# How much is my Super Bowl box worth?

I entered an office Super Bowl box pool. It was \$50 per box. The pool administrator gets 10 free boxes for running the show, so there’s a total pool of \$4,500.

The rules are that every score, including the initial 0-0 score, gets \$100. For touchdowns, this includes the touchdown plus the extra point. Thus, if the Bears score the first touchdown, the 6 (Bears) 0 (Colts) box gets \$100, and then if the extra point is converted, the 7-0 box gets another \$100.

Additionally, the 1st and 3rd quarters get \$150 each, their “reverse” boxes get \$50. The halftime score gets \$400, and its reverse gets \$100. The reverse of the final score gets \$200 and the total remaining dollars go to the final score box. A 4th quarter tie gets \$400, with no reverse. “Reverse” means assigning the opposing team’s score to the other team.

I drew the Colts 7 Bears 3 box. This is a damn good box and my guess is that it is worth substantially more than \$50. Can someone attempt to quantify its value?

Sorry that I don’t have time at the moment to adress your actual topic (work ends in 2 minutes), but I really hope you did a typo to a factor of 10 there. The guy running the pool can take one box as a freebie, two if he’s greedy. Ten boxes?!? That’s greed like I’ve never seen, and would be well deserving of being told where to shove his box pool.

I’m not a math guy, but I’d suggest that right now, your box is worth either the amount you paid for it (\$50), or perhaps slightly less because of the free boxes. I don’t think it matters what numbers are assigned to your box at this point. There may be some speculative potential to “good” numbers, but any digit has some chance of showing up in the score.

Also think the set up for the pool is problematic. Paying out for each score, including extra points, is gonna get expensive if the game turns into a shootout. Isn’t it possible that the pool could bankrupt itself? Probably unlikely, but still…

And I also think giving the guy running the pool 10 free boxes is too much. That’s 10% of the pot…

The pool won’t go bankrupt. There is \$1200 being paid for the 0-0, 1st, 2nd, 3rd and 4th quarter scores. That leaves \$3300 left to pay for scores. At \$100 for each score, that is 33 scores. If a touchdown is 2 scores, then there would need to be > 16 touchdowns to bankrupt the pool.

So the guy running it gets to keep an EXTRA \$3200 if the game ends 3-0?

No. The rules state any extra money goes to the holder of the final score.

Alright, I’ll bite. For purposes of this study, I’ll be using the Super Bowl scores for the last forty years.

Since no team has scored higher than 55 points, and no losing team has ever scored fewer than 3 points, and no total score has ever exceeded 75 points, we can set bounds on the “possible” scores. I ignore the lowest score ever because we’re also looking at all intermediate scores.

I count 5 possible Colts scores (7, 17, 27, 37, and 47) and 6 possible Bears scores (3, 13, 23, 33, 43, and 53), with a few high-scoring games that are too big. I count 6 scores that add to over 75, so you have 24 (thirty minus six) possible ways to score.

Some of the other boxes, for comparison:
1-1 only has 19 chances to score because you can’t score only one point
2-2 has 30 chances, but 11 of them rely on at least one safety (very unlikely), so let’s call that 19 as well.
3-3 has 26 possible scores: 36 possibilities and only 10 excluded for being too high.
4-4 is disastrous, because the only way to score four points is a double safety – this is so unlikely that we disregard the possibility. That leaves 25 possible scores, 10 of which are too high, for a total of 15 possible ways to score.
5-5 is also pretty bad because their single-digit score relies on safeties – also 15 chances to score.
6-6 is much better: 25 possibilities with only 3 scores that are too high. 22 total.

If you go through the rest of the grid, you get a total number of possibilities around 2,000*. If you have more than 21 possibilities, you’re doing better than most other boxes. If you have fewer than 21, then you paid too much for your box. The boxes with only 15 ways to score are particularly bad, since you paid for a full chance but only got about 75% of a chance. You appear to have a square with a 20% better than average chance of winning.

5 scores seems to be the minimum in a Super Bowl, and 16 seems like the max. \$100 is the average payout per score except for the halftime score and the big payout at the end. There are going to be at least nine paying events, and up to twenty. Odds of you randomly hitting one event are (24/2000), so odds of it not being you for each score are 98.8%. The odds of missing nine events in a row are 89.7%, and the odds of missing twenty events in a row are 78.5%. So your expected value is somewhere above \$11 (because you might hit two events, or the big payout at the end). An average square is worth slightly more than \$9, and a bad square could be worth less than \$7.

The bad news is that there are at least 5 squares on the board that have 30 (!) chances of coming up, and if your host knows what he’s doing, he has taken those in advance. Even if he only takes those 5 spots, he takes up 5% of the board but 7.5% of the potential scoring space (while leaving the “sucker” spots with only 15 chances in 2000 for the rest of you). If he takes 0-0, by the rules that you’ve set out, he gets \$100 just for showing up! His expected value for any of those big boxes is something better than \$13, which means that if he really gets ten boxes, he can go nuts and grab something like \$120 in expected value plus the guaranteed \$100 if he grabs the 0-0. He’s a greedy bastard.

All of this is dependent on me getting the right total number of possible scores (which I’m pretty sure I didn’t, but it’s close to 2,000), and assumes that scores are drawn randomly from all possible scores (which they aren’t). There’s probably some combinatorics math that can do this much more easily, but I don’t know it. Is ultrafilter in the house?

Of course I didn’t Google ahead of time and save myself all that work. Check out this article which uses crunched statistics to show the probability of a regular season game ending with a given score. You picked one of the fifteen best squares! There are ten squares with better odds than yours (Hmmm… ten squares, you say?) and five with odds as good as yours. Your expected value is somewhere between \$16 and \$33, which is pretty good.

For the top ten squares, assuming nine paying events (five scores and four paying quarters) the values are at least:

``````

70/07      3.80%     \$30
74/47      3.71%     \$29
03/30      3.21%     \$25
41/14      2.23%     \$19
04/40      2.04%     \$17

``````

Which means if one particularly devious bastard were to take those ten squares, odds are good that he’s walking out with \$240. Next time your buddy screws you like this, tell him you want dinner and flowers first.

Well if this pool is ran like the Grey Cup pool I particpate in, when you choose your square(s), it is on a 10x10 blank grid. East on one axis, west on the other.

Once all the squares are sold, the administrator puts the numbers 0-9 into a hat, they draw 10 numbers, and assign them to one axis, then redraws the 10 numbers and assigns them to the other axis.

And by the way, our pool is only \$10 a square, and the admin gets no freebies! He pays \$10 a square just like everybody else.

Your pool is a total scam, I would be very wary…

MtM

Like McDeath_the_Mad’s Grey Cup pool, the drawing of the numbers was random and audited. So while the administrator is ripping us off by taking 10 boxes, he wasn’t able to choose his boxes. I agree that the administrator is being particularly greedy. The problem is that he is the only one running a pool that pays significant dollars. The other office pools are \$5 or \$10 per box. Plus, he has so much interest that he is actually running another 2 pools with similar rules at \$50 and \$100 per box, both in which he also gets 10 free boxes. The guy has been running all of our office polls since before I started working here 8+ years ago, including weekly and seasonal football pools, plus other sports. No one else has enough free time to perform the work. His free time didn’t go unnoticed since he was laid off in the middle of football season. He is doing these from home now.

I bet he does have lots of interest! How far in advance did he collect the cash? He could put it all in a 30-day CD and, if he combines the whole take together, he’s letting \$14,400 of other people’s money earn money for him. He could make maybe \$60 in interest, and with all the free squares he’s grabbing, he’s holding \$1,600 in expected winnings. Will he actually walk away with \$1,600? Probably not. Still, the more I hear about this (especially now that he’s out of work) the more I think he’s taking you boys for a ride.

Just to clarify, I meant “interest” as in: “lots of people interested in playing”. Of course, your definitions of interest also work. Basically, he’s taking 10% off the top. Usually when someone wins a prize in a pool, they give the administrator back 10% for the work he/she performed. This is a common customary gesture. I guess implicit in his taking 10% of the boxes is that he won’t expect any payback from the winners. At least that’s the way I’m looking at this.

Ten free squares?

Run. Like. Hell.
Admins never get a freebie, they pay to play like everyone else.*

• “Official Rulebook of Office Gambling”

Really? I have been in frequent office pools where the administrator got a (meaning one) free entry. So I guess your “Offical” rulebook ain’t so official.

I have a, er…“friend” who is running his office’s pool in exactly the same manner as McDeath_the_Mad’s pool. It has never occurred to me…I mean, my friend…to take any freebies just for orchestrating it, nor do I think the other participants would stand for it. Besides, it really doesn’t occupy very much time, honestly.

I don’t think I’d want to be part of a pool where someone got such a huge boost. Even if the numbers that the administrator ends up with are all horrible and don’t improve his odds at all (which seems unlikely anyway), that’s still \$500 being taken out of the pot. No thanks.

So JJ did you win any money in your pool?

How much did the crooked Admin make off with?

Just curious…

MtM

I didn’t win, and neither did the crooked admin. I wasn’t keeping track, but I think one of Vinatieri’s misses cost him. I never came close.

Don’t feel too bad, I have played my office Grey Cup pool 9 years in a row (playing 1 or 2 squares per year) and have never won a cent!

Usually some lady in accounting who has no idea who is even playing wins big. We play \$10 a square (\$20 per score change), and the winners usually come out with \$500-\$600.

My wife won \$60 once, I’m usually pretty lucky but not when it comes to football…

MtM