In case you haven’t heard, the St. Louis Rams are running a contest to predict the team’s 2014 schedule. lThe prize is $100,000, which sounds nice until you realize that to win, you must accurately predict not only the opponent each week, but the location and the exact day of the game. Nobody is going to win this contest. Nobody is going to come close to winning the contest. It’s a personal information/PR grab and nothing more.  Normally, this wouldn’t bother me, but it’s not like the Rams are giving away a billion dollars.  For a hundred grand — which is less than two percent of the amount of dead cap space being allocated to Cortland Finnegan this season — the team shouldn’t have needed to make it impossible for anybody to win. Considering the rules, St. Louis might as well have announced that the grand prize is eleventy billion dollars.

So what are the odds of winning this contest? Let’s start with an easier problem than the one at hand: predicting the Rams opponent in each week of the season.

With 17 weeks, there are 17 possible opponents once you include home/road designations and the bye week. Therefore, you have a 1-in-17 chance of correctly guessing the Rams opponent in week one. By extension, you have a 1-in-16 chance of correctly guessing who St. Louis plays in week two, assuming you were correct with your guess in week one (this is what we mean by conditional probabilities). Do this for every week of the season, and by week 17, you have a 100% chance of correctly guessing who is on the team’s schedule.

It may not be intuitive exactly how daunting a task this is. But this is much, much harder than Warren Buffet’s bracket contest.  For example, you only have a a 1-in-272 chance of correctly guessing who the Rams opponents will be in the first two weeks of the season. That drops to 1-in-4,080 through three weeks, 1-in-8.9 million through six weeks, and 1-in-8.8 billion through nine weeks. That already makes it harder than the bracket contest, and you still have the back eight to play. The odds of correctly guessing the opponent each week is 1-in-356 trillion. And remember, this is quite a bit easier than the actual contest!

But let’s make some adjustments based on the information we know (which will lower the odds) and the added conditions one must satisfy (which will drastically increase the odds).

Adjustment #1

The first adjustment to our 1-in-356 trillion likelihood lowers the odds. If we assume that each team plays a division opponent in week 17, that makes the contest ever so slightly easier. If we work in reverse order, you now have a 1-in-6 chance of guessing the week 17 opponent (remember, you need to specify game location), a 1-in-16 chance of guessing the week 16 opponent assuming your week 17 selection was correct, and so on. This improves your odds all the way to 1-in-126 trillion. Hooray?

Adjustment #2

One more adjustment to make the probability ever so slightly more favorable. The bye weeks are a moving target for the NFL, but last year, they were limited to weeks 4 through 12. Since we’re dealing with infinitesimal odds, let’s just make life easy on ourselves and assume 1) the bye weeks will again occur only during those weeks and 2) the Rams have an equally likely chance of having a bye on each of those nine weeks.

Let’s assume you have a 1-in-9 chance of correctly guessing the bye week. Putting that aside, you then have a 1-in-6 chance of predicting the week 17 game, a 1-in-15 chance of predicting week 16, a 1-in-14 of predicting week 15, and so on. Multiply all the conditional probabilities, and this increases your odds to 1 in 70.6 trillion. ^[1]Another way you get to this result: a 1/6 chance in week 17, a 1/15 chance in week 16, a 1/14 chance in week 15, 1/13 in week 14, a 1/12 in week 13, a 1/11 in week 1, a 1/10 in week 2, and a 1/9 in … Continue reading

Adjustment #3

Apparently, the actuaries at the insurance company St. Louis surely hired determined that a 1-in-70 trillion chance was leaving too just much skin in the game. Because the rules provide that you also need to determine the day of the week for each game!

We can assume Sundays for most games, but that still leaves a few odd weeks you need to guess correctly. Consider:

• Last season there were 17 games on Thursday nights spread over 15 weeks (remember, there are three on Thanksgiving). If the same pattern is followed this year (and I don’t even know if that’s the case), that means there’s a 1-in-16 chance the Rams will play two Thursday night games. And since the Seahawks will play in the opener, there’s also a 1-in-8 chance St. Louis could play in the opener. But let’s make the math easy on ourselves and make two assumptions:
  1. St. Louis will only play one Thursday game in 2014.
  2. That game is equally likely to occur in any of weeks 1 through 15.

  Therefore, you have a 1-in-15 chance of guessing which week St. Louis will play on Thursday night. This takes our odds to 1-in-1.6 quadrillion.

• Next, we need to predict the number of Monday Night games for St. Louis. Odds are, it will be zero or one games: after all, the Rams have played in just three Monday night games over the last five years.  One can’t get very precise with estimating the likelihood of Monday night games the Rams will play, but I think the best guess would be to assume one (i.e., that would be the mode if the schedule was played out 10,000 times). The Monday night game can occur in any of the first 16 weeks except the week the Rams play on Thursday night; as a result, this 1/15 probability jumps our odds to 1-in-16 quadrillion. But if we assume there is only a 50% chance the Rams play exactly one Monday Night game this year, ^[2]Only three of the last ten years have the Rams played exactly one Monday Night game. the odds double to 1-in-32 quadrillion.

• But wait, there’s more! Four teams will play on Saturday in week 16 this year, December 20th. So there is a 28/32 chance the Rams will not play a Saturday game: that ups our odds to 1-in-36 quadrillion.

With a grand prize of just $100,000, this has to be in the running for worst contest ever.  The expected value upon entering the contest is $0.0000000000028. It is literally not worth a second of your time to enter this contest.

For the Rams, though, the contest offers some nice benefits. St. Louis will receive some positive PR, particularly among those who are not mathematically-inclined. And to enter, one has to provide the Rams with their home address, email address and phone number, valuable information for the St. Louis marketing department. So this is certainly a good deal for the Rams.

But for the contestant? There’s simply no point in entering. As a practical matter, there isn’t even a grand prize (note: there is only one prize, but that doesn’t stop the Rams from publicizing this as the “grand prize”). That’s because the contest rules provide that anyone involved in the determination of or release of the 2014 NFL Schedule, or with any advance direct or incidental knowledge of the actual 2014 NFL schedule, is not eligible to participate in the contest. As a result, any entry submitted by such an individual will be void and ineligible to claim any prize award.

I see three possible ways to win this contest:

1) Receive advance direct or incidental knowledge of the actual schedule;

2) Use “script, macro or automated devices (or any other devices intended to automate or subvert any aspect of entry)” to give yourself more than one entry. This is expressly prohibited, and any entry through such means will be declared void.

3) Overcome 1-in-36 quadrillion odds by correctly foreseeing the schedule.

Think about this for a second. In my unfounded opinion (ATTN: Rams lawyers), if you enter this contest and predict the Rams exact schedule, you are much, much, much more likely to wind up in a lawsuit than you are the winner of $100,000.