# How to interpret "round up or down" in monster CR calculation

In the "Creating Quick Monster Stats" section of the DMG (p.274) we are given the procedure for determining the CR of a new DM-designed monster. Step 4 of that procedure (pp.274-275) tells us to calculate a defensive challenge rating, an offensive challenge rating, and then the

Average Challenge Rating. The monster's final challenge rating is the average of its defensive and offensive challenge ratings. Round the average up or down to the nearest challenge rating to determine your monster's final challenge rating. For example, if the creature's defensive challenge rating is 2 and its offensive rating is 3, its final rating is 3.

How are we to take the instruction to "round up or down"?

Does the DMG mean to say that it is DM's choice (rather than defined procedure) whether to round up or down? And that once that decision is made you move to the nearer CR in that direction?

Or, is this passage saying that the rounding should take you to the nearest CR, regardless of whether this means rounding up or down? For example, if the DCR was 1/2 and the OCR was 2, the average CR would be 1.25, which we would round down to 1, because 1.25 is nearer to 1 than 2. But if the DCR was 3 and the OCR was 1/4, the average CR would be 1.625, and we would round up to 2 because 1.625 is nearer 2 than it is 1.

The example then given shows rounding up, but in the confusing case of 2.5 being equidistant from both 2 and 3, which doesn't let us parse which of the two possible meanings is intended.

There are a number of CR-calculation questions on this site, but I haven't found this specific question. I understand that the final CR is by DM fiat, involves many other considerations, and is not a direct result of this specific procedure - I am just trying to understand what the actual procedure described in this passage is.

In the given example, 2.5 rounds up because that's how rounding works in DnD 5th Edition when rounding up is allowed. In addition to the given example, the rule for rounding down also indicates that if it were not for the rule, one half would round up.

Round Down General Rule

Whenever you divide a number in the game, round down if you end up with a fraction, even if the fraction is one-half or greater.

For the exact phrase:

Round the average up or down to the nearest challenge rating to determine your monster's final challenge rating.

I believe the extra wording is emphasizing that in this scenario, you consider rounding up and down, as opposed to DnD 5th Edition's General round down rule.

Also as the end of the paragraph it states:

"Its final challenge rating is 3"

and not "You may choose its final challenge rating to be 2 or 3" (or similar verbiage) it's even more evidently clear that you follow the math, not personal preference or 5th ed general rule of rounding down.

How to round

• More to the point, it's a generally bad way to round numbers because it's biased. Aug 11, 2020 at 20:29
• It may be a bad system, but it is the common system in the US (origin of book/ rules) AND is even referenced DIRECTLY in the general rule of Round Down "Even if the fraction is one-half or greater". Further it is the rule used In the example in the question. Aug 11, 2020 at 20:34
• FWIW: Rounding up is also referenced in the Adjudicating Areas of Effect on page 249 of the DMG: (15 ÷ 10 = 1.5, rounded up to 2). Aug 11, 2020 at 20:52
• I will try to come up with a method of working that into the answer so that .5 rounds up (when rounding up is allowed) is an established part of 5th edition rules, even if it is not the only possible way of dealing with rounding 1/2 Aug 11, 2020 at 20:59
• Your recent editing has greatly improved this answer by making it more clear. Now has my upvote.
– Kirt
Aug 12, 2020 at 17:30

It means round to the nearest integer, which, depending on the fractional part, might be a round up or a round down.

This is ambiguous (and the example is therefore unhelpful) when the fractional part is exactly 0.5, which results in a tie-- neither integer is nearest. Suffice to say, there are a multitude of algorithms to handle this seemingly simple exception in an unbiased way.

Probably the simplest this to do in a gaming situation is to flip a coin every time that situation is encountered.

• In a situation where you have many random numbers a coin flip may be appropriate to get statistically unbiased sampling, but in the deterministic process of calculating CR I think randomised rounding might be inappropriate (why add randomness where there was none?). Because CRs cover a relatively narrow range of values, the bias introduced by rounding to odd/even would result in clustering at the odd/even values. Rounding up or down will introduce a bias up or down, but it will be a systematic bias which makes CR slightly less/more potent overall with minimal effect on the relative scale. Aug 12, 2020 at 0:14