Will The Boston Celtics win a Road Game vs the Pistons?
Yes -190
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Based on my back of the envelope calculation assuming a 64.094% of Boston winning a given game at home and a 38.150% probability of winning on the road (determined from backing out of a 56.751% series win probability for Boston). I have the following outcome probabilities:
Now if Boston wins in 4,5, or 6 games then they'll necessarilly have won at least 1 game on the road. So that's 5.979%+16.719%+13.186% = 35.884%.Code:Win In BOS DET Total 4 games 5.979% 4.932% 10.911% 5 games 16.719% 8.506% 25.226% 6 games 13.186% 18.122% 31.308% 7 games 20.866% 11.689% 32.555% Total 56.751% 43.249% 100.000%
If Boston wins in 7 then they'll necessarilly have won at least 1 game on the road provided they don't split perfectly. So that's 20.866%-64.094%4*61.850%3 = 16.873%.
Detroit wins in 5 -- Boston wins 1 on the road with probability 2*35.906%3*61.850%*38.150% = 2.184%.
Detroit wins in 6 -- Boston wins at least 1 on the road with probability 35.906%2 * 61.850% * 38.150% * ( 6*64.094%*61.850% + 38.150%*35.906%) = 7.652%
If Boston loses in 7 then they'll necessarilly have won at least 1 game on the road provided they don't split the first 6 games perfectly. So that's 11.689%-64.094%3*61.850%3*35.906%
= 9.452%.
So that would a total probability of Boston winning at least 1 on the road of 35.884% + 16.873% + 2.184% + 7.652% + 9.452% = 72.046%.
Hence, by this analysis, "Boston wins at least 1 game on the road" at -190 would qualify as an excellent bet (edge of 9.966%, full-Kelly stake of 18.933%).
Now admittedly this analysis is rather less than perfect, most notably because it assumes each team has a constant probability of winning at home and on the road. Nevertheless it does provide an objective and unemotional means of analyzing the value of this bet.
What we can say is that if we took the underlying assumptions as granted (Boston a 64.094% probability of winning any given game at home, a 56.751% probability of winning the series, and Detroit a constant probability of winning any given game at home) then we could conclude that the bet provided tremendous value.
SBR Founder Join Date: 8/28/2005
SBR Founder Join Date: 8/28/2005