Linked Events
Sometimes in MLB Showdown, you may be in tight situations in which you're narrowly escaping loss and need a few more hits to stay alive. But you also have a bench. Your bench has good people for extra base hits, so you could score quickly. But your lineup has a higher chance of getting on base. Which has a higher chance of succeeding if you have two outs? Let's make a situation.
This is complicated. You need one run to tie in the bottom of the ninth inning with two outs and a man on second. You need 2 singles, a double, 3 walks, a triple, or a home run to score(or a combination of walks and singles). The batter coming up specializes in singles and walks-he's a 13 on base with 6 a walk. Same with the batter after him. But will they each come through to hopefully score a run? We don't know. You look to your bench. Your bench is more of a power team. They have less of a chance of getting on base, but they could more easily tie it up with one swing. This sounds like opinion on whether to leave your normal lineup in or Pinch Hit, but really, it's all mathematical. You can find the chances of different chains or Linked Events.
Linked events are two or more events happening sequentially. We can find the chances of certain linked events with the same result and compare the chances of each. Even a small difference helps, so you don't want to make the wrong choice.
First, you may want to make a basic decision: Is a bench player or your batter better at doubles? Multiply the percent chance of pitcher's advantage by chance of the chosen outcome with his advantage(decimal form), and add that to the same thing but for the batter's advantage. This is the chance of that extra base hit that will tie the game up. Do this again for a chosen bench player. Compare the numbers. The higher one is better. But is this too risky for you? Would you rather just try to get on base? Do the same thing as before but replace extra base hits numbers with walks/singles numbers. Do it for the bench player too. But wait-you're not done. You found the first one, but that doesn't score the runner yet. Multiply your current numbers by themself and divide by 100. That is, if you needed only two singles or walks to score that runner. If you did it by walks, you might have to do it a third time. This, if done correctly, should give you the percent chance of this chain of events coming true and scoring a run in that specific way. Compare the bench and lineup players, and see which has a better chance. This is getting complicated, isn't it? Now, you are free to compare other things, such as this chance to the chance of getting an extra base hit to score(if it was a different person you used). To clear things up, I'll demonstrate it in a formula. It may look a little different, but don't be alarmed. This will demonstrate the chance of linked events for a 12 on base, 8-11 walk, 12-15 single, 16-18 double, 19+ home run to get a single followed by two walks against a 5 control, 18-19 walk, 20 single pitcher.
This is complicated. You need one run to tie in the bottom of the ninth inning with two outs and a man on second. You need 2 singles, a double, 3 walks, a triple, or a home run to score(or a combination of walks and singles). The batter coming up specializes in singles and walks-he's a 13 on base with 6 a walk. Same with the batter after him. But will they each come through to hopefully score a run? We don't know. You look to your bench. Your bench is more of a power team. They have less of a chance of getting on base, but they could more easily tie it up with one swing. This sounds like opinion on whether to leave your normal lineup in or Pinch Hit, but really, it's all mathematical. You can find the chances of different chains or Linked Events.
Linked events are two or more events happening sequentially. We can find the chances of certain linked events with the same result and compare the chances of each. Even a small difference helps, so you don't want to make the wrong choice.
First, you may want to make a basic decision: Is a bench player or your batter better at doubles? Multiply the percent chance of pitcher's advantage by chance of the chosen outcome with his advantage(decimal form), and add that to the same thing but for the batter's advantage. This is the chance of that extra base hit that will tie the game up. Do this again for a chosen bench player. Compare the numbers. The higher one is better. But is this too risky for you? Would you rather just try to get on base? Do the same thing as before but replace extra base hits numbers with walks/singles numbers. Do it for the bench player too. But wait-you're not done. You found the first one, but that doesn't score the runner yet. Multiply your current numbers by themself and divide by 100. That is, if you needed only two singles or walks to score that runner. If you did it by walks, you might have to do it a third time. This, if done correctly, should give you the percent chance of this chain of events coming true and scoring a run in that specific way. Compare the bench and lineup players, and see which has a better chance. This is getting complicated, isn't it? Now, you are free to compare other things, such as this chance to the chance of getting an extra base hit to score(if it was a different person you used). To clear things up, I'll demonstrate it in a formula. It may look a little different, but don't be alarmed. This will demonstrate the chance of linked events for a 12 on base, 8-11 walk, 12-15 single, 16-18 double, 19+ home run to get a single followed by two walks against a 5 control, 18-19 walk, 20 single pitcher.
(65x.05+35x.2)x(65x.1+35x.2)x(65x.1+35x.2)/100
18.680625(%)
So, there is an 18.680625% chance of this sequence of events in order to score a run. Now, let's put a different player in to bat. You already know he doesn't get on base as much, but think he may have a good enough chance of an extra base hit to score a run. He's an 11 on base, 7-9 a walk, 12-14 a single, 15-18 a double, 19+ a home run(against the same pitcher). Maybe he has over an 18.680625% chance of an extra base hit, which would score that man from second(and only takes one at bat). Let's figure it out.
30x.3+70x0
9(%)
Nope. His extra base hits weren't great enough so he'd have a good enough chance. But some minor differences would have made him good enough, such as the pitcher having 20 as a double(quite common) or his on base being higher than 11(11 isn't great).
But there's a flip side to this, too. Maybe you're pitching and you're thinking about bringing in a reliever. Use the same formulas, but there's one big difference. You may need to find out the chance of an out. To do this, find the chance (decimal) of getting on base, and subtract from one. This gives you that number for chance of outs with someone's advantage.
But there's a flip side to this, too. Maybe you're pitching and you're thinking about bringing in a reliever. Use the same formulas, but there's one big difference. You may need to find out the chance of an out. To do this, find the chance (decimal) of getting on base, and subtract from one. This gives you that number for chance of outs with someone's advantage.
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posted by Peter @ 1:16 AM
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