Pinch running specialist
The pinch running specialist's primary role is to provide a significant upgrade over at least some of the starters on the basepaths, particularly in late and close, high leverage situations where great base running can create runs. Being able to convert a walk into a double or triple via steals can greatly swing a games likely outcome. Outs in these situations are an absolutely anathema, so the pinch runner need not only be a fast and prolific stealer, but also a reliable one who rarely gets caught. Also note that I focused on stealing ability as modern baserunning stats (extra bases advanced compared to average) only go back about a decade.
Consider the following situation: tie ball game, bottom of the 9th, runner on 1st. Not a great baserunner, or perhaps an overly aggressive one (such as, hmm, Babe Ruth. 1926 World Series, anyone?). The pinch runner specialist is who I put in for that runner to put the game away. A successful steal of 2nd not only removes the double play and puts a runner in scoring position, it adds a about 6% chance to win. And if he can then nab 3rd, he's improved the odds of winning by over 20% (calculated here). That said, I want I guy who knows when not to run, too. An out in such a scenario hurts a lot, hurting my chances of winning by about 12%. If I have Ruth on, he's fairly likely to attempt the steal. Who do I put on to replace him (or, perhaps, anyone else?)
Selection: Tim Raines
The often overlooked Raines holds the highest stolen base percentage of anyone with over 400 steals, at about 84%. Rickey Henderson, no slouch himself, comes in at just over 80%. Raines was also a fantastic hitter with a high peak: .294/.385/.425/.374/134 (avg/obp/slg/woba/wRC+)for his career and a .334/.413/.476/.412/162 season in 1986. His defense was sometimes exceptional, but across his career profiles more as league average.
Raines stole 808 bases, which is not much more than half the number Rickey Henderson stole, but I put that down to a mix of Henderson's amazing logevity and Raines's slightly better judgement on the base paths. I think it's enough to establish that the man could run the bases and swipe one when necessary.
Raines was also a switch hitter, which might lessen the gap between his and Henderson's bats against right handed pitching. Unfortunately, the splits only go back to 2002, so they're not useful here. Still, being a switch hitter (a great switch hitter, even) off the bench is a nice perk.
Ultimately, though, no one else combines Raines's level of base stealing aggressiveness with such a high success rate. 808 steals, 84% success rate. That's what it boils down to. Raines not only runs with best base stealers of all time, he knows better than anyone else when not to run.
He really doesn't need any justification, does he? All time leader in stolen bases (and runs and unintentional walks and who knows what else), 80% stolen base rate, fantastic batter, a little light on power, but with a much higher batting peak than Raines and better career stats, too. The big differentiator between Henderson and Raines is Rickey's sustained level of performance. For 19 years, from 1980 to 1999, Henderson was a better than average left fielder. And he was a great defender for the first ten years, too. Anyway, Rickey hit .279/.401/.419/.386/141 across his lifetime with his best season coming in 1990: .274/.439/.577/.467/204. That's a higher wRC+ than Musial's best season (200 in 1948). Those stolen bases matter.
But since this is the pinch runner specialist, that 4% difference in stolen base rate matters, too.
Beltran actually holds the record for stolen base percentage among batters with at least 299 steals at about 88% (he sits at 299 today). While it's commendable, he never approached Raines's (or Henderson's) prolific baserunning seasons. He's a good pick, with a good bat and good defense (and more time in centerfield than Raines or Henderson), but without the steals as a central part of his game, he doesn't compel me. And his bat is actually, when normalized by era, a bit weaker than Raines. He's had more pop than Raines or Henderson and as a Cardinal fan, I'm gratefuly for it today.
Cool Papa Bell
Really, after Raines, Henderson and Beltran, there isn't any statistical room. The other prolific stealers generally were caught more than 20% of the time. Any of the thieves with better than an 80% success ratio is a decent pick and you could make justifications based on the make up of the rest of your lineup. Joe Morgan, Ichiro Suzuki, Alex Rodriguez, Barry Larkin and Roberto Alomar all bring some really useful tools to either the bench or a starting lineup. But for a pinch runner, Raines reigns.
But not all players have had the opportunity to build the statistical support. Notable among the Negro leagues players who suffered from segregation is James "Cool Papa" Bell. We have only anecdotes and hazy statistical evidence, with a reported round trip time of 12 seconds the batter's box back to the plate. By all accounts, Bell was both ridiculously fast and an excellent base runner. The nlbpa.com article is a good place to start looking.
It's also noteworthy that Bell was born in or around Starkville, MS.