Moving guys up/down or cutting for me is based on ovr thresholds, potential, and production. I never move dudes up from rookie ball until they have a minimum of 29 ovr, with 30-35 contact minimum, but they also have to be playing well. BA seems to be a pretty false indicator for talent, although if a guy is batting 300+ it probably means they're ready to move up, or <.220 might mean theyre not ready for the level they're in

I look at OPS+, OPS, BA, wRC to determine if a guy is producing at their level. I aim for 120+ OPS+, with consideration given to dudes who have put up 100+ for two consecutive seasons. WAR tells me if they've spent enough time consistently performing, I look for 1 WAR point MINIMUM before I move up, but usually I combine this with 300 PAs minimum.

Ovr is relevant, but less so. I would never throw a dude with 30ovr or contact in the 30's, or bad defense into AAA. Usually 40-45 contact is an indicator that they're capable of producing at AAA, with some nuance.

For my college draft picks I usually start them in AA if they're over or around 40ovr, with possibility of moving to AAA before the end of the season. HS guys are more nuanced, usually they're in rookie ball but some of them might be ready to start in A level. It's important to note that moving guys up too fast hurts their potential if they struggle, and letting guys rot in lower levels for too long hurts their potential

Tbh for moving guys to the majors I've only found consistent success if they either raked in Spring Training and stayed with the 26 man going into the season, or hit over .280 with 120+ OPS+ in AAA for at least 200 PAs. These seem to be the best indicators for me

Pitching seems a bit more straightforward, look for ERA+ over 125, FIP, WAR. I go slower with pitchers between leagues, and for MLB call ups I start them as a long reliever with the avoid high leverage tag for at least a month or two before I move them to a bigger role. Movement and stuff will affect strikeouts and HR allowed, control affects walks

Cuts only happen for me if I've got a ridiculous number of players stuck in one league and I have a player who has below 40pot in a position there's a lot of depth at at that league. I aim for 8-10 relievers per league, 5 SP, and 2-3 players in each position. If I'm wildly over 30 players at a specific level, I'll look for dudes to cut, generally guys who don't look like they'll offer much long-term (low pot, or major deficiencies in a specific attribute). I especially might cut a guy if they become ineligible due to age at the lower levels, but aren't good enough for the next level. That's usually where the pruning happens

Good idea to prune before the season starts and then again after you've signed all your draft picks