I’ve often wondered what the odds of winning the Score & Win contest's $1,000,000 grand prize. Every game you see the ad and know that there is almost no chance of actually winning it (especially with the Canucks who can’t even score 5 goals combined). I can’t imagine what it’s like to know you’re the one who has a chance at a million though. Presumably they’ve got some accountant type calculating the odds and making sure they are able to pay award with the advertising if such an unlikely even occurs. So I’m just going to provide you with the accountant’s math so you all know the chances of winning the big prize.
First I looked at 2002-2003 to 2005-2006 data to get this list:
Probability of scoring exactly 1 goal given you scored at least 1 goal
= 0.89279 = P(G=1|G>0)
Probability of scoring exactly 2 goals given you scored at least 1 goal
= 0.09583 = P(G=2|G>0)
Probability of scoring exactly 3 goals given you scored at least 1 goal
= 0.01043 = P(G=3|G>0)
Probability of scoring exactly 4 goals given you scored at least 1 goal
= 0.000953 = P(G=4|G>0)
Using the assumption that goal scoring is Poisson, which is proved to be reasonable by Ryder, implies P(G=X) = exp(-k)*k^x/(x!).
Here’s where it might get confusing. [P(A|B) = P(A and B)/P(B)]
P(G=1|G>0) = P(G=1)/P(G>0)
P(G=2|G>0) = P(G=2)/P(G>0)
P(G=1|G>0)/P(G=2|G>0) = P(G=1)/P(G=2)
P(G=1)/P(G=2) = [exp(-k)*k^1/(1!)]/[exp(-k)*k^2/(2!)] = 0.89279/0.09583 = 9.3
Solve for k: [with computer]
k = 0.215
You can do the same for 2->3 and get K = 0.32 and 3->4 gets K = 0.274
Since I consider 1->2 to be the most accurate I went with 0.215
The probability of an average player getting 5 goals is:
exp(-0.215)*0.215^5/(5!) = 0.000003
The probability that a given player doesn’t score 5 is 99.99969%, so the probability that none of the 18 possible scorers gets 5 is:
(0.9999969)^18 = 99.994%
Or the probability that a player does score 5 in a game is: 0.00005577
Since the prize is an annuity distributed over 20 years it’s only worth about $680,000 when it is won (@ 4% discounting).
Multiply the costs by the odds of winning in a given game:
$680,000*0.00005577 = $38/game
Works out to one 5 goal game every 7-8 seasons. [Does anyone have a list of 5-goal games?]
Your odds: [BC]
There are about 2 million possible shoppers (exaggeration) and Safeway has a 30% market share, so there are about 600,000 entrants (assuming they all shop equally often). Making the final value to the individual viewer:
$0.00006/game or 0.006 cents/game.