Let’s suppose we have a round-robin tournament featuring 8 players. Two of them go 6-1, one losing to the other, and the other losing to someone who went 1-6. If the matches featured no other statistics that might be useful in discriminating them, and there was no possibility that they might meet in a final match to determine a clear winner, which one would you say was the better player? The one who beat the other guy who went 6-1 but lost to a guy who did terribly otherwise, or the one who beat everyone else and only lost to the other best guy in the group? Does it depend on the game/sport?
I personally am of the opinion that there should be no discriminating between the two, and I would view their performances as equally strong when taken as a whole over the entire tournament. Who they gave up their one loss to is not relevant at all. (If there is a need for the competition to have a clear winner, it should have made a provision for tiebreakers in some form.) But I suspect that most people will have an opinion one way or another and I’m wondering how people generally feel about this.
In the OP’s scenario, I would probably award the head to head winner as champion. But I could live with co-champs if that was the decision.
The sport that relies on this head to head debate more than any other is college football, but not everyone plays the same schedule. And so, head to head only matters when the people making the rankings want it to.
That’s true but from another perspective, if one team beats another then common sense says the winner is “better”. It’s a logical way to break what’s otherwise a tie without having to be totally arbitrary or subjective.
This is not an example with equal strength of schedule, unless all players have exactly the same strength.
Imagine we have eight chess players: one grandmaster and seven novices. Look at their strength of schedules. Most participants play against a grandmaster, while one does not.
Let’s compare two novices (call them Alice and Betty) who went 6-1. Alice beat Betty, but lost to the grandmaster. Betty lost to Alice, but won against the grandmaster.
It seems perverse to say that Alice is better than Betty in this case. They have the same strength of schedule (one grandmaster and six novices), but one of them beat a far superior opponent and the other did not.
Yes, I’m aware of the technicality that in a round-robin each of the players has a different strength of schedule unless they are all the same strength, but that feels like a meaningless distinction. The entire point of playing a round-robin tournament or league is that no one can say that someone had a meaningfully easier schedule than someone else. But, you could modify the question to instead be something like athletes trying to complete 8 different feats. If two of them both complete 7 of 8, but one of them misses one that no one else misses, while the other misses one that only the other top competitor managed, which set of achievements should be considered better? It comes down to how you want to treat the ability to overcome a difficult challenge versus the ability to always overcome a lesser challenge. You can extol his ability to complete the hard feat, but discount his strength because he failed somewhere everyone else succeeded. Which is more important?
The win-loss record by itself is not really a good metric for determining the strength of a team. Something like the Elo rating system will give better results.
I think that the main problem is trying to find logic in the NCAA and their bowl selection process. In the last 20-25 years, how often has there not been a question about the #1 team?
Certainly if you’re talking about who is actually the best player, you need a rather large sample size, not just a single round-robin tournament. Well, maybe if it featured 100 players it might be somewhat more accurate, but unless games are arranged (and players find each other) automatically and the games don’t take very long, that’s a rather long tournament.
However, I think most people are generally aware that the winner of a single competition is not necessarily the best overall player there, just the one who performed the best at that competition. The question is how do we treat the various successes and failures at certain tasks beyond their weighting for primary scoring purposes (if any) when trying to break a tie in that primary score in determining who performed the best at that competition when the tasks are varied in difficulty as determined by the success rate at the competition.
By the way, a pure Elo rating system does not care at all who you lose to, only who you face and how many of them you beat.