I appreciate your advocacy for the devil, I do (it helps me wrap my Brian around these concepts more completely), but when you make a "never" statement, it only requires one counterexample to disprove. Consider the following 3 counterexamples to your argument...
Example 1) You're in a prison block with 100 inmates and 20 gaurds who are all average-sized and skill humans except for 1 inmate who is Mike Tyson (in his prime, the heavy weight boxing champion of the world). The prison warden says "We're going to have a boxing match. The prisoners may select a fighter to represent them from the inmates, and I will select a fighter from the guards. If the prisoner fighter wins, everyone goes free. However, if the guard wins, we add 2 years to everyone's sentences."
Here is just one case where it's very important to know that Mike Tyson is statistically the "strongest" (fighter in this case) over any other individual human candidate (gaurd or prisoner) in the set of candidates.
Example 2: A small zoo has only 3 types of animals: an Elephant, a monkey, and a wolf. Each animal is pregnant and will have a baby this month. The zoo attendants have a $1000 pool going and you have to bet on which baby will weigh the most when born. In this case, you clearly wager on the elephant as they are statistically "the strongest" over all other individual candidates with respect to the body mass of their offspring.
Example 3: Back to your tennis example (I play and follow tennis, not that that matters much). Hyperbollically, if you have 5 players and each plays each other 100 times, and player #3 beats all other players 90/100 times, whereas all other matches result in a 50/50 split. In this case, yes, player #3 is the strongest player and is favored to win over any of the other 4 players in the set in a head-to-head match.
Yes, very often we rate and characterize the "strongest" as being the candidate that is statistically more likely to beat any other individual candidates in a set.
None of those are counterexamples. You're arguing that it's possible for the strongest player to be favored to win against everyone else. I said that that isn't a requirement of being the strongest. Obviously it is true that, where one player is favored to win against every other player, that player is the strongest. That's the Condorcet criterion. But it doesn't come close to being true that, if one player is the strongest, that player is favored to win against every other player.
You said it's "never assumed" and I think in many realms it would be assumed. And if the top ranked player consistently lost to certain other players, there would be active debates about whether they are the strongest or not.
> Example 2: ... The zoo attendants have a $1000 pool going and you have to bet on which baby will weigh the most when born.
There are some games that have a single property that is clearly sortable, like weight. In this case clearly the there is one winner. (Actually, here you have a distribution of weight, like the average and the dispersion. So it may be more complicated.)
There are more complicated games. When I was young we had cards with the properties of cars, like weight, length, price, and other stuff. The game was to pick the card at the top and pick a property, and compare with the same property of the top card of the other player. Some cards were stronger than other. I don't remember the strongest card, but I guess there was one. Anyway, that card didn't win against all cards, it was just good against most card, but you could be unlucky if it was at the top of your deck and the other player selected one of the bad properties of the best card.
IIRC in Starcraft II, at some point Serral was #1 and Reynor #2. In a match between them Reynor had a slightly better chance to win, but against everyone else Serral has a better chance to win than Reynor.
