How can you tell what the hay quality is like without a hay analysis? The truth is you can’t. Even when equipped with information on plant maturity, species, etc., the same “type” of hay from two different, but neighbouring, fields might yield very different results. That said, you can get an idea about the range of nutrition with some information about the hay that you can get from the hay dealer or through plant recognition. For example, legume types of hay (alfalfa, clover) tend to have higher protein (14-20%) and calcium (1-3%) than grass hays (6-14% protein, 0.2-0.8% calcium).
Similarly, hay quality is greatly affected by maturity, whereby a younger plant tends to have more protein and less fibre than an older plant. For example, a young timothy hay where the seed heads are tiny will have higher protein (maybe around 12%) and only about 30-35% acid detergent fibre (ADF), poorly fermented fibre (an indicator of digestible energy, where lower values are more digestible and yield more calories), while timothy hay with big long seed heads would have lower protein (<8%) and upwards of 40% ADF.
It is impossible to tell how much phosphorus, iron, copper, zinc, etc. there is in hay without a hay analysis. The cut of the hay doesn’t yield consistent differences in nutrition composition per se, but affects what species (or weed) may be predominant in a mixed field and the maturity level of the plant.