The answer is, it depends. The balance between luck and skill is a huge part of what differentiates various games and part of what draws or pushes away fans. The obvious extreme examples are chess and poker, and I quite love both games and both involve an enormous amount of strategy, but they’re still fundamentally different. So we really need to consider what makes them different.
Chess is an example of a complete information game. Both players have exactly the same information about the state of the game and there’s no randomness involved. Theoretically, either player could compute all the possible future states from the current state and there’s an ideal way to play it. Checkers, Go, Othello, and a few others are also good examples. IMO, this sort of game should heavily favor the better player because it’s just all about who can do the most with the same information. Thus, in Chess, or any complete information game, the better player should win considerably more often than the worse player, otherwise the game is “solved”, like Tic-Tac-Toe.
There’s another class of game that’s partial information. There’s no luck involved, but each player has only some of the information available. Some good examples of this would be Battleship, Guess Who, Mafia/Werewolf, etc. In general, I think the better should still have a considerable advantage, but less of one, because a better player ought to be able to have a good way of estimating or putting limits on what he doesn’t know and minimizing that factor, but there’s a chance he is wrong. If the better player doesn’t win a lot more often, it just means that the game is either too simple, and thus it’s really easy for low skill players to figure out what they don’t know, or it’s too complex, and skilled players can’t put any effective boundaries on their lack of knowledge. But ultimately, a large part of what makes the skill in these types of games IS the ability to estimate that information you don’t know, not simply calculating future states from what you do.
There’s also luck based games. A lot of board games fall in here, Monopoly is probably the best example, and most other board games fall here. Every player knows all the same information, but you can’t “solve” the game because you still have to have luck with dice rolls and where you do or don’t land and on what turns. I’d say that the better player ought to win reasonably often, but because of the luck, and that that luck is based on a binomial distribution, you ought to be able to model how likely they are to win with overlapping those distributions with the means separated by the difference in skill. You do have some of these types of games that, while technically having information, don’t actually require any skill on the part of the player, like Chutes and Ladders requires no decision on the part of the player, just rolling the die and moving the piece, so there’s no measurable difference in skill.
Finally, you have the luck-based, partial information games, and Poker is the obvious example here. If the better player wins too much, it downplays the luck part of the game, and if he doesn’t win enough, it downplays the information based part. Obviously, because of both the partial information and the luck based part, the better player ought to win less in this type than any other type of game.
So, we have four sub-types of games, and I think we can use that as a baseline for judging how often the better player ought to win and we can generalize this to sports too. Take soccer, for instance, the games are generally very low scoring, so luck will play a larger role and it’s no surprise that upsets happen often. Contrast it with Basketball or Tennis, and there’s WAY more scoring, so it’s more likely to converge on the difference in skill in the game, so the better ought to win more often. But when you compare all of that to, say, racing, there’s no randomness there and we consistently see the best runners, drivers, swimmers, or cyclists performing at the top there.