A little different situation, but as far as the baserunning is concerned, Boston sent Roberts in the 9th inning in last years playoff. They only needed one run. But similar in the tightness and meaning of the game.
Whenever I analyze situations I first make a decision based on MY side of the story. Then, I analyze the other side. The other teams point of view. You'll be surprised how often you see their fear as greater than your desire.
In other words, if I'm analyzing the other teams viewpoint and I am facing a 95% basestealer, I'm dreading they send him. If I'm analyzing my teams viewpoint, and it's my player, I may be nervous and not send him. Which way is correct? Probably neither BUT, this is where CoachB25's philosophy comes in. Go with what you do and teach. If we teach steals, do it. What sense does it make to teach it and build your team around it and then have a very fast runner on first and not send him.
95% is very high odds. If you can't pull the trigger then then you better find other work. No matter the situation.