Let's focus on FIDE classical chess finals historically.
Caruana is always behind in time control, thinks more, waste more energy.
Statistically speaking, did the players who played faster won more titles? Is Caruana showing signs of weakness?
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Not sure what point you are trying to make. There can be all kinds of reason for being behind in time such as personal time management, the opponent playing a novelty, etc. I would not dare to draw a direct correlation between time used and and number of titles. Also, how would you measure "time" here? Time until move 30, time per move, time for whole game....?– user1583209Commented Nov 12, 2018 at 20:17
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@user1583209 I would measure the total time spent in the whole tournament, per player, so lets say Carlsen finished the game and spent 3h in game 1 + time game 2..... etc, the whole tournament, so I just want to check on the time left when the game is done– LynobCommented Nov 12, 2018 at 20:35
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@user1583209 the point I'm trying to make is simple, Chess is mathematics and you can observe that good math students finish well before average students, I just want to see if the same applies to chess, it might be time management but it might also be that is not as good, I just want to know what statistics say.– LynobCommented Nov 12, 2018 at 20:39
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How do you exclude that it is a spurious correlation? I also don't see how your maths example fits in here. Chess players are not asked to find a solution in the shortest amount of time, but to find the best solution using all the time that is available to them. Also, the players in your statistics faced different opponents, (in your analogy, different maths problems). How would you compare them...?– user1583209Commented Nov 12, 2018 at 20:54
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1@user1583209 I flagged this question to be deleted, since I asked here opendata.stackexchange.com/questions/13503/…, after all, I just want data dump, and that site is the right site for that not this one.. . As for what would stats tell? I don't know and don't care, it's a side project for fun in my free time, unless someone already crunched the numbers– LynobCommented Nov 12, 2018 at 21:59
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I don't know about statistics, but I do know that they are not "bound" to lose. It depends on the position. Is it easy to play, or is it a very sharp, tactical position? Also, is there a time-increment? Often, in classical FIDE games, there is. Based on experience, I can tell you that it can be very stressful being low on time in a long game, even if there is an increment. However, if psychological (personal) influences are ignored, it very much depends on the position and on the time-increment.
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2I do understand that and I upvoted it because you are right, but I'm only here looking for either stats or championship games PGN with time control, on which I can do stats myself, since it's easy to do if I have the PGN and time spent per game– LynobCommented Nov 12, 2018 at 21:35