Assume Player A has a floor of 1800, but has not been playing up to that level so that, except for the floor, his rating would be 1650.
Player B has a rating of 1500 and defeats Player A.
When Player B’s rating is calculated, would it be based on defeating an 1800 level player, or a 1650 level player?
I’m not looking for a mathematical answer, just curious.
Thanks!
Grant Neilley
This question is answered in the Ratings Formula, available at math.bu.edu/people/mg/ratings/rating.system.pdf, and I think I’ve answered it here more than once. 
A player’s rating can never go below the ‘hard deck’ floor of 100, if it does at any point during the intermediate steps it is set to 100 before moving on to the next step.
However, a player with a higher floor (such as 1800) can have an intermediate step rating below 1800, but the final stage after step 5 of the ratings computation process is to raise all players whose rating would now be below their floor back up to their floor, and this is the ONLY TIME that is done. That means for the purpose of computing the new ratings of that player’s opponents during step 5, that player’s rating could be below 1800.
Thanks for the info… and thanks for taking the time to answer this question yet one more time. 
Grant Neilley.
But only a little below, correct? His pre-tournament rating would still be taken as 1800, and his pre-step-5 rating would not likely be less than 1750 or so, at least if the 1800 rating is an established rating.
Bill Smythe
I don’t have an easy way to check on what someone’s step 5 rating was (we don’t keep the intermediate step ratings in the database), but there are 4 cases so far during 2007 where someone with a regular rating floor of 1400 or higher has dropped 100 or more points in a single event and 24 cases where a player lost between 75 and 99 points in a single event.
I was just thinking that your answer may have been invertently misleading, given the original question:
1800 is a better answer here than 1650, isn’t it? (Of course, as you point out, due to some technicalities, the 1800 answer may be a bit of an oversimplification.)
Bill Smythe
No, I don’t think my original answer was misleading, a player who is at (and sometimes even just near) his floor and has a poor result (ie, below the expected performance of his floor) will be under his floor at the time that we compute the new ratings of his opponents.
How much under is the question. For a player with an 1800 floor, probably not 1650. (It’s possible but VERY unlikely, though I suppose it would become somewhat more possible in longer events.)
We have looked at the ratings of a few players at their floor (who will mercifully remain nameless.) In several cases if they had no floor and we re-rated their last year’s worth of games their ‘true’ ratings could be as much as 500 points below their floor.
So does this mean my opponents aren’t getting credit for beating a 1700, but perhaps a 1650 to 1675 if my performance in the particular tournament warrented such a drop without a floor? 
I remember the number you told me last year in Oakbrook, hopefully it hasn’t gotten worse. 
Even I wouldn’t have been a member of the 500 club. (I hope!) PM me with an update.
But that’s a drop of only 25-50 points, resulting in a difference of probably only 1-2 points for each of your opponents.
But if your performance in your last several tournaments would have put you significantly (a few hundred) points below your floor, your opponents would suffer only as much as they would if only your last tournament had dropped you below your floor. For example, if you have a 1700 floor but your rating would be 1400 without the floor, instead of this costing your opponents 12 points each (the cost of beating only a 1400 instead of a 1700), it will cost them only 2 points each (the cost of beating only a 1650 rather than a 1700).
At least that’s about right (I think).
Bill Smythe
That’s why rating floors are considered mildly inflationary.
Polly, if you REALLY want to know what your ‘true’ rating would be without floors, I’ll rerun it, but maybe I should wait until after the holidays?
BTW, I wasn’t thinking of you but of someone who has a floor of, I believe, 1600 but whose performance over the last several years has been more like 1100. But unless that player ASKS for a lowered floor, the 1600 floor will remain in effect. (Floors are political in nature, not mathematical.)
I’d be interested to know at the end of the year. This will be my most active year. I’ll have over 400 games on the regular rating system. (Damn, I’m getting like Jay Bonin!) Even though I’ve lost over twice as many as I’ve won, I’ve playd mostly higher rated opponents. I suspect even without a floor I don’t lose many points for going 0-4 in a section where my opponents have outrated me by at least 300 points.
I’m immensely relieved to know that I haven’t performed that much below my floor. :mrgreen: