Quote:
Originally Posted by chumdawg
The point of the article I mentioned, which I will try to find, is that if you could reduce the game down to a small enough size, you would find there is not much difference in skill level. Everybody on the court--or field, as I think the article may have been about football as well--being a professional and all. Or looked at another way, if there *is* a large difference in relative skill levels, much of it is "lost" to the game conditions, as the one-possession format levels the playing field, as it were.
As an illustration, if you were an NFL team that was completely outmatched in terms of talent, would you prefer to play your opponent the full four quarters or instead play a sudden-death overtime? Or do you think there is no difference between the two?
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I think in my longer post I explain why this kind of reasoning is wrong. It's not that the skill level differential will be lost, but the size (coefficient, weight) of the error i.e randomness on the final outcome would be much larger.
And yes, a bad team would prefer a shorter game in basketball and football. But the reasoning is that with a much larger impact of the error they have a larger probability of getting a better score. However, that probability would be the same for a getting a worse result than they would normally.
Think of it as a bell shaped distribution. With no randomness the distribution isn't one at all, it's just a vertical line at the mean. As the error gets larger, the tails get fatter and fatter. Therefore the probability of getting results that deviate from the mean gets larger and larger.