for what its worth there are ppl including myself who play online chess same as blitz, i dont take much time on a move at all.
Players that play live chess and Online Chess have a biger Online chess rating then live chess.

DrawMaster, I believe Reb addressed your question. Not everybody uses databases and the analysis board. Many do.
Yes ... the differential use of tools will smear the distribution of ratings, but won't necessarily displace the mean rating. So, in Online, I might expect a wider distribution of ratings ... and YES, that is exactly what you will see if you compare the stats for Blitz and Online. The differential use of databases and analysis board does not explain the 200+ point bias between Online and Live Chess Blitz.

for what its worth there are ppl including myself who play online chess same as blitz, i dont take much time on a move at all.
In your case then both the ratings should be close... for me it is different. In the tactics trainer I cannot solve most of the harder problems in 2 minutes - I can solve then in 10-20 minutes, though (when scoring does not count).
I think people with "young"(=faster) brains do not comprehend the problems faced by slower brains - I know of a person who laughed when he heard someone has a stomach upset - let him grow old, then only he will understand. People who cannot "think in other people's shoes" will go on arguing till time's end without really understanding other's situations.

dsakar, the overall strength of a group is a value that cannot be known per se, but it is NOT automatically equal to the overall rating of a group.
The rating is the product of a measurement process and can - and usually will - bring in measurement bias. Indeed, that's the question within the original question that was asked: What is the explanation for the difference between Live and Online ratings?
I am suggesting that the answer to the original question is this:
Yes, Online mean rating is higher (200+ points) than Live Chess Blitz. No, it is NOT due PRINCIPALLY to a difference in players' abilities or tools (though the distribution of ratings may point to a difference in the use of such tools), but is largely due to two factors: the rating system's propensity for conservation (or lack thereof) and the difference over time between the players entering the pool and those leaving (those staying steal rating points from those leaving).

DrawMaster, I believe Reb addressed your question. Not everybody uses databases and the analysis board. Many do.
Yes ... the differential use of tools will smear the distribution of ratings, but won't necessarily displace the mean rating. So, in Online, I might expect a wider distribution of ratings ... and YES, that is exactly what you will see if you compare the stats for Blitz and Online. The differential use of databases and analysis board does not explain the 200+ point bias between Online and Live Chess Blitz.
Please read my points above for the explanation... I don't know how more can I drive my logic home... It is not only tools, there are two more points please...

Neither thinking speed nor time constraints will change the mean rating, but they do have a profound effect on individual performance. To the extent that we're only interested in individual effects, all your points are excellent ones. This, I never disputed, only the effect of any of these on the Online pool mean, which is 200+ rating points higher than Live Chess Blitz.
At this juncture, I'll leave this thread to those who are not interested in the aspect to which I was referring.
Thanks for the lively banter. Very good points raised here about this great game and our challenge to master it.

dsakar, the overall strength of a group is a value that cannot be known per se, but it is NOT automatically equal to the overall rating of a group.
The rating is the product of a measurement process and can - and usually will - bring in measurement bias. Indeed, that's the question within the original question that was asked: What is the explanation for the difference between Live and Online ratings?
I am suggesting that the answer to the original question is this:
Yes, Online mean rating is higher (200+ points) than Live Chess Blitz. No, it is NOT due PRINCIPALLY to a difference in players' abilities or tools (though the distribution of ratings may point to a difference in the use of such tools), but is largely due to two factors: the rating system's propensity for conservation (or lack thereof) and the difference over time between the players entering the pool and those leaving (those staying steal rating points from those leaving).
I give up! Evidently you understand statistics and maths well, but you have not dwelt much on applied stats or maths. That is why the point that is clear as day to me is incomprehensible to you. The rating system does not differentiate or recognize the time factor (that's its fallacy I admit), which makes all the difference! It gives the same rating to performance in 2 minutes and performance in 2 days! And that is responsible for the bias. It gives the same rankings to persons who walks a mile in 5 minutes and who walk a mile in 1 hour! To the rating system the distance travelled is important, not the time taken! Thus a car is equal to a caterpillar if both travelled the same distance.
'Hope I could make some sense...

I think there is the very real possibility that strong blitz players end up playing on other sites, because of the frequent disconnections on chess.com's Live Chess. Strong correspondence players are more likely to stay here than go elsewhere.

DrawMaster,
OK, I think I understand your logic - let me bring in another factor, which will make everything clear.
suppose there are m number of people type A who play online and live same. and n number of people type B who play online and live different.
Now m is huge, n is comparative small. So n number of people have much higher rating. Now, of that m number of type A, a considerable number leave that site after disgustingly poor performance! New people of 1200 ratings are joining constantly. That makes the average of type A only slightly lower, but the average of type B is much higher. Thus the final average of A plus B will be much higher, because we are not counting those people who joined with 1200, left with lower score!
Hope this makes it clear...

(1) Thinking speed. Younger people can think faster - as we grow old (or if we are out of touch for a long time) our mental speed falls - such a slow-brained person will do poorly in live chess, but do much better in online chess.
(2) Crutches. In online chess people are allowed to consult opening books and even opening databases (NOT endgame databases). That elevates the opening of any player to GM level!
(3) Time Constraints: On cannot spend more than a certain time per move in live. In online, there is no time pressure - you can take all the time you need.
(4) Analysis Board. Those who cannot visualise well can use analysis board to think quite a several moves (in special cases even 8-9 move variations) ahead - that person can only think 2-3 moves in live chess.
Perfect description! Well done! Specially number 1 for me...

Let's be very careful with our words:
Claiming that one's absolute playing strength when playing Online Chess is greater than one's absolute playing strength when playing Blitz or Quick in Live Chess is NOT the same thing as claiming that one's rating in Online Chess should be higher than one's rating in Blitz or Quick in Live Chess. Both may be true, but not because they are identical claims.
(An example of counter-intuitiveness is the fact that the mean Live Chess Quick rating is nearly 100 points higher than the Live Chess Blitz rating, clearly indicating that there's more at play than the speed of the game.)
One's rating from a rating system is NOT a measure of one's absolute strength but only a measure of one's strength relative to the pool of players one encounters under the conditions of play (and, of course, the numerics of the rating system, such as initial incoming rating, rating points conservation within the system, etc.).
I know I am being REALLY picky with terms here. But choosing not be to picky can easily result in incorrect declarations.

DrawMaster, well said. I agree 100% and I appreciate other people who are as deliberate with their usage of terms as I am.

In blitz play, the ability to use a mouse quickly and skillfully probably plays an important part in your results. Older players who don't have quick reflexes can win games at correspondence through experience and better positional judgement, but they may find it more difficult to do well at blitz. Fedor Bohatirchuk is one player who comes to mind. Before World War II, he beat Botvinnik fairly regularly, but after the war, he found it hard to do well over-the-board, so he took up correspondence chess becoming a CCIM in his sixties.
Also, I have chatted with players who use blitz as a testing ground for unsound or speculative ideas that they would never try at correspondence speeds. They view blitz games as a diversion, not as a skill you work at, and try to improve.

In blitz play, the ability to use a mouse quickly and skillfully probably plays an important part in your results. Older players who don't have quick reflexes can win games at correspondence through experience and better positional judgement, but they may find it more difficult to do well at blitz. Fedor Bohatirchuk is one player who comes to mind. Before World War II, he beat Botvinnik fairly regularly, but after the war, he found it hard to do well over-the-board, so he took up correspondence chess becoming a CCIM in his sixties.
Also, I have chatted with players who use blitz as a testing ground for unsound or speculative ideas that they would never try at correspondence speeds. They view blitz games as a diversion, not as a skill you work at, and try to improve.
I 200% agree!!

Response to visual stimulus and mechanical reaction time are relevant issues as aging progresses, well-noted by the last few posts. Some of you may be familiar with the response test where another person drops a stick that you have to catch. Here's some serious research describing that test and looking at the effects of aging on results. I would proffer that particularly in Quick mode of Live Chess, at least two components of stimulus response measured by this test are relevant: a) recognizing the incoming visual stimuli, and b) moving/clicking the mouse to make a move in response. Here's one chart from some research:
If one takes these data for a young man (160 ms) and a 65-year old (220 ms), the difference of 60 ms grows into a full 2.4 seconds for a 40-move game. Many games of Quick Chess are lost on time by that amount or less. And this doesn't include ANY additional time for the cognitive delay needed to find, evaluate and choose from among candidate moves. Quick Chess definitely favors the young from these perspectives. Experience better be worth something or the old dudes are in big trouble.

It seems very logical/normal to me that anyone would play better chess given more time per move, so why shouldnt one's online rating be better than one's live chess rating ? There is also the added benefit that in online (turn based play ) you can use books and databases which should also increase results/rating.
I agree...
Me to

The question as a whole does not make sense because the first premise cannot be true unless the scales; the minima and maxima, start at different numbers. Excluding differences in scales and ranges some otb will be higher than cc while other otb will be lower than cc. All the ratings are matters of performance; not so?
Indiviuals members are most able to answer the question for themselves. Perhaps the cogent issue mentioned is the time pressure. Some perform better under time pressure, to others time pressure is stress that is only distracting.
I have done better at otb because at home by my computer I'm constantly dealing with other issues and projects. To compensate for that I take up the
Tactics Trainer and Chess Mentor.
I agree with all your points EXCEPT for their effect on the average Online rating. They certainly affect INDIVIDUAL Online ratings. They certainly affect the overall strength of play of the entire group. But the overall strength of the group does NOT raise the overall rating of a group. Only the influx of rating points greater than the efflux of rating points - due either to a ratings formula which has the capacity or tendency for inflation, or an accumulation of rating points generated by the the exodus of lower-rated people. Indeed, that's precisely the spectrum of player I would expect to depart from the pool: lower-rated, less successful players.
Perhaps, I'm debating the wrong point, however.
Average is mean of individual ratings, or not?
What do you mean by "overall strength of a group" and how do you calculate it, except from the limits and the average?
I think we are talking at cross-purposes...