Several factors play into the quantity of hay that gets produced on any given acre of ground. Some of those factors are variable, some are not. Some of the factors you have control over, some you do not. These same factors come into play when I need to calculate stocking rate on a given farm based on pasture, and I have a couple additional factors I must consider when considering grazing vs haying, but I'll discuss grazing later if someone wants me to.
Given no other variables to consider, (there are many), the soil present at the site will be the determining factor on the quantity of hay that is produced per acre. I've seen values anywhere from 1.2 tons per acre to 8-9 tons per acre. These are averages and both values I've listed here are extremes. Neither are particularly common though. The soil is one of two factors that doesn't change. The second factor that doesn't change is day length or growing hours. These do not change from year to year. I 'could' refer to season in place of day length, but weather, another factor, also plays into season and weather is variable.
Weather is a variable factor playing into hay quantity produced of which moisture timing and availability make up part of weather. Weather is also composed of temperature which can be too hot, too cold, or just right (Goldilocks factor?
) as well as the time of day the temperatures are occurring at.
The one factor we do have control over (arguably not the only factor if you are irrigating your hay) is soil amendments. This includes fertilization but it also includes pH which affects nutrient availability to the hay plants.
Then you need to consider (or could anyway) the species, AND variety, of the hay that you are producing. Prior to me going south to play for awhile, I didn't consider variety within a species to have a whole lot of impact on quantity. Bermuda grass changed my thought on that, significantly. The quantity of forage produced by a variety of a particular species often only becomes evident when other factors that are normally limiting are adjusted in a way that they are no longer the limiting factor. An example of what I'm saying here, and I'll use the Bermuda I mentioned, is when the fields of Bermuda are fertilized, one variety will nearly double its production while the other variety of the same species might show only a 10-20 percent increase, if that in some instances.
Latitude and elevation I suppose are additional factors that come into play that affect production, although these two factors might have more of a role in being factor having an effect on the other factors already mentioned. Everything tends to have an effect on everything else and very little is truly independent.