Early game taming is all about the best way to cheese an animal, nobody is asking this to change - instead add another system to taming that requires no fighting but time.
Tie'ing up the animal or letting the animal roam does not effect the taming process, an animal enters generation 1 of being tamed when given a clover.
A menu can be accessed when a tame enters generation 1, reading generation, female/male, Food bar, rowdiness bar, agitated bar and tame bar till next generation and two buttons ~ force feed to tame and beat to tame.
Beat to tame reduces rowdiness bar less and increases tame bar more, while force feeding reduces the rowdiness more and tame less.
Agitated bar should be anything that might provoke the animal to attack, 100% agitated animals will instantly attack. Agitation rate should lower 0.20-0.50 an hour.
There is a chance when having a female and male in the same pen with rowdiness bar bellow X0% (X0 being it's generation) for them to have a baby, a baby should skip a generation from the current lowest adult. (female gen 1, male gen 4 = baby gen 2)
There should be a total 10 generation before full domestication happens.
Values of quality are not effected until higher generations such as 5+. The chance for the quality to change during lower generations is very low.
Aurochs can still be milked daily at generation 1 and could pull wagons during generation 1.
Mouflon should regrow their hair daily, but have the agitated bar go up by X% (X=100-(Generation*10) ).
Wildgoat agitated should be one of the highest.
Horse can be ridden during generation 1 but their agitated bar and rate should be very high to a point that it's not very ridable, almost X% per minute (X=100-(Generation*10) )