# Is there a name for numbers between 0 and 1?

In the world of competitive esports, players often discuss kill/death ratios, where higher is better. My friends sometimes call a poor ratio, like 1 kill to 4 deaths, as 'negative', but that's not quite right. Is there another word to describe values between 0.0 and 1.0, vs values larger than 1.0?

• Why not "less than 1"? Jan 25 '16 at 20:03
• More generally, ratios like -10/2 are still < 1, but the magnitude |-10/2| is > 1. Jan 25 '16 at 20:34
• Yes, but in your example you have already ruled out the possibility of a negative ratio, since you do not have negative kills. More generally, you asked to distinguish $0 \leq x < 1$ from $x \geq 1$, not to distinguish $0 \leq x < 1$ from all other possible values of $x$. Jan 25 '16 at 21:16
• @DavidK "Negative kills" can be a thing in some games - where if you kill yourself (usually accidentally...) your actual kill count goes down (and your death count goes up), so if you railgun 3 players but trip and fall into the void 6 times then your K/D would be -0.5 (from (3-6)/6 == -3/6 == -1/2.
– Dai
Sep 10 at 22:38
• @Dai Technically that's not a $K/D$ ratio, that's a $(K-D)/D$ ratio -- a useful metric, but it is not apparent from anything in the question that that's what OP had in mind. Generally when $K/D < 1$ we will also find that $(K-D)/D < 0$ (assuming $K$ and $D$ are still non-negative numbers), so yes, under the latter metric the distinction could be between a positive ratio and a negative ratio. Sep 11 at 0:36

Since you seem to be primarily interested in rational numbers, a good candidate is proper fraction.

• Thanks! I'll try using proper vs. improper to describe KDRs. Jan 25 '16 at 19:50
• Although this answer is responsive and accurate (and therefore deserves its votes), I'll point out that in actual practice, (a) you'd have to explain the terminology to anyone not familiar with it (and a good handful of those who are), and (b) it has the unintuitive and unsettling correspondence of "proper" = "bad" and "improper" = "good". Jan 25 '16 at 23:32
• I agree with @Brian that this is not an ideal solution. Jan 25 '16 at 23:55

Your friends aren't wrong for describing a 1kill, 4 deaths score as negative. They are simply using a different metric, kills-deaths, instead of what you're using, kills/deaths. Both are useful in different scenarios and you should aim to go positive with an improper fraction for a kdr.

It can be called the Unit Interval

In mathematics, the unit interval is the closed interval [0,1], that is, the set of all real numbers that are greater than or equal to 0 and less than or equal to 1. It is often denoted I (capital letter I). In addition to its role in real analysis, the unit interval is used to study homotopy theory in the field of topology.

A simple mathematical way of describing this is by using the log function.

A number between 0 and 1 has a negative log and a number larger than 1 has a positive log...

So "negative log" and "positive log" could be a way of referring to this.

Note that with this notation, your kills/deaths ration becomes $$\log (\frac{kills}{deaths})=\log(kills)- \log (deaths)$$

• The problem is that one starts out with an undefined log. Even assuming that we define $0/0 = 1$, then if you die before you get a kill, your log is now infinitely negative. Such a common occurrence should not get an infinitely bad result. Jan 26 '16 at 0:47
• @BrianTung Well, log has a limit at $x=0$ (from the right) so often we use the convention $log(0)=- \infty$.... Jan 26 '16 at 3:13
• Oh yes, I agree. I just wonder if that's a reasonable metric. It means that $0$ kills and $1$ death is infinitely worse than $1$ kill and arbitrarily many deaths... Jan 26 '16 at 3:15
• @BrianTung And in the given ratio what does 1 kill and 0 deaths means? ;) Jan 26 '16 at 3:17
• :) I'm not sure that's a problem that your formulation solves, though. ¶ Personally, I prefer $\frac{K}{K+D}$ (range $[0, 1]$), or perhaps $\frac{K-D}{K+D}$ (range $[-1, 1]$). But that wasn't really the question. Jan 26 '16 at 4:35

I'm not sure that I would use a term from mathematics. You might consider using a term like "subpar", where "par" would be $1:1$, as in "One kill to four deaths is a subpar kill/death ratio."