from Amazon
Thursday, June 17, 2010
The next Ensberg challenge
He asks:
Scenario: You are the runner on 2nd base and there is 1 out. The score is 3 to 3 and it is the 4th inning. A fly ball is hit to right center field and the right fielder will attempt to catch the ball. As a runner you have average Major League speed. If you choose to tag, you will be safe at 3rd base, but you will have to slide. The next batter up hits in 7th in your lineup and he is a career .250 hitter with 10 HR’s and 60 RBI’s. What do you do and why?
My answer:
Here are the possible outcomes:
a. RF catches ball, you tag up, you make it to 3B, 100% of the time
b. RF catches ball, you are somewhere between 2B and 3B, you need to get back to 2B, and will be thrown out there proportionate to how close you were to 3B
c. RF just misses getting the ball, you tag up, you make it to 3B, 100% of the time
d. RF just misses getting the ball, you round 3B, the RF throws it in, and you attempt to score proportionately to how close you were to 3B when the ball dropped in, and you will be thrown out a fixed percentage of your attempt rate (say 10%)
Now, give me about 10 minutes to look into my WE charts, and I’ll give you my answer.
UPDATE:
Presuming bottom of the 4th, the chance of winning to start that plate appearance is .5832. Let’s do it:
a. Tag up: Runner on 3B, 2 outs makes it .5466 win probability
b. Take a lead:
(i) Runner on 2B, 2 outs makes it .5412 win probability
(ii) DP makes it .5000
c. Base hit: Runners on corners, 1 out makes it .6384 win probability
d. Base hit:
(i). You stick at 3B, so same as c. above
(ii). You try to score, the batter-runner holds at 1B, and you are:
1. Safe at home: Up by 1, runner on 1B, 1 out: .6824
2. Out at home: Runner on 1B, 2 outs: .5291
(iii). You try to score, the batter-runner goes to 2B on the throw, and you are:
1. Safe at home: Up by 1, runner on 2B, 1 out: .6983
2. Out at home: Runner on 2B, 2 outs: same as b(i) above
Ok, you need to have all those numbers in your head when you have to make your decision!
The difference between a. and b. above is so small that on a play that you think is a sure out, that it doesn’t really matter if you tag up or not. That is, being on 2B with 2 outs and being on 3B with 2 outs is almost the same thing. (That’s because the SF is now out.) So, tagging up is not really an option, not unless you are 100% sure that the RF will make the out.
Now, the tougher part: you are not sure if the RF will make the out. If you take a big enough lead, you will score easy, and your win probability is around 68% to 70%. If you take a good lead, but not big lead, you might get thrown out at home, in which case the win probability is 53% to 54%. If you play “station-to-station” ball, the win probability is 64%.
So, let’s try to work it out, presuming it’s a 50/50 play (you are not sure if the RF will make the out or not). You take a good lead (say halfway), but not big lead.
Batter is out, you make it back 45% of the time, and are doubled up 5% of the time.
Basehit, you score 40% of the time, and are thrown out 10% of the time.
That’s a .595 win probability.
If you simply played station-to-station (half the time a., and half the time c.), it would have been .593.
As you can see, you have to take a lead such that you have at most a 10% chance of being doubled up on a catch, and at most a 20% chance of being thrown out at home. Sounds therefore that you should be about one-third to half-way to 3B.
That’s on a 50/50 play.
I think assumption b is a little off. Under this assumption, someone who is 10% of the distance between 2B and 3B will be thrown out 10% of the time. But 10% of the distance is only 9 feet. I would think the runner would get back 100% of the time if he’s only 9 feet from the bag, especially if the assunption is that the ball is hit deep enough so that he could get successfully tag up 100% of the time.