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Fide has a rule saying that if one player is rated more than 400 points higher than his opponent, their difference should be set to 400 when calculating rating gain/loss. That means no matter how weak the opposition is, a GM (or anyone) will receive minimum 0.8 rating points for winning. What is the reason behind this?

To me it just seems like a giant weakness in the rating system, making any strong GM able to get as high rating as he wants just by playing weak opponents. Wouldn't it be better if the gain approached 0 when the difference increased (like the basic formula for calculating rating actually does)?

EDIT: As most of the answers don't really seem to get the point, I will add an example which points out the problem:

One of the top 10 players in the world (say Magnus Carlsen), wants to increase his rating to 3000. He has a good friend who has 1200 in rating, and who is willing to play a match of 200 games (2 each day for 100 days) against him. His friend will of course play his best, so this is by no means considered cheating.

According to https://wismuth.com/elo/calculator.html, Magnus will have way more than 99 % chance of winning a single game, but for simplicity, let's say he has 99 % chance of winning a game (which is an understatement). If we then forget about draws (for simplicity), Magnus would be expected a score of 198/200. That means a rating gain of 0.8*198 - 9.2*2 = 140 rating points. That is if he scores as expected. And he used less than 1/3 of a year, and is extremely close to 3000 already. What if he does it again? (And again?) Even if he plays really poorly and loses 5 and draws another 5 out of the 200 games, he will gain 85 rating points. That is by scoring FAR below expected.

If there was no rating difference cap, playing an expected result (say 198/200), would by definition give a rating gain/loss of 0. So who came up with the idea of making a loop-hole for any top GM to become extremely high rated?

Of course it would be looked at as bad sportmanship to do something like this, and I doubt any of the top players of the world would consider doing so, but that doesn't justify the possibility being there. In a serious sport with a serious rating system there shouldn't be these kind of loop-holes.

Can anyone find any arguments justifying this rule?

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    My guess is that this is FIDE encouraging high level players to still compete in tournaments that have weak players too. If you didn't have this type of system in place, then I imagine most GMs would exclusively play in GM-only tournaments. – NoseKnowsAll Aug 21 '18 at 21:58
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    Not sure it is feasible to gain much rating by this method. You'd have to find tournaments with only weak opponents and score 100% in them. Likely there would not be much price money to be won in such competitions either. – user1583209 Aug 21 '18 at 22:31
  • @NoseKnowsAll judging from the answers, which point out the significant point loss should the GM lose, which would also be a reason for GM players to not play lower tournaments. Risk vs reward. – JAD Aug 22 '18 at 6:31
  • @NoseKnowsAll: they wish, there aren't anywhere near enough GM-only tournaments for them to play in. I think many GMs never get to play in one at all. – RemcoGerlich Aug 22 '18 at 7:50
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    @JAD The risk only decreases from 10 to 9.2 rating points, which isn't a lot – Mr. Eivind Aug 22 '18 at 11:59
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Fide has a rule saying that if one player is rated more than 400 points higher than his opponent, their difference should be set to 400 when calculating rating gain/loss. That means no matter how weak the opposition is, a GM (or anyone) will receive minimum 0.8 rating points for winning. What is the reason behind this?

This is an historical anomaly. Currently, apart from your first ever rating, every game is rated individually. This means that you can never lose rating points by winning a game (LRPBWAG). It wasn't always so.

I don't remember exactly when the change happened, 2008 I think, but before this ratings were calculated per tournament. What happened was that your rating was calculated using your score for the tournament, the average of your opponents' ratings and your expected score against them. This opened up the possibility of winning the tournament but losing rating points because some low rated players in the tournament, who you crushed, lowered the average rating for the tournament so much that even though you scored well against similarly rated players as yourself your rating went down.

The original solution to this was to limit the difference to 350 points. Later this was changed to 400. Now that games are rated individually it could be scrapped.

There was an article on Chessbase 6 years ago discussing this point between Jeff Sonas, Ken Thompson and John Nunn.

Part of John Nunn's contribution is worth quoting -

The original rating rules had no 350-point rule. It must be remembered that in 1970 the rating list was very small and it was never envisaged that it would be extended substantially. Only top tournaments were rated (and these were invariably all-play-all events) and all calculations were done by hand. The 'Losing Rating Points For Winning A Game' problem didn't really arise. The top players always skipped the first round or two of an Olympiad, and in any case any weak opponents would be unrated, so the games simply didn't count.

But times changed, the rating list expanded and started including more and more weaker players. Open tournaments appeared, and the LRPFWAG problem started to become significant. I don't remember exactly when the 350-point rule was introduced to deal with this, but I believe it was around 1980. Later, in 1988 or 1989, Karpov was unhappy about losing points when he had won a tournament, arguing that the aim of taking part in a tournament was to win it, and if you have achieved that then you shouldn't lose points through not having won by a large margin. For a time the 'Karpov rule' was in effect, that you couldn't lose points for winning an event. This was later scrapped.

Rating games individually is a fairly recent innovation, and for the vast bulk of the lifetime of the Elo system it was done on a tournament basis (because it made the calculations easier, especially for all-play-all events). The current rule is in a way a hangover from the earlier times, but I think there is some logic in it, although one can argue over the exact details. Rapidly improving young players, for example, can be massively underrated.

  • I was under the impression that the "Karpov rule" originated due to Fischer losing rating points after winning the world championship from Spassky – Herb Wolfe Aug 22 '18 at 16:47
  • @HerbWolfe Yeah, right. That makes perfect sense. Something called the "Karpov Rule" arose out of the experiences of a completely different player several years before Karpov came to ascendancy. In those days ratings were calculated to the nearest 5 points. Fischer lost 5 points, the minimum possible loss, by virtue of not beating Spassky comprehensively enough. Given the fact that Fischer defaulted one of the games out of childishness, 5 points seems fair. I suspect John Nunn knows better than either of us. – Brian Towers Aug 22 '18 at 17:29
  • Let me clarify. I'm not saying the rule is called the "Karpov Rule" because of Fischer, but rather that a similar, unnamed, rule was put in place much earlier, and that it was due to Fischer losing rating points. I admit I could be remembering something that I read wrong, as it could have been 20-30 years ago that I read about it. – Herb Wolfe Aug 23 '18 at 16:38
  • "Currently, apart from your first ever rating, every game is rated individually." You're correct that LRPFWAG problem doesn't exist anymore because expected results are calculated game-by-game. But a slight correction: the rating change is still computed on a tournament basis, the ratings used for each game are the ratings before a tournament, they're not adjusted mid-tournament. – JiK Aug 28 '18 at 11:07
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The rule makes total sense to me as statistics for rating is not so accurate when the difference in playing strength is too much. Capping to 400 minimises the statistical damage.

No GM would risk a hefty rating penalty by playing only weak tournaments. Too much risk for very little gains. A single tactical oversight (GM is human too!!) could be deadly.

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    But you would only lose 10 rating points per loss (max) instead of 9.2 now. Not really the biggest difference... – Mr. Eivind Aug 22 '18 at 11:57
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    @Mr.Eivind : if I score 8/9 in the tournament against players 600 elo lower than me, I would lose more than 9 points instead of circa 0 with the current rule. – Evargalo Aug 22 '18 at 14:00
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    If you have a larger k-value, yes. Maximum k-value is 40, meaning you could maximum lose 36.8 points in a single game (instead of 40 points). So the current rule only saves you 3.2 rating points. – Mr. Eivind Aug 22 '18 at 14:03
  • @Mr.Eivind : let's keep k=10 for the sake of simplicity. In games with much lower rated opponents, with the current rule I lose very slightly less points per defeat than I would without the rule (as you correctly point out), but, more importantly, I also gain 1 point per victory (instead of 0,05 or so) which can bring some compensation and prevents me from shying away from lower-level tournaments. – Evargalo Aug 24 '18 at 8:34
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The higher rated player should get something for winning a game, and 0.8 seems to be the least to award the winner and still get recognition.

https://en.wikipedia.org/wiki/Claude_Bloodgood exploited the this system to achieve a rating of 2759.

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    Interesting story! The argument of "a win should give you something" is a good one, but when it causes these issues I still think it's better to remove the rule – Mr. Eivind Aug 22 '18 at 11:56
  • As far as I can see, the cheating of Claude Bloodgood involved deliberate losing of some players, so is not exactly the situation described in this question. – user1583209 Aug 22 '18 at 20:11
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    In the USCF system (which Bloodgood was in, not FIDE) there's no 0.8 minimum gain, so that's not how he did it. Bloodgood's high rating was not from beating players with a rating far below him; it was from beating players whose ratings were too high for their strength. – D M Aug 23 '18 at 21:24
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For starters, eight-tenths of a point really isn't that much of a ratings gain, especially for someone rated 2600 or more. At that rate, it would take 100 wins (without an upset loss) against these lower rated players just to gain 80 points. Given that a GM would mostly have to limit him/herself to the 3 to 6 round weekend tournaments that most of us lower rated players primarily participate in, it would take a while to gain those 80 points. Also, some tournaments might not allow a GM into the lower rated sections. Additionally, the prize money would be almost insignificant for a player at that level. As noted in Jossie Calderon's answer, such a point grab would invite challenges from other GM's looking for a big point gain. All in all, it just doesn't seem like a smart way to gain points.

As I see it, this isn't about guaranteeing a minimal increase for a GM. It's more about capping the gain for a lower rated player and minimizing the loss for the higher rated player if somehow some patzer manages to upset a GM, or a seriously underrated player beats the GM.

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    I think the last is wrong, as the maximum gain/loss (without this 400 max difference rule) is 10 rating points (with k=10). A rating gain in the range [0.8, 9.2] instead of [0, 10] doesn't really make much of a difference. – Mr. Eivind Aug 22 '18 at 8:45
  • @Mr.Eivind: 10 is the maximum gain? Admittedly I've never played in an FIDE rated event, but I've personally gained much more than that a couple times in tournaments where I pulled off significant upsets (300 points in one case, 500 points in another); in one case (the 500 point upset) I didn't do very well the rest of the tournament (I was pretty exhausted), so it seems safe to say the (40 point) gain was attributable to that win alone. – GreenMatt Aug 23 '18 at 13:28
  • The best players have something called a k-value equal to 10, but for lower rated players it might be as high as 40. The maximum rating you can win (or lose) in a single game is equal to your k-value. – Mr. Eivind Aug 23 '18 at 13:31
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It all evens out when an underrated opponent defeats the GM.

Assume the GM only plays weak opponents, so he gets a considerably large rating.

Then when he gets inevitably famous (he's a GM) people are going to look up his playing history and notice a discrepancy. This guy is only good because he plays patzers!

So when an underdog defeats him (this underdog being several hundred points stronger than he is on paper) the GM's rating will shift towards a truer description.

EDIT As a response to your edit, you do realize everyone around the world can see Carlsen's playing history, right?

Don't you think this would affect his image somewhat...I don't know...NEGATIVELY?

You're just asking a theoretical question that doesn't have a basis in real life. That's why you're not getting the answer you want: there is no solution.

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    As I've now explained in the edit, it won't "even out" at all – Mr. Eivind Aug 22 '18 at 11:49
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    Elo ratings/system already do the evening-out process. Artificially imposing changes on top of it can only add distortion (or at least create opportunities for it). – mbrig Aug 22 '18 at 15:02
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    This answer doesn't explain why the effect of the cap would even out, it just says that the rating of a GM would sometimes go up and sometimes down. – JiK Aug 22 '18 at 19:34
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    "That's why you're not getting the answer you want: there is no solution." - The question is asking why there's a cap, so are you saying there's no reason for the cap? – D M Aug 22 '18 at 23:39
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    @JossieCalderon A few games can happen if a GM feels like playing a tournament in his hometown, and wouldn't get much "scrutiny". 5 games would result in (at most) a 4 ratings points difference compared to an uncapped system. Yes, that's hardly anything, and yes, it will all even out eventually assuming he doesn't do this every weekend... but that still doesn't answer the question of why we have this minimum gain at all. And a few rating points can matter for things like qualifying for (or getting a better seed in) the Chess World Cup, which has implications for the world championship. – D M Aug 23 '18 at 5:48

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