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Re: Strikeforce Los Angeles June Card
I'll comment on the rest of the thread later, but first: my math homework (lol).
Well, I don't think the problem has been completely specified, but here's something close:
Suppose an organization has 50 fighters, that are ranked in skill from #1 to #50. When they fight, it's a coin toss 20% of the time and the rest of the time, the better fighter wins. Basically, that would mean each match is 90%-10% in favor of the more skilled fighter. If you're numero uno, you have odds of going 33-0 that are 0.9^33 or about 3%. You also have odds of going exactly 32-1 that are 33*(.1)*(.9)^32 = 11.3%.
For any other fighter except the worst, you would have to make some kind of assumptions about the scheduling. But I'd say if the number 2 or 3 guys went on a tear, they would almost certainly get matched up against #1 at some point and would have a 90% chance to lose that fight. So their odds are probably 10 times smaller than the percentages above.
What you're getting at is similar to something I consider when making guesses about fighters that I don't know anything about other than their W/L record against small-time opposition.
There's an anecdote related in Sagan's "The Demon-Haunted World" about Enrico Fermi that goes like this:
So what I like to do is think about how likely it is that someone could get their record purely by coin-toss. So by that reasoning, 8-1 (3.5%) is juuust a hair worse than 5-0 (3.1%) , but 9-1 (1.9%) is better.
I'll comment on the rest of the thread later, but first: my math homework (lol).
Originally posted by MMA_scientist
Suppose an organization has 50 fighters, that are ranked in skill from #1 to #50. When they fight, it's a coin toss 20% of the time and the rest of the time, the better fighter wins. Basically, that would mean each match is 90%-10% in favor of the more skilled fighter. If you're numero uno, you have odds of going 33-0 that are 0.9^33 or about 3%. You also have odds of going exactly 32-1 that are 33*(.1)*(.9)^32 = 11.3%.
For any other fighter except the worst, you would have to make some kind of assumptions about the scheduling. But I'd say if the number 2 or 3 guys went on a tear, they would almost certainly get matched up against #1 at some point and would have a 90% chance to lose that fight. So their odds are probably 10 times smaller than the percentages above.
What you're getting at is similar to something I consider when making guesses about fighters that I don't know anything about other than their W/L record against small-time opposition.
There's an anecdote related in Sagan's "The Demon-Haunted World" about Enrico Fermi that goes like this:
My favorite example is this story, told about the Italian physicist Enrico Fermi, newly arrived on American shores, enlisted in the Manhattan nuclear weapons project, and brought face-to-face in the midst of World War Two with US flag officers:
So-and-so is a great general, he was told.
"What is the definition of a great general?" Fermi characteristically asked.
"I guess it's a general who's won many consecutive battles"
"How many?"
After some back and forth they settled on five.
"What fraction of American generals are great?"
After some more back and forth, they settled on a few per cent.
But imagine, Fermi rejoined, that there is no such thing as a great general, that all armies are equally matched, and that winning a battle is purely a matter of chance. Then the chance of winning one battle is one out of two, or 1/2; two battles 1/4, three 1/8, four 1/16 and five consecutive battles 1/32, which is about three per cent. You would expect a few per cent of American generals to win five consecutive battles, purely by chance. Now has any of them won ten consecutive battles ..... ?
So-and-so is a great general, he was told.
"What is the definition of a great general?" Fermi characteristically asked.
"I guess it's a general who's won many consecutive battles"
"How many?"
After some back and forth they settled on five.
"What fraction of American generals are great?"
After some more back and forth, they settled on a few per cent.
But imagine, Fermi rejoined, that there is no such thing as a great general, that all armies are equally matched, and that winning a battle is purely a matter of chance. Then the chance of winning one battle is one out of two, or 1/2; two battles 1/4, three 1/8, four 1/16 and five consecutive battles 1/32, which is about three per cent. You would expect a few per cent of American generals to win five consecutive battles, purely by chance. Now has any of them won ten consecutive battles ..... ?
LOL SPX
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