Average Time per Move

Having just read the FAQ:http://support.chess.com/index.php?_m=knowledgebase&_a=viewarticle&kbarticleid=710

I am slightly disappointed that the average time per move stat seems to be based on the whole history of every move you have played on your account.

The problem with the current system is that your average time per move is so intransient. If you have been playing on the site for a long time, and change your playing habits, so that you become more or less active, this never truly gets reflected.

My suggestion is for the average time per move stat to be based on your last months moves, and thus only to be updated once a month.

Note: ideally I would prefer a system which worked, on say, your last 500 moves, but as a computer programmer myself, I realise this would require 500 stored data points for each account - which seems a little over the top - hence my alternate suggestion.

Games last more than a month. This stat has to be at least a year to account for the change in online behaviour of students, golfers, ...

It wouldn't matter since we're not talking about the time-out ratio. With the 'time per move' statistic, an average of a week or a month would suffice in telling your opponent your approximate speed of play.

Not if your opponent has only played a few (or none) games in the last month. I quit CC for the summer, 'cause I'm usually not at a computer. In September, I wouldn't have a time per move stat, even though I'm a pretty active player September-March.

storing 500 data points and averaging uses the concept of moving average. We can use auto-recursive which statistically produce the similar result without any storage points.

I really like the concept of having the average speed reflecting the current activity of the player.

We could have both, one shown more clearly.

If you had made no moves in the previous month, then by default, it could just keep your current move speed. I'm sure the devs could come up with something practical that could work.

I would just like the time per move stat to be more reflective of your current move rate. This is especially important, because some tournaments use this stat to restrict entry.

Actually it is possible to make an effective moving average storing only two pieces of data:

y = current average time (in seconds)

n = number of moves made (max 500).

A new move is made in x seconds,

If n<500, then the average is just calculated as usual:

Y = (y * n + x) / (n + 1)

N = n + 1

If n=500, then the new average is calculated as follows:

Y = (y * 499 + x) / 500

This method does not give you exactly the same results as a proper moving average based on a certain number of data points. I believe, the average would be a little more "sluggish", though it would still respond pretty rapidly to change in play rate.

This is called auto-recursive, All you need is the average speed and new instantaneous speed. Statistically(mean of the estimated average) it gives the same result.

And this will address the concern of Puchiko

Ah ok, and I thought I'd just had a flash of inspiration!

I never did like statistics, I did my degree mostly in Pure Mathematics: Number Theory, Galois Theory, Topology etc.

This "auto-recursive" method does give slightly different results though. Imagine a new player makes 250 moves at exactly 1 day per move. Then makes a further 250 moves at 2 hours per move. In both cases their average now is 13 hours per move.

Now suppose they make a further 250 moves at exactly 2 hours per move. With a moving average over 500 data points all their slow moves have "dropped" off, giving them an average of exactly 2 hours.

With the "auto-recursive" method their average will still be greater than 2 hours.

In my muddled brain, it somehow reminds me of momentum/inertia.

But I think we are both agreed that the auto-recursive method is the way to go!

Please can we have an opinion from someone from chess.com?

you are right. thats why I used the term estimated average. I should of used expected average.

The given rating is estimated value of the true rating. When you play continuously your true rating is unaffected. But the estimated rating changes with results of every game and oscillates close to your true rating.

Similarly the average speed is estimated one. Average of 'N' number will give you an estimated average speed with an expected variance (or tolerance level). The variance reflects the possible differnce between true speed and estimated average speed.

The variance is same when the average speed is computed by "moving average" or "auto-recursive" (some derivation based on exponential window and rectangular window which I do not recollect now), however the estimated average speed varies between them.

That's why the results are statistically same.

:)

Rather than start another thread...anyone noticed that the time per move stat doesn't seem to be working atm...mine is frozen at 2 h 30 m and has done for sometime even though I am definitely slowing down...

@DJAbacus: Have patience man, it will change 

Oh, it did already, you now have an average time per move of 5h 30min, congrats! See what 3 years can do.

Yeah, the average of your lifetime moves currently used is ridiculous, it is very hard to change if you have already played a boatload of games. Something that weighs recent moves heavier is sorely missed.