increment/decrement: is there a neutral noun like "crement"?

Question

If a value (e.g. in mathematics or information science) can either decrease or increase let's say by one, does there exist a neutral expression based on increment and decrement which covers both cases?

Here's an example:

The number of players may only increase or decrease exactly by one.

Here's my phantasy English sentence:

The negative player crement is -1. The positive player crement is +1.

I could use the word "change", but what I am really looking for is a noun which precisely describes that the changes are always equidistant, i.e. of the same kind and value.

Answer 1

There is no direct root to use, such as crement. Increment and decrement come from the Latin increscere, and decrescere which themselves are further rooted in the Latin cresco which itself means to grow or to come into being. So, even following the etymology of the word, crement would basically mean the same as increment as crement is simply a verb which has that meaning.

Answer 2

You asked for a noun even though your example uses a verb. You could use the word variation. The Oxford Dictionary has

variation
NOUN
A change or slight difference in condition, amount, or level, typically within certain limits.

Your sentence can be

The variation in number of players may be plus or minus one.

But the verb vary is perhaps less clumsy

The number of players may vary by plus or minus one.

This is more like your original sentence.

Answer 3

Deviation n. and deviate v. is what mathematicians and statisticians would use.

e.g.

In the case of normally distributed data, the three sigma rule means that roughly 1 in 22 observations will differ by twice the standard deviation or more from the mean, and 1 in 370 will deviate by three times the standard deviation^[1]

[1]: Ruan, Da; Chen, Guoqing; Kerre, Etienne (2005). Wets, G., ed. Intelligent Data Mining: Techniques and Applications. Studies in Computational Intelligence Vol. 5. Springer. p. 318. ISBN 978-3-540-26256-5.