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#1




UPHILL RATING?
What is your "UPHILL RATING"? This is what your rating would be, taking
into account only those games where your opponent was at least 150 points stronger than you. How do you play against strong opposition? Do you get intimidated and fall apart? Do you summon every resource and play an extra sharp game? This is a dimension of your game which can be quantified, and, in fact, is one of many analytics published by Chess Express Ratings as part of the CXR System. Take a look for yourself: www.chessexpress.com 
#2




UPHILL RATING?
"Squark" writes:
What is your "UPHILL RATING"? This is what your rating would be, taking into account only those games where your opponent was at least 150 points stronger than you. How do you play against strong opposition? Do you get intimidated and fall apart? Do you summon every resource and play an extra sharp game? This is a dimension of your game which can be quantified, and, in fact, is one of many analytics published by Chess Express Ratings as part of the CXR System. Take a look for yourself: www.chessexpress.com This is a great shill. Theory says that your "uphill rating" should be considerably above your actual rating. I predict that this term will become very popular with the players  at least those who are not statisticians.  Kenneth Sloan Computer and Information Sciences (205) 9342213 University of Alabama at Birmingham FAX (205) 9345473 Birmingham, AL 352941170 http://www.cis.uab.edu/sloan/ 
#3




UPHILL RATING?
Kenneth Sloan wrote in message ...
"Squark" writes: What is your "UPHILL RATING"? This is what your rating would be, taking into account only those games where your opponent was at least 150 points stronger than you. How do you play against strong opposition? Do you get intimidated and fall apart? Do you summon every resource and play an extra sharp game? This is a dimension of your game which can be quantified, and, in fact, is one of many analytics published by Chess Express Ratings as part of the CXR System. Take a look for yourself: www.chessexpress.com This is a great shill. Theory says that your "uphill rating" should be considerably above your actual rating. I was surprised to read this. Of course, my knowledge of the rating system is completely out of date. But I was under the impression that I would get about the same rating by playing stronger players as by playing weaker. I assume that there might be "boundary" effects, due to rounding or whatever, if my opposition were 400 points stronger or weaker, but I would think this wouldn't be too important at 150 points. Also there might be some psychological effects ("he beats a master one round, then loses to a B player the next round"), but that these likewise would not be too important overall. I predict that this term will become very popular with the players  at least those who are not statisticians. 
#5




UPHILL RATING?
Kenneth Sloan wrote in message ...
(Bruce Leverett) writes: Kenneth Sloan wrote in message ... ... Theory says that your "uphill rating" should be considerably above your actual rating. I was surprised to read this. Of course, my knowledge of the rating system is completely out of date. But I was under the impression that I would get about the same rating by playing stronger players as by playing weaker. I assume that there might be "boundary" effects, due to rounding or whatever, if my opposition were 400 points stronger or weaker, but I would think this wouldn't be too important at 150 points. Also there might be some psychological effects ("he beats a master one round, then loses to a B player the next round"), but that these likewise would not be too important overall. You are assuming that ratings are known perfectly. First  let's assume that ratings are completely random. What is the probability that a higher rated player will lose to a lower rated player? Answer: 50%. Now  assume that ratings are known perfectly. Then, the scoring probability of the higher rated player is known. Finally  assume that the ratings are some mix of the perfect value with a random value. Then, the observed results will be a mix of the predicted result and the 50% results. Therefore, the observed results will be better for the lower rated player. Hence...if you consider only your results against higher rated players, you will appear to be doing better than expected (from your rating). The rating that you compute using only these results will be *higher* than the rating you compute using all of your games. I think this is correct but that the explanation is not very clear. Suppose we choose some cutoff like 2000 and look at the games you play against opponents rated 2000 or higher. Since the rating system is imperfect some of these opponents will actually be of less than 2000 strength. So you will score a little better than expected. James B. Shearer 
#6




UPHILL RATING?
"James B. Shearer" wrote:
I think this is correct but that the explanation is not very clear. Suppose we choose some cutoff like 2000 and look at the games you play against opponents rated 2000 or higher. Since the rating system is imperfect some of these opponents will actually be of less than 2000 strength. So you will score a little better than expected. To carry this a little further, some of the opponents will actually be of more than 2000 strength, too. But these won't have as much of an effect, because, if you are rated 1700 for example, the difference in your winning probabilities against opponents rated 1900 vs 2000 is greater than the difference in your winning probabilities against opponents rated 2000 vs 2100. Are we getting close yet? Bill Smythe 
#7




UPHILL RATING?
(James B. Shearer) writes:
... I think this is correct but that the explanation is not very clear. Suppose we choose some cutoff like 2000 and look at the games you play against opponents rated 2000 or higher. Since the rating system is imperfect some of these opponents will actually be of less than 2000 strength. So you will score a little better than expected. James B. Shearer And some of them will actually be of greater than 2000 strength. So you will score a little worse than expected. Hmmm. I like my explanation better.  Kenneth Sloan Computer and Information Sciences (205) 9342213 University of Alabama at Birmingham FAX (205) 9345473 Birmingham, AL 352941170 http://www.cis.uab.edu/sloan/ 
#8




UPHILL RATING?
"Bill Smythe" wrote in message ...
"James B. Shearer" wrote: I think this is correct but that the explanation is not very clear. Suppose we choose some cutoff like 2000 and look at the games you play against opponents rated 2000 or higher. Since the rating system is imperfect some of these opponents will actually be of less than 2000 strength. So you will score a little better than expected. To carry this a little further, some of the opponents will actually be of more than 2000 strength, too. But these won't have as much of an effect, because, if you are rated 1700 for example, the difference in your winning probabilities against opponents rated 1900 vs 2000 is greater than the difference in your winning probabilities against opponents rated 2000 vs 2100. Are we getting close yet? It depends on the audience. I'm the one who originally asked the question, and I was perfectly OK with Ken Sloan's answer. I suppose, however, that before this kind of answer feels intuitive to you, your intuition has to be twisted, like mine, and presumably Ken's. I find it intriguing that uphill ratings and downhill ratings are likely to be different. Ken, would you care to estimate the magnitude of this effect? 
#9




UPHILL RATING?
(Bruce Leverett) writes:
... I find it intriguing that uphill ratings and downhill ratings are likely to be different. Ken, would you care to estimate the magnitude of this effect? Nope. Actually, I prefer to do the reverse. The difference between the "uphill rating" and the "downhill rating" may tell us something about how precise the ratings are. [but, feel free to try it yourself  use your favorite backoftheenvelope computation to generate a Performance Rating for your last 100 games. With luck, it should be reasonably close to your current published rating. Now segregate your games into "uphill" and "downhill" catagories and do it again. Report results, to 8 significant digits]  Kenneth Sloan Computer and Information Sciences (205) 9342213 University of Alabama at Birmingham FAX (205) 9345473 Birmingham, AL 352941170 http://www.cis.uab.edu/sloan/ 
#10




UPHILL RATING?
Kenneth Sloan wrote in message ...
(James B. Shearer) writes: ... I think this is correct but that the explanation is not very clear. Suppose we choose some cutoff like 2000 and look at the games you play against opponents rated 2000 or higher. Since the rating system is imperfect some of these opponents will actually be of less than 2000 strength. So you will score a little better than expected. James B. Shearer And some of them will actually be of greater than 2000 strength. So you will score a little worse than expected. Hmmm. I like my explanation better. My claim was the pool of people rated over 2000 at any given point in time will be weaker than the pool of people with true strength over 2000 as ratings error will include some weaker players with true strength under 2000 and exclude some stronger players with true strength over 2000. Are you disputing this? However let me try again. Suppose you have pool of players whose true strength never changes. Let them play a large number of games and assume the outcome of each game is independently random depending only on the difference in true strength of the opponents in accordance with the rating model. Consider a player X. Over time his rating will randomly fluctuate. Some of the time X will be rated above 2000 (or any other arbitrary cutoff), some of the time below. Of course if X's true strength is well under 2000 he will spend little time rated above 2000 and if X's true strength is well over 2000 he will spend little time rated below 2000. Now consider your games against X. Since X's true strength is not changing you will score as well when X is rated above 2000 as your overall score against X. But clearly your performance rating will be higher considering just those games in which X is rated above 2000. This is true for every other player in the pool. So your performance rating in games against opponents rated over 2000 will exceed your performance rating in all games as you are selecting games in which your opponents are over rated on average. James B. Shearer 
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