Cardinal numbers are numbers when used to count as exemplified by the statement "3 things" when given the set {y, &, *} or the set {u, @, £}

Ordinal numbers are numbers used when we wish to order/rank objects; for instance they're commonly used in games to rank players with 1st, 2nd, and so on assigned to the champion, runners-up, and so on respectively.

The 1st cardinal number is 1, the 2nd is 2, and so on with the nth cardinal number being n.

Consider now the game of javelin throw which I use here to stand for, not all, but most games. Points are awarded based on the distance the javelin travels. Imagine 4 players A, B, C and D with throw distances, 10 feet, 20 feet, 30 feet and 40 feet respectively. D's distance earns him 1st place, C's distance earns him 2nd place, B's distance gets B to 3rd place and A is in 4th place. This describes the normal point scoring system and ranking system in most competitions.

Notice here that the largest cardinal number, 40 feet, is assigned to the lowest ordinal number, 1st place, and the smallest cardinal number, 10 feet, goes to the largest ordinal number, 4th place.

I'm not saying there's no logic to this, since the maximum points does belong to the highest ranking competitor. However, this kind of point scoring and ranking system violates the ordering 1 is 1st, 2 is 2nd, and so on, where the smallest ordinal number is matched with the smallest cardinal number.

In addition there's a loss of information in terms of how tough the competition was. This can be illustrated by many jokes in which a person is ridiculed for having come 2nd in a game of only two competitors, exposing, as it were, the flaw with such systems.

If, on the other hand, the system had stayed true to that of 1 being 1st, 2 being 2nd, and so on, a very valuable piece of information can be retained viz. an idea of how many competitors took part in the game. For instance in the javelin game above, had the champion been awarded 4th position, we would know from the champion's position, the ordinal number assigned to him, that there were a total of 4 players. Then if n players were taking part and the champion was awarded, like I'm suggesting here, the nth rank, we would immediately know there were n players and would come to know how tough the competition and so how great the win was.

Why is it this way? Should we change the system like I'm suggesting? Why and why not?

If I may offer a theory for why the ranking system in sports is inverted with respect to the points scored then we must travel back in time to the first Olympics

At the first recorded ancient Olympic Games in 760 BC, there was only one event, a footrace — History of Sports

In a footrace, the objective is to run faster than your opponent i.e. to try and attain a speed greater than the competition; this inevitably results in the player ranking being based on how much time it took the players to complete the footrace. Imagine 3 players in the footrace: A, B and C. A is the fastest and so completes the race in 15 seconds, B is next fast and completes the race in 20 seconds and B is the slowest and completes the race in 25 seconds. Now, calling A 1st, B 2nd and C 3rd doesn't violate the actual mathematical ordering of the cardinals in which 1 is 1st, 2 is 2nd and so on.

If the first sports competition was a footrace and since in races it makes sense to call the winner 1st (he completes the race first), this practice spilled over into other sports as well.