Is competing at multiple regionals REALLY fair ?

[Wayne C.]

Originally Posted by Nikhil Bajaj

Let's say that the probability of winning a regional is 3/50, and we want to win at least one regional. Well, then the probability of NOT winning a regional is 47/50. THIS quantity will multiply.

So then we say, well, the probability of winning at least regional as a function of N, where N is the number of regionals we attend, is:

P(N) = 1 - (47/50)^N

Because (47/50)^N is the probability of NOT winning a regional, and the sum of the probabilities of all outcomes must equal 1.

And the result?

1 Regional: 3/50 or 6%
2 Regionals: 11.64%
3 Regionals: 16.95%

Note that this is the probability of winning at least one regional. If you wanted to get the probability of winning exactly two, then it would be (3/50)*(3/50)*(47/50). The probability of winning three would be (3/50)*(3/50)*(3/50). So the teams that won three had a 0.022% chance of doing so. Congratulations, 1114 and 1024, you guy beat the odds! Or maybe winning multiple regionals has more to do with robot quality, drive team skill, and a good autonomous than pure luck...though luck certainly is always involved.

Thus, it does go up (given that EVERYTHING else is equal, which it isn't) which makes sense--more chances equals more probability, but it doesn't quite scale linearly with regionals. Think about it, if they just added, then if you had a 3/50 shot of winning a regional, then if you went to 17 regionals you would be guaranteed a berth at Nationals, and your probability would be OVER 1.0, which is not really possible.

flawed logic- just showing up doesnt give you an equal probability of winning anything. A robot can win multiple regionals due to quality play or be the worst robot at every regional.

and besides- it isnt just about the winning........