It depends what you mean by "substitute." If by that you mean function symbolically than yes, I think sports can work as a substitute for war. Just consider some of the lingo in football. The long pass is the bomb and we talk of an offense as having a lot of weapons and of the qb as a general. I suppose that sports might also be considered as a way of sublimating aggressions and reinforcing communal bonds. For instance, when I lived in central Florida many people who seemed to share very little else in common, thought of themselves as "Gators" and could always relate to each other along those lines. And they got hyped up for certain games as though it were a kind of symbolic war. In thinking about the uses of sport, we should also consider that famous soccer game that took place between enemies during a cease fire. The men played together, embraced, shared food etc and the next day went back to bayoneting one another.
Sean has correctly pointed out that part of what you are asking calls for empirical answers. But your last sentence - about sports being the least thing humans ace invented - raises an issue of value. And what you seem to be saying is that since sports produce no tangible outcome, in your words, it's hard to see what their value could be.
I'd like to suggest that this isn't the best way to look at the matter. After all, why are activities that produce tangible results (making shoes, or painting pictures, or building houses) valuable? The plausible answer is that they contribute in some way or another to human welfare, happiness, or flourishing. Some things we need for basic survival - food for example. But a flourishing life calls for a lot more than mere survival. And if something is a reliable source of otherwise harmless pleasure, that pretty clearly gives it value.
I suggest that this gives us at least part of the answer to your question. Playing sports gives many people a great deal of complex enjoyment. (Exercises of skill tend to do that, or so the psychologists tell us.) But watching sports also provides people with a good deal of pleasure - as do listening to music, looking at paintings, and a great many other activities.
Not everyone enjoys sports, but that doesn't take away from the point. After all, not everyone appreciates Beethoven. And the fact that sports are reliable sources of pleasure need by no means be the end of the story. But I'd suggest it goes a long way towards taking the mystery out of the value question.
It's not illegal but practitioners of the game would certainly be judged to be immoral if it was done with the intention of hurting someone. It is true though that we can do things in sports that would be judged to be immoral in other contexts and on this point I agree with Douglas Burnham that it is a matter of giving consent - accepting the rules of the game.
I am a boxing trainer so I suppose that is my answer to your question. Boxing should be much more carefully regulated at the professional level of that there can be no doubt. But amateur boxing is quite safe and has been a lifesaver to many young people who are perhaps on the edge- and are often not involved in other sports. While the physical demands of wrestling and boxing are similar, ask anyone who has done both - boxing offers some different challenges. I argue in a forthcoming article in the NY TIMES (Philosophers Stone) that the sweet science provides some unique exercises in dealing with fear - and I think that can be incredibly valuable. Also, while there are of course exceptions, the objective in boxing is not to harm the other person - but instead just to win the contest.
Alas, probably not, especially if (a) the crowd is very large and (b) your seat would have been filled by another fan, especially if (c) that fan would have been cheering for your team and about as loudly as you. But even if a-c are not true, it's not clear how much the cheering of the fans changes the players' performances and hence the outcome of the game. On the other hand, it always amazes me how significant the home field/court advantage is in every sport, including soccer (I presume that when you said "football match" you were referring to the beautiful game, not American football). What could explain the fact that a team is at least 10% more likely to win at home than away against the same opponent? (OK, I'm making up the 10% figure, but if anything I bet it's low, and Wikipedia says in English Premier League home teams are almost 40% more likely to score goals.)
Well, several things could explain home field advantage other than the crowds, such as familiarity with the environment and not having to travel. And as far as I can tell, contributing to the crowd noise is the only chance we have of influencing the outcome of a game. Hence if a-c are true, it's not clear how you could have an influence on the outcome, barring a belief in weird causal powers (e.g., you can give the opposing players cramps by looking at them funny) or exceptional circumstances (e.g., you are close enough to yell insults at David Beckham which make him perform worse--watch out, they may make him perform better!).
On the other hand, it's kind of like voting. You should vote even if it is unlikely that your vote will make a causal difference in the outcome, because if people stopped voting based on that belief, it would make a difference. If all the fans started thinking their cheers made no difference, the overall silence would make a difference.
Anyway, I still like to believe I can influence the outcome of a game ... even by watching it on TV! Hence, there's no way I'm going to Tivo an important Duke basketball game--they need my magical energy to flow in real time! (Yes, philosophers can believe irrational things, though I'm not sure it's accurate to say I believe something I know is false, but that's a question for another day...)
If Tiger Woods gets a hole-in-one on a rather short hole, he's got lucky. But he is a great golfer. He hit the ball with immensely practiced skill: and it is because he hit it with that practiced skill that he got the ball onto the green and then it happened to go down the hole. Indeed he can, let's suppose, get the ball from the tee onto this green nineteen times out of twenty. That's not luck at all but the result of a finely honed talent.
Now, let's suppose, Tiger Woods would always try to hit the green from the tee on this hole, and he is very good at doing that. But even for him, intending to get the ball as close as possible to the pin isn't enough. He is at the mercy of the caprices of the wind, the manufacturing flaws of the ball, etc. But just once in a while he may fluke it and sink the ball on the first stroke. It is, to be sure, a bit of luck when the attempt succeeds, rather than the ball landing fairly near the hole but needing a putt or two. If he tried even fifty times more he probably wouldn't succeed again. But still, as they say, Tiger Woods "made his own luck" here -- it's no matter of luck that he gets the ball into just the right vicinity, and he's so good that he will get lucky from time to time and sink the hole-in-one -- and a lot more often than once in a billion years let's suppose (his hard work has at least considerably reduced the odds).
Now you pass me a club (despite my never having held one in my life). I take a wild swing at the ball. Unbelievably I make contact and the ball sails off the right direction ... and plops down the hole. Now that is the sheerest luck at staggering odds. I am exercising no skill here whatsoever. Far from reaching the green with my stroke, nineteen out of twenty times my swing wouldn't even make contact with the ball. Even give me a billions years' worth of attempts (at my current level of coordination and skill) and it wouldn't happen again.
So the initial, rough-and-ready, distinction we need is that between mere luck (succeeding irrespective of skill, etc., as with my golfing triumph) and what we might call skillful good luck, worked-for luck, we might even say deserved luck (where skill has markedly reduced the odds). True, it was a matter of luck that Tiger Woods's shot came off on this occasion while most of his attempts don't. But it evidently wasn't mere luck.
The idea behind many sporting competitions is to equalize the physical attributes of the competitors as much as possible, so that skill can be the deciding factor. This is why there are weight classes in wrestling and boxing, and handicapping in horse racing and in golf. Since women are, on average, physically different from men in lots of ways that are relevant to lots of sports -- e.g, tennis, basketball, track & field events -- it has seemed reasonable to separate men and women into separate competition classes for those sports. Automobile racing doesn't implicate physical skills that vary systematically between men and women, so there are no gender divisions there.
There are also some fairness considerations: using classes within sports gives more people the opportunity to play. If there were no classes, then men who currently box in lightweight divisions would nearly always lose, and sports like basketball and track & field, even at the high school level, would be virtually devoid of women.
But of course the main priniciple -- achieving physical parity among the competitors -- is very imperfectly implemented. Some sports have only male and female classes, but make no allowances for large physical differences within those classes. So -- women are, on average, shorter than men, but there are no "height classes" within basketball. This leads to a new problem about fairness. A man who is "only" 5'8" would be at a serious competitive disadvantage on a college men's basketball team (if he even made the team), but could possibly excel on a women's basketball team.Theoretically speaking, the ideal solution would be to come up with a larger number of classes, based on detailed physical characteristics -- Body Mass Indices, location of muscles, flexibility, pelvic characteristics (this affects gait, and so has implications for how fast women can run relative to men), etc. -- and then assign individuals to these categories regardless of their sex. There might still be significant gender segregation on this plan, but it would be a consequence of a more principled classification. Practically speaking, though, such a system is unlikely to happen, both because of the difficulty of constructing such a system, and because of historical and cultural inertia.
You're right to observe that the evaluative word "best" as applied to a chess move appears to be used in many different ways. In some circumstances, the best move will be the one that ineluctably leads to checkmate of one's opponent. (Though if that move demands subsequent overwhelming calculations, there is another sense in which it's not the best. It's the best move from God's point of view -- or Deep Blue's -- but not from ours.) Often, we can't find tactical maneuvers that will promote a win and so must make a strategic move, and now the best move will be one that clearly satisfies a range of strategic goals (e.g., developing one's pieces, controlling the center, etc.). One cannot even say that "best" always involves a move that promotes a win: for instance, if one is on the ropes, the best move will be the one that increases one's prospects for a draw.
A philosophical issue is broached if one asks whether there is something in common to all these uses of the word "best". Some philosophers have held that there is, indeed that there must be; it is easy to read Socrates as insisting on this. Others have held that there isn't, that there is simply an overlapping family of uses of the word; Wittgenstein famously suggested this.