J15
Registered User
- Mar 18, 2009
- 1,057
- 305
Hope I've found the correct forum for this post but I had a few questions about how to interpret the draft lottery odds that are published by the NHL. This started because I decided to try and build my own lottery simulator, but now it's more a matter of curiosity. The team which finishes last has the following odds for the draft lottery.
1 OA - 18.5%
2 OA - 16.5%
3 OA - 14.4%
The lottery for 1 OA is pretty straight forward, but it's unclear to me exactly how odds are determined after this. From what I can gather online, it seems like these that these odds represent the marginal probability for the team picking at each position. This would mean given an infinite amount of simulations the last place team would actually pick 1st in 18.5% of the time, pick second 16.5% of the time, etc. This would mean that team X having a 16.5% chance of picking 2 OA implies the following equation must be satisfied
16.5% = P(team X picks second | team 1 picked first)*P(team 1 picked first) + ... + P(team X picks second | team N picked first)*P(team N picked first)
While this provides a constraint on the set conditionals, P(team X picks second | team i picked first) , it doesn't uniquely determine them. As far as I can tell, it's also not trivial to come up with a method of generating these conditionals.
For example a trivial way of generating a given conditional P(team X picks second | team i picked first) would be to just re-normalize all the odds to account for the team that picked first.
P(team X picks second | team i picked first) = P(team X picks second) / (1 - P(team i picks second))
While this method is simple, the conditionals generated won't satisfy the constraint for the total marginal probability. I was wondering if anyone knew exactly how these odds are determined?
1 OA - 18.5%
2 OA - 16.5%
3 OA - 14.4%
The lottery for 1 OA is pretty straight forward, but it's unclear to me exactly how odds are determined after this. From what I can gather online, it seems like these that these odds represent the marginal probability for the team picking at each position. This would mean given an infinite amount of simulations the last place team would actually pick 1st in 18.5% of the time, pick second 16.5% of the time, etc. This would mean that team X having a 16.5% chance of picking 2 OA implies the following equation must be satisfied
16.5% = P(team X picks second | team 1 picked first)*P(team 1 picked first) + ... + P(team X picks second | team N picked first)*P(team N picked first)
While this provides a constraint on the set conditionals, P(team X picks second | team i picked first) , it doesn't uniquely determine them. As far as I can tell, it's also not trivial to come up with a method of generating these conditionals.
For example a trivial way of generating a given conditional P(team X picks second | team i picked first) would be to just re-normalize all the odds to account for the team that picked first.
P(team X picks second | team i picked first) = P(team X picks second) / (1 - P(team i picks second))
While this method is simple, the conditionals generated won't satisfy the constraint for the total marginal probability. I was wondering if anyone knew exactly how these odds are determined?
