Odds Ratios can be safely described as “times more likely”.
An Odds Ratio or Risk Ratio tells you relative strength, but commercial ROI depends on volume. See how these rates translate to actual conversions across customer audience sizes:
Configure inputs above to generate a plain-language interpretation.
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Now that you’ve explored the numbers, here’s the theory behind them.
Probability is the chance of something happening, expressed as a number between 0 and 1. If 12 out of 100 customers convert, the probability is 0.12 (or 12%).
Odds compare the chance of it happening to the chance of it NOT happening. With a probability of 0.12, the odds are 0.12 / 0.88 = 0.136 : 1. Think of it as “for every 1 non-converter, there are 0.136 converters.”
Quick mental model
Probability = successes ÷ total attempts
Odds = successes ÷ failures
| Metric | Formula | Best for |
|---|---|---|
| Risk Ratio (RR) | PA ÷ PB | Cohort studies, A/B tests — intuitive “X times as likely” |
| Odds Ratio (OR) | OddsA ÷ OddsB | Case–control studies, logistic regression output |
When the outcome is rare (< 10%), the Odds Ratio closely approximates the Risk Ratio. As outcomes become more common, the OR exaggerates the effect relative to the RR.