Carry as many as you feel like drafting. It really depends on who they are more than anything else. If you have two solid guys with secure jobs then that's fine. If you're drafting from the bottom of the barrel you need to carry more guys since some of them won't work out. In a 10 team league there will always be solid starters on the wire, so I'd probably err on the side of more closers rather than less coming out of the draft. So maybe three, with a list of watch candidates set as well so you can swoop in a grab guys when they break out.
Also, because we're talking hth, you also need to consider whether you might be punting that category (i.e. not even attempting to be competitive) or possibly even setting it as a real strength for your team. If you want to win saves every week then you'll probably need 3 or even 4 guys. My personal preference for hth is to carry more relief guys than normal, but there's endless ways to build a team.
What are your scoring categories and roster positions? It makes a big difference. In our league, we are required to start five SP, three RP and three P. Our scoring categories are Quality Starts, Strikeouts, WHIP, ERA, Saves, and Holds. The optimal pitching staff in our league is five starters, three closers and three setup men but - given that it's a 16-team league - there are always teams that have to get creative and start more setup men or starters to compensate for the lack of closers.
I'm a little different in strategy......and I've won my league 3 years going.....
I carry two closers and two mid relievers, like Venters (Atl.) and Robertson (NYY).....and I play all four instead of playing more starters.
If you have a good SP staff, you'll get the wins, era, whip,etc.......guys like mid relievers help lower the era and whip, get strikes, etc to help in each category.
That works up to a point, but it's iffy if more than one other guy has the same idea. There really aren't that many MRs who really rack up wins and Ks with great % peripherals. Sure, if you draft Venters and Clippard (or Robertson) you look like a genius, but when the talent pool gets a little slimmer it's not quite so fantastic. If no one else is really following your lead then it'll work pretty much every year and the discount you get on your pitching staff means you should have enough offensive juice to win most weeks. It's great for public leagues and fun office pools, but when you're playing with top-tier guys those quality MRs get harder to come by, since those guys know exactly how good a couple of top-drawer MRs look compared to one mediocre starter.
Not that the strategy won't work in more competitive leagues, because it can, it's just a little harder to execute on draft day and you need to make sure you have the MR ranks down pat.
I am a little different but I spend a little more time doing research/analyzing matchups than most. I like to have about 4 or 5 closers, 1 or 2 really good rp's that strike out a lot of people (Clippard/Jansen). Then 2-3 top tier pitchers (Halladay, verlander, lincecum). Then i will just leave one bench spot as a streaming spot and just pick up and drop Starting pitchers based on matchups/categories that i am lacking in that week.
*Note this method is not for the feint of heart
Streamers Yesterday > NONE (used all of weeks moves shuffling batting) Today > NONE Tomorrow > Duane Below Vs KC *Worley (> My guy ) (* Wanted but taken)