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It's about advancing bases on singles and doubles
From 2000-2006, with no outs, a runner went first-to-third on a single 23.4% of the time, and scored from first .4% of the time (note that these stats include advancing on errors). The baserunner got thrown out 1.0% of the time. 2.1% of the time, batter who hit the single advanced to second and .3% of the time the batter advanced to third, either on an error or while the defense was trying to throw out the lead runner. .4% of the time, the batter was thrown out trying to stretch the single.
Actually, I'll try to sum it up nicely. Since mostly we care about going first-to-third on a single, scoring from second on singles, and scoring from first on doubles, I'll just look at those cases:
First-to-third:
zero outs: 23.4%
1 out: 25.5%
2 outs: 31.9%
This makes sense, because with 2 outs, you're off with the crack of the bat no matter what...you dont have to hold up to see if the ball will be caught.
However, the highest percentage of times that the runner is thrown out is with two outs (1.7%)...this goes against the "dont make the thrid out at third base" mantra
Score from second on a single:
Zero outs: 41.0%
1 out: 52.8%
2 outs: 76.4%
Once again this makes sense. With nobody out, you dont take the risk...If you're on third with nobody out, you're almost guaranteed to score. You can take a little bit more of a risk with one out, but you still need to be cautious. Then, with two outs, you take even more of a risk. This is evidenced by the percentage of runners that get thrown out. It's 4.6% with 2 outs, compared to 2.6% with 1 out and 1.2% with 2 outs.
Plus, once again, you're off with the crack of the bat, so you dont need to wait to see if the ball drops. That accounts for the big increase in scoring from second with 2 outs.
Score from first on a double:
Zero outs: 33.7%
1 out: 36.0%
2 outs: 55.3%
All the stuff in the last section still applies. Even the thrown out %s...4.5% with 2 outs, 2.6% with 1 out, 1.3% with 0 outs