Predicting Monday/Thursday games
We know the last game of the season always takes place on a Sunday. We know each team must play at least one Thursday night game, and we will assume the Rams play exactly one Thursday night game.
No Monday night games are guaranteed. Last year eight teams appeared in two Monday night games, 18 appeared in one, and six never appeared.
Chance of picking the date of the Rams’ one Thursday night game: 1/15. (It would be 1/16, but we’ve already guessed the date of the Rams’ bye week.)
Determining the number of possible combinations for Monday night games is tricky, and depends on our assumption of the number of Monday games the Rams will play.
If the Rams were to play two Monday night games, and you knew in advance that they were going to play two Monday night games, there would be (15*14)/2 = 120 possible ways to place two Monday Night Football appearances on the schedule. (This ignores the added probability of the first Monday night of the season, which features two games. It also ignores the fact that the Rams would not appear on Monday night in consecutive weeks.) The chance, then, of picking the two weeks they would have a Monday night game would be 1/120.
If the Rams were to play one Monday night game, and you knew they were going to play one Monday night game, there would be 15 possible games that could be on Monday, meaning your chance of a correct guess is 1/15.
And if the Rams were to play no Monday night games, and you knew they were going to play no Monday night games, you would have nothing to guess.
So picking the correct combination of Rams’ Monday night games (if any) depends on how many Monday night games you think the Rams will have.
We will guess that the chance of the Rams appearing in two Monday night games is 20 percent, the chance of them appearing once is 50 percent, and the chance of them appearing in no Monday night games at all is 30 percent. These guesses are based on the Rams’ poor record in recent years and relative lack of national popularity.
If you assumed those chances were correct, then you’d be best served to guess that the Rams would not play a single Monday night game. In that case, you’d be right (if your assumption were right) 30 percent of the time. If you guessed they would play exactly one Monday night game, and that it was in Week 7, your chance of being correct would be much lower.
For our purposes, though, we will assume you guess randomly between zero, one, and two Monday night games at a rate of 30 percent, 50 percent, and 20 percent. If these were the correct percentages (again, that’s an assumption), the chance you’d predict the correct Monday night schedule would be:
(30%)*(1/1)+(50%)*(1/15)+(20%)*(1/120) = 67/200
The probabilities above, based on many assumptions, account for everything the Rams require to win the $100,000 (location, date, and opponent). If we multiply all those chances together, we get … 1 out of 16,294,782,089,552,200.
This is about 560 times easier than picking a perfect NCAA bracket blindly, but up to 135,000 times harder than picking the perfect bracket with some skill.
Yes, we could make additional assumptions to cut down the odds even more. If the Rams do play on Monday night, it’s more likely to be against a top team like the Cowboys or Seahawks than a lowly finisher like the Raiders. Some other factors, such as making sure the Rams do not play more than three games in a row at home, would limit the number of options as well.
But even with some more guesswork, it’s close to impossible that anyone will predict the Rams’ 2014 schedule. So don’t insult us with that $100,000 offer, St. Louis. To make it worth anyone’s while to complete the exercise, you should pony up a lot more than $1 billion—135,000 times more. What do you say, Rams? Make things interesting and offer $135 trillion. Do that, and maybe I’ll consider giving this contest a shot.