I just skimmed the article. I guess that the calculations are correct, but it seems to me that they miss the point. Such statistics should be used for random phenomena, independent of each other. (I apologize for a wrong terminology, but expert are clever enough to understand what I mean.)
If a player A plays against player B at 46 random times of the weak, the score will never be 45.5-0.5. But if the games are played all at once, at the same time of the same day, with one player in a great form, the other in a terrible and the latter increasingly depressed by the results, it is much more likely to occur. I guess that when someone scores 45.5/46, usually it is not against the same opponent. That said, the form of the stronger player still matters a lot. As far as I can remember, young GM Morozevich many times scored 8/9 or even 8.5/9 in strong round-robin tournaments. (Back then there was less opening theory, so it was easier than now, but still an amazing achievement.) My own results in blitz are quite unstable, with big ups and downs. I have suffered many losing streaks in my OTB blitz events, including three losses in a row in a tournament where I scored 11.5/15 or 4 losses in a row in a strong event where I scored 7.5/14 (Biel 2023).
I have missed the previous discussion regarding the score 45.5/46. Personally I find it very unlikely to occur, but still many, many times more likely than such statistics would suggest.
If a player A plays against player B at 46 random times of the weak, the score will never be 45.5-0.5. But if the games are played all at once, at the same time of the same day, with one player in a great form, the other in a terrible and the latter increasingly depressed by the results, it is much more likely to occur. I guess that when someone scores 45.5/46, usually it is not against the same opponent. That said, the form of the stronger player still matters a lot. As far as I can remember, young GM Morozevich many times scored 8/9 or even 8.5/9 in strong round-robin tournaments. (Back then there was less opening theory, so it was easier than now, but still an amazing achievement.) My own results in blitz are quite unstable, with big ups and downs. I have suffered many losing streaks in my OTB blitz events, including three losses in a row in a tournament where I scored 11.5/15 or 4 losses in a row in a strong event where I scored 7.5/14 (Biel 2023).
I have missed the previous discussion regarding the score 45.5/46. Personally I find it very unlikely to occur, but still many, many times more likely than such statistics would suggest.
I just skimmed the article. I guess that the calculations are correct, but it seems to me that they miss the point. Such statistics should be used for random phenomena, independent of each other. (I apologize for a wrong terminology, but expert are clever enough to understand what I mean.)
If a player A plays against player B at 46 random times of the weak, the score will never be 45.5-0.5. But if the games are played all at once, at the same time of the same day, with one player in a great form, the other in a terrible and the latter increasingly depressed by the results, it is much more likely to occur. I guess that when someone scores 45.5/46, usually it is not against the same opponent. That said, the form of the stronger player still matters a lot. As far as I can remember, young GM Morozevich many times scored 8/9 or even 8.5/9 in strong round-robin tournaments. (Back then there was less opening theory, so it was easier than now, but still an amazing achievement.) My own results in blitz are quite unstable, with big ups and downs. I have suffered many losing streaks in my OTB blitz events, including three losses in a row in a tournament where I scored 11.5/15 or 4 losses in a row in a strong event where I scored 7.5/14 (Biel 2023).
I have missed the previous discussion regarding the score 45.5/46. Personally I find it very unlikely to occur, but still many, many times more likely than such statistics would suggest.
If a player A plays against player B at 46 random times of the weak, the score will never be 45.5-0.5. But if the games are played all at once, at the same time of the same day, with one player in a great form, the other in a terrible and the latter increasingly depressed by the results, it is much more likely to occur. I guess that when someone scores 45.5/46, usually it is not against the same opponent. That said, the form of the stronger player still matters a lot. As far as I can remember, young GM Morozevich many times scored 8/9 or even 8.5/9 in strong round-robin tournaments. (Back then there was less opening theory, so it was easier than now, but still an amazing achievement.) My own results in blitz are quite unstable, with big ups and downs. I have suffered many losing streaks in my OTB blitz events, including three losses in a row in a tournament where I scored 11.5/15 or 4 losses in a row in a strong event where I scored 7.5/14 (Biel 2023).
I have missed the previous discussion regarding the score 45.5/46. Personally I find it very unlikely to occur, but still many, many times more likely than such statistics would suggest.
@RealDavidNavara said in #2:
> I just skimmed the article. I guess that the calculations are correct, but it seems to me that they miss the point. Such statistics should be used for random phenomena, independent of each other. (I apologize for a wrong terminology, but expert are clever enough to understand what I mean.)
> If a player A plays against player B at 46 random times of the weak, the score will never be 45.5-0.5. But if the games are played all at once, at the same time of the same day, with one player in a great form, the other in a terrible and the latter increasingly depressed by the results, it is much more likely to occur. I guess that when someone scores 45.5/46, usually it is not against the same opponent. That said, the form of the stronger player still matters a lot. As far as I can remember, young GM Morozevich many times scored 8/9 or even 8.5/9 in strong round-robin tournaments. (Back then there was less opening theory, so it was easier than now, but still an amazing achievement.) My own results in blitz are quite unstable, with big ups and downs. I have suffered many losing streaks in my OTB blitz events, including three losses in a row in a tournament where I scored 11.5/15 or 4 losses in a row in a strong event where I scored 7.5/14 (Biel 2023).
> I have missed the previous discussion regarding the score 45.5/46. Personally I find it very unlikely to occur, but still many, many times more likely than such statistics would suggest.
It's true that there is an assumption of independence between the games which as you rightly point out may not hold true. In fact a theme that I didn't touch in the article is the conditional probability that is, for instance, the probability of a player winning a game given that he won the previous game, i.e., P(A winning| A won the previous game). If there is independence P(A winning) = P(A winning| A won the previous game) and it is not equal if there is no independence. This cold be tested by looking at the data. An interesting theme for another blog.
Also I agree with you that a player form can and probably will have a significant impact on performance. A bit more difficult to measure.
Finally, as I wrote I have no idea if the probabilities I used in the article are correct. Again it would be necessary to look at the data to check it these probabilities agree with reality.
My aim was just to try to show those without statistical background how the probability a player winning/drawing/loosing against another could be calculated.
> I just skimmed the article. I guess that the calculations are correct, but it seems to me that they miss the point. Such statistics should be used for random phenomena, independent of each other. (I apologize for a wrong terminology, but expert are clever enough to understand what I mean.)
> If a player A plays against player B at 46 random times of the weak, the score will never be 45.5-0.5. But if the games are played all at once, at the same time of the same day, with one player in a great form, the other in a terrible and the latter increasingly depressed by the results, it is much more likely to occur. I guess that when someone scores 45.5/46, usually it is not against the same opponent. That said, the form of the stronger player still matters a lot. As far as I can remember, young GM Morozevich many times scored 8/9 or even 8.5/9 in strong round-robin tournaments. (Back then there was less opening theory, so it was easier than now, but still an amazing achievement.) My own results in blitz are quite unstable, with big ups and downs. I have suffered many losing streaks in my OTB blitz events, including three losses in a row in a tournament where I scored 11.5/15 or 4 losses in a row in a strong event where I scored 7.5/14 (Biel 2023).
> I have missed the previous discussion regarding the score 45.5/46. Personally I find it very unlikely to occur, but still many, many times more likely than such statistics would suggest.
It's true that there is an assumption of independence between the games which as you rightly point out may not hold true. In fact a theme that I didn't touch in the article is the conditional probability that is, for instance, the probability of a player winning a game given that he won the previous game, i.e., P(A winning| A won the previous game). If there is independence P(A winning) = P(A winning| A won the previous game) and it is not equal if there is no independence. This cold be tested by looking at the data. An interesting theme for another blog.
Also I agree with you that a player form can and probably will have a significant impact on performance. A bit more difficult to measure.
Finally, as I wrote I have no idea if the probabilities I used in the article are correct. Again it would be necessary to look at the data to check it these probabilities agree with reality.
My aim was just to try to show those without statistical background how the probability a player winning/drawing/loosing against another could be calculated.
I just skimmed the article. I guess that the calculations are correct, but it seems to me that they miss the point. Such statistics should be used for random phenomena, independent of each other. (I apologize for a wrong terminology, but expert are clever enough to understand what I mean.)
>If a player A plays against player B at 46 random times of the weak, the score will never be 45.5-0.5. But if the games are played all at once, at the same time of the same day, with one player in a great form, the other in a terrible and the latter increasingly depressed by the results, it is much more likely to occur. I guess that when someone scores 45.5/46, usually it is not against the same opponent. That said, the form of the stronger player still matters a lot. As far as I can remember, young GM Morozevich many times scored 8/9 or even 8.5/9 in strong round-robin tournaments. (Back then there was less opening theory, so it was easier than now, but still an amazing achievement.) My own results in blitz are quite unstable, with big ups and downs. I have suffered many losing streaks in my OTB blitz events, including three losses in a row in a tournament where I scored 11.5/15 or 4 losses in a row in a strong event where I scored 7.5/14 (Biel 2023).
>I have missed the previous discussion regarding the score 45.5/46. Personally I find it very unlikely to occur, but still many, many times more likely than such statistics would suggest.
It's true that there is an assumption of independence between the games which as you rightly point out may not hold true. In fact a theme that I didn't touch in the article is the conditional probability that is, for instance, the probability of a player winning a game given that he won the previous game, i.e., P(A winning| A won the previous game). If there is independence P(A winning) = P(A winning| A won the previous game) and it is not equal if there is no independence. This cold be tested by looking at the data. An interesting theme for another blog.
Also I agree with you that a player form can and probably will have a significant impact on performance. A bit more difficult to measure.
Finally, as I wrote I have no idea if the probabilities I used in the article are correct. Again it would be necessary to look at the data to check it these probabilities agree with reality.
My aim was just to try to show those without statistical background how the probability a player winning/drawing/loosing against another could be calculated.
+1
-1
laugh
thinking
heart
>If a player A plays against player B at 46 random times of the weak, the score will never be 45.5-0.5. But if the games are played all at once, at the same time of the same day, with one player in a great form, the other in a terrible and the latter increasingly depressed by the results, it is much more likely to occur. I guess that when someone scores 45.5/46, usually it is not against the same opponent. That said, the form of the stronger player still matters a lot. As far as I can remember, young GM Morozevich many times scored 8/9 or even 8.5/9 in strong round-robin tournaments. (Back then there was less opening theory, so it was easier than now, but still an amazing achievement.) My own results in blitz are quite unstable, with big ups and downs. I have suffered many losing streaks in my OTB blitz events, including three losses in a row in a tournament where I scored 11.5/15 or 4 losses in a row in a strong event where I scored 7.5/14 (Biel 2023).
>I have missed the previous discussion regarding the score 45.5/46. Personally I find it very unlikely to occur, but still many, many times more likely than such statistics would suggest.
It's true that there is an assumption of independence between the games which as you rightly point out may not hold true. In fact a theme that I didn't touch in the article is the conditional probability that is, for instance, the probability of a player winning a game given that he won the previous game, i.e., P(A winning| A won the previous game). If there is independence P(A winning) = P(A winning| A won the previous game) and it is not equal if there is no independence. This cold be tested by looking at the data. An interesting theme for another blog.
Also I agree with you that a player form can and probably will have a significant impact on performance. A bit more difficult to measure.
Finally, as I wrote I have no idea if the probabilities I used in the article are correct. Again it would be necessary to look at the data to check it these probabilities agree with reality.
My aim was just to try to show those without statistical background how the probability a player winning/drawing/loosing against another could be calculated.
+1
-1
laugh
thinking
heart