There are 32 NFL Teams.
Each NFL team plays 16 games out of 17 weeks in the NFL schedule. The game that they don’t play is called their “bye week“, it is a date in which they don’t have to play.
This season the bye weeks only occur in Weeks 3 thru 9. This season they are distributed
Week 1 None
Week 2 None
Week 3-- 4 Teams Bye
Week 4 – 4 teams Bye
Week 5 – 4 Teams Bye
Week 6 – 6 Teams Bye
Week 7 — 6 Teams Bye
Week 8 ---- 4 Teams Bye
Week 9 — 4 Teams Bye
Week 10 None
Week 11 None
Week 12 None
Week 13 None
Week 14 None
Week 15 None
Week 16 None
Week 17 None
My Team has to play 3 Teams coming off their Bye week this season.
Can anyone with a larger brain than mine compute the chances of that happening assuming a random assignment of scheduling dates?
Ballpark estimate (nyuck nyuck nyuck): There are seven weeks in which a team has a chance of playing a team coming off a bye week. On average, there are approximately 4.57 teams coming of a bye week on one of those seven possible weeks. Out of a total of 31 possible opponents, 4.57 teams represent 14.75% of the possible opponents. The odds of an event with a 14.57% chance happening 3 out of 7 possible times is, if my calculations are correct, approximately .75% or about 133-1.
The only problem I see with that as a ballpark is that the team in question will also have a bye in one of those seven weeks. Should their bye occur in the first week, your ballpark is fine. If it does not, then that is one less week they can encounter an opponent coming off a bye.
That’s not the only problem, but it’s a decent first stab at it.
There are only 13 opponents on a schedule, not 31.
It is possible to play a division rival twice inside that 7 week span.
The caps must be considered. (The ball park method above allows all 32 teams to have the same bye.)
The actual calculation to determine the exact numbers are well beyond my math skills, but I’d love to see a breakdown like:
Week 3: 0 chance of playing a team coming off a bye
Week 4: 4/32 chance = 12.5%
Week 6: 6/32 chance = 18.75%
Week 7: 6/32 chance = 18.75%
Week 8: 4/32 chance = 12.5%
Week 9: 4/32 chance = 12.5%
Week 10: 4/32 chance = 12.5%
One of these will be YOUR bye week, and that affects the calculation, depending on the week 6/7 factor.
I’m not clever enough to do the actual stat calculation, but it looks to me like a reasonable estimate is 12.5% squared…call it 1.5%. If true, then–given 32 teams–this will happen about 1 season out of 3.
Your team’s own bye status isn’t that big of a factor - the question is whether the opposing team had a bye week so your team’s bye status is irrelevant. But I’ll admit it might change the 4.57 figure (average number of teams coming off a bye week) to 4.43 (average number of possible opposing teams coming off a bye week). This would change the percentage of possible opposing teams coming of a bye week to 14.3%.
The total number of opponents on a schedule isn’t relevant. The relevant statistic is what percentage of the total set belongs to the designated subset.
The possibility of playing the same team twice in the seven week period seemed minor enough to be disregarded as it was not directly related to bye status. If you feel otherwise factor it in and show us the difference.
What I was trying to say is that weeks 4-10 are the weeks it is possible to play against a team coming from a bye. This is, as you note, 7 weeks. but there is only a 4/32 = 1/8 chance that your team plays every one of those seven weeks – that is, your team had a bye in week three. Otherwise one of those seven weeks, your team is sitting it out on their own bye. So 7/8 of the time it’s a 3 out of 6 event rather than the 3 out of 7 I have quoted above.