Calculating 5e character build combat power

Many character builds have abilities that they can only use a limited number of time per day or per short rest. For comparing builds and determining expected damage output, it's useful to know the number of fights in a day, and the number of rounds in a fight, so one can estimate how much these abilities can be expected to contribute. 

For combat estimations, unless the question is specifically concerned with high level play, it is a good approximation to look at the play in tier one and tier two (levels 1 to 10), as 90% of all games play in this level range.

Combat rounds per Encounter: estimates range from 3 to 5 rounds. An average of four rounds per combat is a good compromise to use. 

Combats per day: An in depth exploration based on DMG math, published adventures, and survey staticstics  points at a best estimate of three combat encounters per day. (Some petty sticklers point out that there could be non-combat encounters, but that does not matter, as long as the encounter consumes the limited  daily resources. In practice, nearly 100% of encounters that are rewarded with XP are combat anyways, so those guys are just splitting hairs for the purpse of creating arguments, not to any practical use.)

Short Rests Per Day. The DMG talks about a typcial group taking about 2 short rests per day, but there is nothing that blocks you from taking more. For narrative sense, you probably need to have some strenuous activity between two short rests or they would bleed into one extended short rest. You also need 8 hours for a long rest, so that leaves 16 hours, or at most 15 short rests.  If we assume only three combat encounters per day, then even at the suggested 2 short rests, you would go into every combat encounter rested, and able to access any ability that depends on having taken a short rest. That also matches my experience: players of character classes that refresh important features on short rests will push for taking such short rests after any noteworthy fight. It therefore is probably a fair default assumption that abilities that reset on short rest will be available for every combat.

Average Damage per Attack

Average damage per attack strongly depends on the individual build, varying easily by a factor of two between different builds. So this should be calculated for each build and its special abilities, assuming the combatant is short-rested. Good assumptions are probably three encounters per day, each of four rounds of combat (as if there are fewer encounters, they tend to be more difficult and longer).