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The problem with double round robin (or long tournament in any non-ko form) is that after some time most players play for nothing or not so much. It's not ideal that the winner of the tournament is a person who scores the most points against opponents who already lost their chances and are not so motivated anymore. Another problem is that it's just another tournament, we have a lot of those in chess. If you want a system to determine the strongest player just look at the rating list which is formed from results of all those tournaments. You don't need to play long additional one.

On the other hand world championship matches have tradition. Most chess fans remember at least some of those. Maybe Fisher's match, maybe Kasparov-Karpov battles, maybe the one when Kasparov destroyed Anand or maybe the one when he banged his head (unsuccesfully) vs Kramnik's Berlin Wall. Matches are popular, they excite the audience, people talk about them long before and long after. The winner guarantees his place in history as a member of very narrow group of players (only 15 of them, for what is over 100 years of world championship history). People yelling "anachronism" don't understand what value this tradition have for chess players and chess fans around the world. Every sport has its own. Tennis has grand slams, football has the world cup, athletics has Olimpics. Chess has world championship matches and please all the armchair revolutionizers leave them alone.

The kinds of top chess players that participate in the supertournaments we're talking about are extremely serious about every game, even if they have no chances in the tournament. Their ELO rating is equally affected by every game in the tournament, and their ELO often determines which tournaments they'll be invited to next.

Their personal 'career records' against other players in the field are also very hotly-contested. Nobody in the top 20 would give up a win or a draw against anyone else in the top 20 without a very serious fight.

It's very difficult to remain serious for 18 rounds when you play last 12 with no hopes for anything. It's not even about being serious. You will have less motivation for preparation, you may be willing to gamble more etc. once your chances are gone. Those soft forms of not caring that much matter and in my opinion they are human nature - it's difficult to put 100% of effort if you already lost.

I don't think the existence of ELO means we should make more use of it - rather, it means we don't need a world championship if the objective is to measure who is best in the win=1 draw=0.5 loss=0 scheme of things (this is, I think, part of Someone's point above). Everyone in the chess world knows Carlsen is the better player, even before we know the results of this match. Likewise, we knew Kasparov and Fischer were the better players. But the matches against Karpov and Spassky were still phenomenal, because they involved psychological and technical depth that couldn't have existed in a mere "tally up the [bigger tournament/overall rating] points" system.

Also, 1-vs-1 gets beyond the ongoing debate about whether draws should count for 0.5 or less, which is nice. More specifically, the question of whether and how to reward being consistent (many draws, few wins and fewer losses) but rarely brilliant versus uneven but generally great isn't as pressing in a match, since it'd (likely) end up not mattering.

That's true. My comment was premised on the assumption that we want to retain a World Champion title. And there is definitely a whole new element that comes into play with matches. If we still want to stick to the tradition of a world championship match, perhaps the best way to do it is to have a double round robin of the top 10 players, and the top two finishers then play a match for the title of World Champion.

Your comment about rewarding consistent but rarely brilliant versus uneven but great bring up another interesting nuance about matches versus tournaments. Fischer complained that once a player gets ahead in a match, there is no motivation to play fighting chess because every half point bring him closer to winning a match, and players are therefore incentivized to play for a draw. In a tournament, that usually isn't the case since the leader will typically have a few players nipping at his heels.

> ... every half point bring him closer to winning a match, and players are therefore incentivized to play for a draw.

This tendency could be discouraged by making wins more weighted realtively than draws: win = 2 points (or, may be 1.5 pts), draw = .5 pts, loss = 0 pts.

Regarding 1/2 points for drawing: the "masters' draw" (where on the last days to positions draw after the opening to cement their positions) is a cancer to tournaments, perhaps 0.25 points for drawing or similar will help a bit.

Is your app open source? I presume it's what's listed under [3] though you don't make that explicit (thanks for posting that).

Yup! Pull requests are welcome. https://github.com/gnarizzy/GameRatingCalculator

How is the tennis points system arbitrary? Each tournament has set points depending on ranking of the tournament, each placing in the tournament has a set number of points. The points won are carried for 1 year.

Rankings are seen to be pretty accurate when you look at who gets through each Grand Slam round.

The system works for the top players, but I think once you move below the elite rank the rankings aren't really accurate. I think the system is arbitrary for a few reasons:

1) The number of points awarded for tournament performance seems pretty arbitrary. For instance, winning a grand slam results in 2000 points, while coming in second is worth 1200 points and coming in third/fourth is worth 720 points [1]. Is coming in second really only 60% as good as coming in first? It's hard to believe there's some deep, evidence-based rationale behind picking these precise values.

2) The tournament hierarchy is also arbitrary. A win at a Grand Slam is worth 2000 points, while winning gold in the Olympics is worth 750 points [1]. Why? Shouldn't the points awarded be based purely on the strength of your competition?

There are other issues, such as rewarding someone who plays a ton of tournaments with mediocre performances, versus someone who plays less often but with better results (though this is somewhat offset with the difference in points awarded based on performance). I've had friends complain about similar systems in video games-- apparently in Halo the top rung of players is full of mediocre players who play a lot, racking up points in the process and moving up the ranks.

Since tennis doesn't have a concept of "World Champion," I think the sport would be better served to switch to the Elo system like chess. It provides an accurate comparison of relative player strengths, it does a decent job dealing with the plays a lot vs. better results problem, and it functions exactly the same regardless of the tournament you play in-- you only get more points if you perform better or play stronger opponents. Another interesting tidbit is that it gives you a statistical probability of any player beating any other, which isn't possible under the ATP system.

[1] https://en.wikipedia.org/wiki/ATP_ranking

Edit: One other problem with ATP points--since most tennis tournaments are knockout (as opposed to swiss pairings used in chess tournaments [2]) the only thing you know for sure is that the winner as the best player in the tournament, assuming tennis results are transitive (a big assumption). But if you're unlucky enough to be in the knockout branch that features the best player, you could be knocked out earlier than your would otherwise merit, which means you could get far less points than you deserve.

[2] https://en.wikipedia.org/wiki/Swiss_pairings