Of course “upsets” (weaker seed teams defeating stronger seed teams) happen in sports. They simply don’t happen enough in modern college basketball, and hence provide most enthusiasts with a false sense for how low their likelihood is. The most extreme example of an upset occurring is if a worst seed (seed 16) team defeats a best seed (seed 1). There are four such match-ups, very year, in Round 1 of the March Madness competition. As our conditional math here shows, the probability for any upset is quite low relative to what odds-makers have assigned to it. Yet high enough that corporations should consider this in any sort of promotional sweepstakes.
p(extreme upset)
= 1 - p(no upsets)
= 1 - (62.5/64)^4
= 1 - (0.977)^4
= 8% (once every 13 or so years)
And while this has never happened in the men’s competition prior to this year (instantly annihilating all of tens of millions of potential perfect brackets though the Final Four while other downstream brackets might still be fine; anyway an unheard of feat in the past decade), it has occurred in the women’s competition. Should Little Caesars have run a “free pizza lunch” contest for this stated “extreme” probability of occurring? Well that’s unclear, though the probability they assigned to having to payout on this marketing gimmick was likely much lower (by a factor of three!)
Let’s first look at these Bayesian probabilities some more (particularly the chance of seeing or not seeing past observations of upsets given these probabilities shown above). Then you decide. Let’s assume we use 8% probability; then we’d never have seen an upset in 13 years:
p(never among just men)
= (1-8%)^13
= 34%
p(never among men or women)
= [(1-8%)^13)^2]
= 12%
So even when there is a 1 in 13 years or so chance for any competition to have this extreme upset, there was a 34% chance we’d never have seen one anyway over 16 years. Note that the men's competition, in the current bracket format, has been in place for a few decades. Nonetheless, there has been a 12% chance we’d never see such an upset recently, in either the men’s or women’s competitions (but of course we now have seen it in both).
Last, as noted also here, there are generally a couple more upsets during these games than what one would infer from the generally accepted “odds” going around for these brackets. The empirical fact that this year we have such an extreme bracket buster is a lesson for office-pool speculators and odds-making bookies (the latter of top casinos are now following this website).
p(extreme upset)
= 1 - p(no upsets)
= 1 - (62.5/64)^4
= 1 - (0.977)^4
= 8% (once every 13 or so years)
And while this has never happened in the men’s competition prior to this year (instantly annihilating all of tens of millions of potential perfect brackets though the Final Four while other downstream brackets might still be fine; anyway an unheard of feat in the past decade), it has occurred in the women’s competition. Should Little Caesars have run a “free pizza lunch” contest for this stated “extreme” probability of occurring? Well that’s unclear, though the probability they assigned to having to payout on this marketing gimmick was likely much lower (by a factor of three!)
Let’s first look at these Bayesian probabilities some more (particularly the chance of seeing or not seeing past observations of upsets given these probabilities shown above). Then you decide. Let’s assume we use 8% probability; then we’d never have seen an upset in 13 years:
p(never among just men)
= (1-8%)^13
= 34%
p(never among men or women)
= [(1-8%)^13)^2]
= 12%
So even when there is a 1 in 13 years or so chance for any competition to have this extreme upset, there was a 34% chance we’d never have seen one anyway over 16 years. Note that the men's competition, in the current bracket format, has been in place for a few decades. Nonetheless, there has been a 12% chance we’d never see such an upset recently, in either the men’s or women’s competitions (but of course we now have seen it in both).
Last, as noted also here, there are generally a couple more upsets during these games than what one would infer from the generally accepted “odds” going around for these brackets. The empirical fact that this year we have such an extreme bracket buster is a lesson for office-pool speculators and odds-making bookies (the latter of top casinos are now following this website).
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