Is there an unbeatable Cross-Country score?

moran alert wrote:

Jsksoekcnjdoamx wrote:

[quote]malmo wrote:

You cannot deny that there is a scenario where your team can score 34 points, and is still unbeatable. Which is my point.

You also cannot deny that there is a scenario where your team can score 100 points and is still unbeatable. That scenario would be if all the other teams scored at least 101 points. FFS, let the 34 points notion rest

You aren’t reading. The reason 34 points is significant is because it is the stand alone scenario where the 2nd place team can place its runners as high as possible and still lose. There is no other stand alone scenario with a higher score than 34 (35 if using ncaa tiebreaker) in which the 2nd place team can do that.

If I scored 100 points in any scenario any team could beat me because 1-2-3-4 is 10 points, plus your 5th in 90th would be 100. A team could go 5-6-7-8-9 and would easily beat you.

If you go 1-4 and 25, for 35 points, and they took the next best spots, they’d win on a tiebreaker (assuming their 6th finished 10th)

If you go 1-2-3-5-24 and they take the next best spots of 4-6-7-8-9, they would win 34-35.

How do you people not see this? No one is denying that 27 points wins no matter what, but what we are saying is there are certain scenarios where you can score more points than 27 and regardless of how a teams runners finish, you will always win no matter what.

29 would also be significant in that case. If a team places 1, 2, 3, and as long as their 4th and 5th runners score 23 between the two of them, that team will always win. Even if the other team places 4, 5, 6, 7, 8 they will score 30 and lose by one point.

Possible scenarios:

1-2-3-9-14

1-2-3-10-13

1-2-3-11-12

snow blow wrote:

You could "reverse" my example and have Team 31 win and Team 1 lose by reversing the distribution of 63-93 for the 3rd runners:

Team 31: 61, 62, 63, 94, 95 = 375

Team 30: 59, 60, 64, 96, 97 = 376

...

Team 1: 1, 2, 93, 154, 155 = 405

So Team 31 could win even though they have worst 1st and 2nd runners. Of course, they also have the best 3rd, 4th, and 5th runners.

Also I am quite certain now that 375 is the highest possible amount a team could score at NCAA XC and still win. Because there is an odd number of scorers (5), there is no way for all teams earn the same amount of points. As another poster noted, there are 12,090 points totaled among the top 155 spots. This would yield 390 points if evenly divided among the 31 teams, but it is not possible for every team to score this number. The closest possible scores between the first place and last place team has to be 375 and 405.

If there were an even number of scorers per team, then all team could possibly have the same score. With 4 scorers among 31 teams, all teams could tie with 250 points, and team standings would be determined by pushers. With 6 scorers, all teams could tie with 561 points.

Meet of 5 teams. 4 of the teams finish before the winning team. No matter how you split up teams 2-5 they can’t beat the winning team.

Team Kenya=35

1,2,3,4,25

Team Ethiopia=35

5,6,7,8,9

Team NAU=60

10,11,12,13,14

Team BYU=85

15,16,17,18,19

Team Hobby Jogger=110

20,21,22,23,24

Let's say "unbeatable" means "no team can beat you, no matter what they do."

If you score 27 with any combination of individual scores, it doesn't matter what any other team did; you win. The same can't be said of 28 or any higher score.

If you score 34 with a particular combination of individual scores (1,2,3,4,24), it doesn't matter what any other team did; you win. The same can't be said of 35 or any higher score.

This means 27 is the highest score that is unbeatable in all configurations. And 34 is the highest score that has at least one unbeatable configuration (regardless of what any other team did).

Of course, as others have pointed out, if ties stand unbroken then a score of 35, if achieved in a particular way, could be impossible to beat--but not impossible to tie.