Why do top professional sport players get usually paid so much? I'd like to find an answer to this question as I can't see how something like this can be happening. I can see three reasons that they would earn that much but any of them if thought better is wrong.

1) They generate all the money they win. I don't deny that they generate lots of money, but news like this one: http://www.euroweeklynews.com/news/axarquia-malaga-east/item/126022-la-liga-clubs-threaten-strike, or this one http://www.forbes.com/sites/mikeozanian/2015/01/22/nba-adding-1-1-billion-of-debt-while-getting-its-best-credit-rating-ever/ make clear that there are going to be a lot of times where their salary is clearly overvalued, and according to only economic terms they should earn maybe something that's a third of their salary.

2) They generate the money on its own. I consider that also mostly false, if they generate that much is because mass media is always talking about them and showing them, if they wished they could take any other thing and with time put it on top being that thing much less expensive for them on the beginning.

3) What the do not earn economically , they earn in entertaining people and making them less aware of their problems, ok, so do a lot of other things, like computer games or books or whatever, and none of them get that much of hype usually, moreover, they are likely to be victims on piracy with a lot more frequency than, let's say, a televised sport event.

Maybe this is applied for other professionals like top actors or singers, but I don't know of such huge debts on their case, and I get the impression that there much more top sport players with huge winnings rather than actors or singers.

I'm not a economist, but I find this question intriguing, hope you can help me to understand why.

Thanks for your time.
tl;dr There is a lot of demand for what they produce.

A proper answer should have some evidence, perhaps I will add that when I have more time.

Even within a category, say, football (soccer) players, you see a lot of discrimination: Top players at top clubs in top leagues get most of the cake. This is anecdotal evidence for the demand side story:


Only the best leagues earn much money through television rights, because only there is most of the demand (how much media coverage do you have for your national third league anyways?)
Only the best teams in these leagues get most of this money, mostly because leagues partly pay teams based on their performance ranking wise 
Only the best players get the highest share, which is a combination of the previous two facts, and that these guys are quite unique and have hence an even higher demand:

They make more marketing money (people really want to see them)


Due to their uniqueness, they can bargain better deals with teams and sponsors



Note that the last point is really the only supply-side story. If you ignore super stars, the supply of good players is huge. Most of the twist really comes from some of them being marginally better / lucky, making it into the better leagues, which happen to be the one that mass media demand, and get the high compensation.