I almost never have a Mop up, and usually don't have a Long B, but do occasionally depending on the composition of my pitching staff. I might go a bit over the min salary for one of those guys, but wouldn't go over $1M.

What I look for is the ability to eat innings... high STA/DUR and good enough CNTRL (50-60), VR (60+) and 1P (70+). Since I don't really expect this guy to get into games where he is going to factor into whether its a win or loss, these are all just very rough guidelines but I'm basically looking for a barely adequate ML/AAAA pitcher who can eat a bunch of innings and save the pen... if I'm carrying one at all. 

Typically during the season, I don't set anyone to Mop up. In the postseason, my 4th and 5th starter move to Long A or Long B, my Long A either stay put or move to Long B, and my Long B move to mopup.

For ratings, my ideal long relievers have the stamina/durability combo to join the rotation if necessary (60+/20+). For contending teams, I usually have Long Bs with 70+ control, 60+ splits, and decent pitches. For rebuilding teams, those numbers drop to 60+ control with 50+ splits.

My ideal situation is to have this type of guy coming up from the minors, but if not I have different pay scales based on the team. On the contending teams, I typically sign the guys later in free agency for between $2-4M. On the rebuilds, they get signed at the end of free agency or even partway into spring training for ~$1M.

Mop Up and LRB are the guys not good enough to be SP or LRA.    Ideally, I'm not carrying either.   If you want someone to just eat innings, take your best AAAA-type pitcher and use him until he goes to arb.   Then find another minimum salary guy to take his place.

I don't have a LRB or MOP, usually a L and R LRA. Only time I think of putting a guy LRB or MOP is if I drafted him too high and he's a bust or spent too much on him as an IFA. The. I can go 'hey look! He made the majors'

Don't ever designate a closer.

I like when position players pitch.  I'd call that mop up.  

Never pay more than minimum for one - any AAAA worthy pitcher will do.  Or if you have a good team, you don't need a LRB or Mopup at all.

Thank you all for the responses, very helpful.

Actually, looking back at my San Diego squad this past year I have a perfect example of how the Mopup position was super helpful.

http://www.whatifsports.com/HBD/Pages/Popups/FranchiseProfile.aspx?fid=1729

Early in the season Denny Gurerra went down long term on the DL. I needed to call someone up to take his place, so I took my most ready AAA guy in Bruce Lincoln. He did ok but was obviously over his head in the majors. When Gurerra came back, there wasn't a spot for Lincoln on the ML squad. Problem is, if I demoted him back to AAA I was fairly certain he would take a ratings hit, so I moved some pieces around and slotted him in at Mopup. He was still able to get the innings in needed for growth, but was never in danger of costing my team any games.

Food for thought anyways.

My  pitching model calls for 4 high quality SP.   Need at least one horse who has the capacity to throw a complete game, preferably two guys like that.    The 5th spot is hard to fill with another high quaity SP, so I am often experimenting with that spot.   I will sign an aging ace in the 36-38 age range.   They can step in and rest the first 4 guys if need be with a spot start.   Otherwise that aging vet will usually be in the mop up or Set Up B until he is needed in the regular rotation.    If someone goes down with an injury, the aging vet can step in for that too.   I use pitcher ball parks and the aging vets really seem to find a revival when I plug 'em in.