What are Q1, Q2, Q3 and the interquartile range (IQR)?

On the /crunch page distribution charts you will spot markers labelled "Q1", "Q2" and "Q3", along with a shaded band. These are "quartiles", and they're a simple way to describe how spread out your results are.

If you lined up every simulated result from lowest to highest, the quartiles are the three points that split that line into four equal-sized groups:

• Q1 (the first quartile) is the result that a quarter (25%) of the outcomes land at or below.
• Q2 (the second quartile) is the middle result, better known as the median. Half of the outcomes land at or below it. This is the same value UnitCrunch shows as the "expected result".
• Q3 (the third quartile) is the result that three quarters (75%) of the outcomes land at or below.

The interquartile range (IQR) is just the range between Q1 and Q3. It's the shaded band on the chart, and it covers the middle 50% of your results. A narrow band means your results are fairly consistent, a wide band means they're more swingy.

Why bother with this instead of just the average? UnitCrunch results are often lopsided rather than a neat bell curve, so a single average can hide how reliable an attack really is. The quartiles give you a quick feel for the range you can realistically expect in-game.

If you're after the full mathematical detail, the Wikipedia entries for "Quartile" and "Interquartile range" are good starting points.