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Friday, September 16, 2011
Do the Tigers have a 100% chance of making the playoffs?
This BPro reader, Juris, says not so:
What caught my eye on this is that you now have the Tigers listed as 100% likely to win their division. But the Magic Number as of this morning is 6 versus the Indians and 5 versus the WhiteSox. Neither of those teams is mathematically eliminated from winning the division, though the probability of either one of them winning is very very small. I would therefore list the Tigers’ chances as 99.9%.
However, Cool Standings ALSO has the same 100%, whether you use the “smart” or “dumb” options (dumb implying every team is a true talent .500 team). So, what gives?
Well, it’s easier to see with Clay’s report here, where he gives the Tigers a 99.99985% chance of making the playoffs.
It’s basically a rounding issue. Clay runs one million sims, and he rounds not at all. That is, out of one million sims, the Tigers make the playoffs 999,998.5 (the fraction presumably because there was a tie that has to go to a one-game “playoff”, but is, technically, not a playoff).
I think it’s probably better, in these cases, that if you need to round, to round away from the extremes (100% and 0%). At the very least, at least cap at 99.9% or 0.1%, unless the sim truly showed 100% and 0%.
Good job Juris! A nit pick close to my heart.
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