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