[gjfeldman]

I wrote a program to randomly deal a million hands to see what the statistics are for best hand tournaments. The results are shown in the two graphs below, one for the the best hand and one for the best hand partnership. Each shows the percentage of the time for getting HCP and total points. The total point count is basic with no corrections (e.g. honors in a short suit, partner's suit, etc.).




Some conclusions:
The most common HCP for the best hand is 14 and the average is 15.1; the most common total points is 16 and the average is 16.7. The same numbers for the best hand partnership are HCP: 23 and 23.4, and total points 26 and 26.6.

If you take an opening hand to be 13+ total points, then you will get an opening hand 97.4% of the time. If you take game to be 26+ total points, then the your partnership will get game 60.4% of the time.

Your opponents will have more HCP than you 11.2% of the time, the same number (20) 8.2% of the time, and fewer HCP as you 79.6% of the time.

[dsLawsd]

Yes, it is a bidders game.
Interesting data.