Getting some new equipment and new thermostats on some older equipment. The reason for a new thermostat on the old equipment is because the air handler / heat pump is short cycling. On for a couple minutes then off for a couple minutes then repeat, constantly, turns on at 70 shuts off on 71 then back on at 70. Obviously it is oversized and the old thermostat does not have any way to compensate.
My new thermostat can be adjusted for cycle rate. My questions are: The cycle rate is only a maximum amount of times the system will run a cycle, (turn on, fulfill demand, shut off) per hour correct? Or is it a set amount of times it will cycle per hour? With the cold temps we are having now my heat pump is running almost constantly to meet the demand, will the CPH effect this at all?

CPH is just compensating for an increase or decrease in temp variance. Lower the CPH the greater temp difference from on/off, the higher the CPH the lower the temp difference from on/off.

3 is normally recommended for compressor equipment. As you don't want the system to cycle often, as it will cost you more to operate.

As the structure reaches its design temp, the equipment will run longer to maintain temp and CPH are basically ignored (with equipment running constantly at 100% load).

Maybe the thermostat is located too close to the output duct and not in the middle of the room.

Thank you
The old is a Lennox thermostat and has a very small dead band for on/off, I think its only 1 degree. The contractor put in a 2 ton unit for a 800 ft/2 single room addition which now they admit is oversized. Their solution is to run a couple more runs into the main house but that defeats the purpose of zoning. I think the CPH lowering will fix the problem, at least mask it. More temperature variations but that won't be a problem. It short cycles mainly on AC at night after it cools down outside.

I do have one more question for when its short cycling:
If the CPH is set to 3 it will only run 3 cycles per hour, I understand this. But will it short cycle 3 times in its normal 15 minutes then stay off for 45 minutes or does it divide the cycles into 20 minutes each?

Evens run time out over the 1 hour period.

24K for 800SQFT is probably a little oversized for Ohio, unless its not insulated well or has several windows/skylights.