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we get out, what we put in

Posted By: rambiz
Date: Thursday, 29 January 2015, at 5:27 a.m.

In Response To: we get out, what we put in (Bob Koca)

Thank you for your comment.
Let's assume in a game we have a lot of decisions to make, say you come to throw 100 times. Now if your success rate is %90 all the time you score 90 times and if your success rate is %70 all the time, obviously you'd score 70 times. If we alternate between the two cases, on average you'd score 80 times.
If we now alternate between %90 and 70% from throw to throw we get also 0.9x50+0.7x50=80. So I think, either way, we get the same result; if I put the quiz factor, namely, being challenged by you, aside.

Actually I was using a similar model as Timothy Chow, while thinking about this problem.
However, it turns out that the equation: result=0.50+skill difference+ luck difference contains all the information, we try to model and make sense of.
Now consider this example:
Assume player A is a 80-20 favorite over B, in 10 games A wins 8 on average. Below are 10 equations listed for the above case:
Result=0.5+skill difference+luck difference

1 =0.5+ 0.3 +0.2

1 =0.5+ 0.3 +0.2

1 =0.5+ 0.3 +0.2

1 =0.5+ 0.3 +0.2

0 =0.5+ 0.3 -0.8

0 =0.5+ 0.3 -0.8

1 =0.5+ 0.3 +0.2

1 =0.5+ 0.3 +0.2

1 =0.5+ 0.3 +0.2

1 =0.5+ 0.3 +0.2
The number 0.3 in the above list shows that A was consistently outplaying B, by a skill difference of 0.3. And as we can see, he was luckier in 8 cases, the majority of time as mentioned by Timothy Chow.
Now consider the performance of a somewhat inconsistent A(I deliberately exaggerate the inconsistency), who is still a 80-20 favorite against B:
Result=0.5+skill difference+luck difference

1 =0.5+ 0.6 -0.1

1 =0.5+ 0 +0.5

1 =0.5+ 0.6 -0.1

1 =0.5+ 0 +0.5

0 =0.5+ 0.6 -1.1

0 =0.5+ 0 -0.5

1 =0.5+ 0.6 -0.1

1 =0.5+ 0 +0.5

1 =0.5+ 0.6 -0.1

1 =0.5+ 0 +0.5
So the inconsistent A, wins also 8 games, averaging a skill difference of 0.3, but was lucky in only 4 games.
It is noteworthy that to win a game, although being unlucky, you must be be more than a %100 favorite in that very game. This is dictated by the used equation.

What is FT, please?

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