From yesterday, in the comments section of the Win Probability Added post:
I decided to go ahead and do the legwork during the A's game today. Before we get to the WPA, though, let's see some adjusted batting lines. Remember, Ichiro was 45-47 in stolen base attempts, and Willie was 16-19. (I'm not including the time Ichiro was picked off on August 14th, because he wasn't actually running on the play, he just took too large of a lead.)
It doesn't work quite like that, of course - stealing second isn't as valuable as hitting a double because it doesn't advance the runners, so SB's shouldn't be directly added into a player's slugging percentage - but it gives you some idea of how Ichiro and Willie's straight batting lines undershot their actual value. The stathead movement has pretty much completely discredited the stolen base as a worthwhile weapon, but used properly by the right players, it can actually be of significant help. It should never be the main focal point of an entire offense, but it shouldn't be abandoned, either, not if you have the personnel to pull it off.
To the WPA.
Ichiro, total for 47 attempts: +64.9%
Ichiro, per 45 successful SB: +1.6%
Willie, total for 19 attempts: +37.3%
Willie, per 16 successful SB: +3.1%
Between the two of them, Ichiro and Willie's steals added more than a full win, with Ichiro doing two-thirds of the work. The total contribution may seem lower than you expected, but steals generally don't have a major impact; they're one of those things that just adds up over time, rather than something that can totally change the direction of a game by itself. The most valuable possible stolen base (stealing 3rd with one out in the bottom of the ninth, down by one) is worth just +13.2%, and most others are considerably lower than that, so keep this in mind.
What's most interesting about those numbers, though, is that, on average, Willie's steals were twice as valuable as Ichiro's. The reason for this? Willie stole more "money bags," as Rizzs would say, grabbing the extra base in the later innings of close games. Ichiro, meanwhile, preferred to steal his bases in lower-leverage situations, be they earier in the game, or during blowouts. He had a few important steals of his own, but not as many as Willie did.
The natural inclination, then, is to suggest that Ichiro should run more often in close games. After all, if he's going to be successful 96% of the time, why not take advantage of this when it matters a little more? I don't know if that's fair, though. I can't pretend to know what's going on in Ichiro's head, but I'm guessing he only runs when he thinks he's highly likely to make it safely. In the later innings of close games, opponents will pay more attention to him on the basepaths, which makes it more difficult on him to read the situation and get a good jump. Therefore Ichiro won't run as often, because he won't feel confident doing so, and while this seems like a partial waste of his talent, I'd much rather have him err on the side of caution than the alternative. Getting caught stealing in a close game deals a ton of damage to your chances of winning, so in many cases it's better to stand still than risk yourself on the basepaths.
Could Ichiro run more in higher-leverage situations? Possibly, but because I can't speak for his mindset, I'm going to trust that he's always doing what he thinks is best on the basepaths. As for Willie, what can you say? He's just a phenomenal base-stealer. We tend to make a lot of jokes at his expense over the season, but his legs are a valuable weapon to have lying around provided you aren't giving the rest of his body 250 at bats a year. You'd be hard-pressed to find a better pinch-runner in baseball.