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Or viewed another way if it isn't inevitable that we sign someone and there is a possibility, no matter how small, that we dont sign anyone then each day that passes makes that possibility more likely. So, if we accept that it isn't 100% certain that we will sign someone, the odds that we won't...

Its the opposite actually. Lets say the probability of us signing a player on any given day is 50%. The probability of us signing a player tomorrow is 50%. The probability of us signing a player on Friday is 50% multiplied by 50% which is 25%. The probability of us signing a player on Sat is...