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The phrase "average gain per" is correct and usable in written English.
It can be used in contexts where you are discussing the average increase or improvement in a specific metric over a defined period or per unit.
Example: "The average gain per investment over the last five years has been impressive, indicating strong market performance."
Alternatives: "mean increase per" or "typical gain per".
Exact(11)
Brady's average gain per pass play was 4.6 yards; Warner's was 7.2 yards.
Walker is a proud man who likes to see his average gain per catch at 20 yards or more.
In average gain per pass attempt, he ranks second all-time for both a career (8.42) and a single season (10.86 in 1943).
Jones was the sleek and speedy end, in jersey No. 45, who ran under so many long passes from Fran Tarkenton that his career average gain per catch was 22.3 yards, which is still a league record.
In other words, as the number of repetitions of a gamble approaches infinity, the average gain per trial will become arbitrarily close to the gamble's expected value with probability 1.
In other words, in a long run of similar gamble, the average gain per trial is highly likely to become arbitrarily close to the gamble's expected value within a finite amount of time.
Similar(49)
He found that the strategy does work, giving the team doing the hacking an average gain of.9 points per hundred possessions.
Across all households, ministers say there will be an average gain of £16 per month.
Across all households, ministers have said there will be an average gain of £16 per month.
Monthly job growth in this industry has averaged 55,000 thus far in 2013, almost twice the average gain of 30,000 per month in 2012.
Thanks to vaccines, better nutrition, and all-around improvements in public health and medicine, life expectancy at birth in wealthy nations has doubled from 40 to around 80 years, an average gain of 2.5 years per decade.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com