[relknes]

The average points per hand is easy to calculate, because the total points in every deal is the same. There are 40 points and 4 players, so 10 points each... easy.
It is much more difficult, however, to calculate the average number of "Playing tricks" per hand, because a deal dosn't always (in fact dosn't usually) add to 13. The more distributional the hands, the more playing tricks there tend to be. The most extreeme example would of course be where everyone is dealt a 13 card suit... each player has 13 playing tricks, for 52 total.
Likewise, the "Loosing trick count" dosn't have a cirtain number that it always adds to. The LTC tends to drop as the hands become more distributional. In the above (extreeme) example, none of the players would have a single loosing trick, while each player having AKQJ of one suit and xxx of all the others would lead to a total LTC of 36.
Now, these three hand evaluations are not independant of each other. It is impossible to have 12 playing tricks with only 4 points, for instance.
So my first question is, what is the average number of playing tricks for a hand, and what is the average losing trick count for a hand? My intuition tells me that the average playing tricks should be greater than 3.25 and the average losing trick count should be less than 9.75, since both evaluations seem to assume that you are playing in your best suit, but I could be wrong.
My second question is, how related are these three evaluations? Clearly there is not a direct dependance, but nor are they totally independant variables.

[manudude03]

I haven't done any kind of statistical research on these, but from experience, I think the average playing tricks (playing in your best suit) is about 4.5, the average LTC is 8. The evaluations are reasonably closely related, especially if you use working points (where you discount stiff K/Q/J etc).

These are only estimates and not based on any formal analysis.

[BillHiggin]

In the past there was a time when I clearly had too much time on my hands. I calculated the number of hands for each possible distribution and each losing trick count. From that exercise, I can state that the average raw losing trick count is 7.56. That would be consistent with the 4.5 playing tricks mentioned above (only under the limited conditions where the ltc rule of 24 has some validity).

[Zelandakh]

Culbertson's "Rule of 8" stated that the typical number of Honour Tricks (HT) per deal added up to approximately 8. Playing Tricks (PT) are roughly HT + distribution, where you add 1 for each card above 3 in your primary suit and 1 for each card above 4 in your secondary suit (and +1/2 PT) for a secondary 4 card suit. This is not completely accurate (for example an 8 card suit is 6PT rather than 5) but is a reasonable guide if that is the desire. So you can assign an amount of distributional PT to any deal and add 8 to get an approximation - do this for each deal pattern weighted for probability and you have your answer...well, sort of. The problem of course is that we have to play in the same suit as partner so we have to first choose a suit together and then use Responder's PT (which traditionally count shortage rather than length) for the dummy hand. Unfortunately I do not think there is a simply way of achieving this so you are probably stuck with the simple method which counts the PT for each hand in isolation from partner's.