Melbourne Cup probability question.
I set up a sweepstake and each participant pulled the names of 5 horses out of a hat.
My 5 horses included all three of first, second and third. What is the probability of that?
Can that occurrence be explained in part by: cherry picking, texas sharpshooter, confirmation bias, other?
mollwollfumble said:
Melbourne Cup probability question.I set up a sweepstake and each participant pulled the names of 5 horses out of a hat.
My 5 horses included all three of first, second and third. What is the probability of that?
Can that occurrence be explained in part by: cherry picking, texas sharpshooter, confirmation bias, other?
Are you assuming that each horse has an equal chance of winning?
mollwollfumble said:
Melbourne Cup probability question.I set up a sweepstake and each participant pulled the names of 5 horses out of a hat.
My 5 horses included all three of first, second and third. What is the probability of that?
The probability that it would happen to you specifically would be 0.5%.
The probability that it would happen to any of the participants would depend on how many participants there were.
Can that occurrence be explained in part by: cherry picking, texas sharpshooter, confirmation bias, other?No. Also, there’s nothing to really explain.
dv said:
mollwollfumble said:
Melbourne Cup probability question.I set up a sweepstake and each participant pulled the names of 5 horses out of a hat.
My 5 horses included all three of first, second and third. What is the probability of that?
The probability that it would happen to you specifically would be 0.5%.
The probability that it would happen to any of the participants would depend on how many participants there were.
Good. You spotted a subtlety there, only two participants in the sweepstake. ¿How come, because I rejected the horses I thought were least likely to win before putting the names in the hat.
party_pants said:
Are you assuming that each horse has an equal chance of winning?
No. That’s part of it. For example, none of the three horses was the favourite, Finche.
mollwollfumble said:
dv said:
mollwollfumble said:
Melbourne Cup probability question.I set up a sweepstake and each participant pulled the names of 5 horses out of a hat.
My 5 horses included all three of first, second and third. What is the probability of that?
The probability that it would happen to you specifically would be 0.5%.
The probability that it would happen to any of the participants would depend on how many participants there were.
Good. You spotted a subtlety there, only two participants in the sweepstake. ¿How come, because I rejected the horses I thought were least likely to win before putting the names in the hat.
party_pants said:
Are you assuming that each horse has an equal chance of winning?
No. That’s part of it. For example, none of the three horses was the favourite, Finche.
Hold on a moment. 3rd place was Il Paradiso? I thought it was Master of Reality – but that was fourth. Was there a protest, or was I just blind?
mollwollfumble said:
mollwollfumble said:
dv said:Good. You spotted a subtlety there, only two participants in the sweepstake. ¿How come, because I rejected the horses I thought were least likely to win before putting the names in the hat.
party_pants said:
Are you assuming that each horse has an equal chance of winning?
No. That’s part of it. For example, none of the three horses was the favourite, Finche.
Hold on a moment. 3rd place was Il Paradiso? I thought it was Master of Reality – but that was fourth. Was there a protest, or was I just blind?
I’m sure I saw Master of Reality in the photo finish. There was a protest.
“A protest on behalf of Il Paradiso against Master Of Reality sparked high-drama soon after the race. Master Of Reality crossed the line second but was ruled to have interfered with Il Paradiso. As a result, Prince Of Arran was promoted from third to second, Il Paradiso was promoted from fourth to third and Master Of Reality was relegated from second to fourth.”
So only first, second and fourth. Much more likely, or it is?
mollwollfumble said:
mollwollfumble said:
dv said:Good. You spotted a subtlety there, only two participants in the sweepstake. ¿How come, because I rejected the horses I thought were least likely to win before putting the names in the hat.
party_pants said:
Are you assuming that each horse has an equal chance of winning?
No. That’s part of it. For example, none of the three horses was the favourite, Finche.
Hold on a moment. 3rd place was Il Paradiso? I thought it was Master of Reality – but that was fourth. Was there a protest, or was I just blind?
I’d love toi know the Byzantine rules that relegated MoR to fourth instead of a disqualification etc. I imagine fourth place still wins some money.
mollwollfumble said:
No. That’s part of it. For example, none of the three horses was the favourite, Finche.
Hold on a moment. 3rd place was Il Paradiso? I thought it was Master of Reality – but that was fourth. Was there a protest, or was I just blind?
I’m sure I saw Master of Reality in the photo finish. There was a protest.
“A protest on behalf of Il Paradiso against Master Of Reality sparked high-drama soon after the race. Master Of Reality crossed the line second but was ruled to have interfered with Il Paradiso. As a result, Prince Of Arran was promoted from third to second, Il Paradiso was promoted from fourth to third and Master Of Reality was relegated from second to fourth.”
So only first, second and fourth. Much more likely, or it is?
Or to rephrase that question Is it more likely for three horses chosen at random to be the first second and third over the line or for three horses chosen at random to be first, second and third after protests? This is where Texas sharpshooter comes in.
Preselecting the ten horses I thought had the best chance before putting them in the hat is where confirmation bias comes in.
By preselection, the TAB odds say that there was a 58% chance that one of those ten horses would come first. Let’s say similar odds for second place, and 4/9 odds that both first and second place are in the same hand. 0.58*0.58*4/9 = 15%.
> The probability that it would happen to you specifically would be 0.5%.
So without Texas sharpshooter and confirmation bias that 0.5% chance has rocketted to 15%.
Then add in the cherry picking effect. Suppose I’ve been entering Melbourne Cup sweeps to 50 years. Then the chance of this occurring in one of those years is 1-(1-0.15)^50 = 99.97%
So by taking into account texas sharpshooter, confirmation bias and cherry picking, what appears to be a probability of 0.5% is actually a probability of 99.97%.
This is why it pays to be extremely careful in interpretting probabilities in scientific papers.