The likelihood of a hand containing a certain number of high card points is plotted in the graphs below:

The following tables summarize the likelihoods of a hand holding a certain range of high card points.

Weak Count (0 to 11 HCPs) - 65.3%
      •   0 pts (Yarborough) - 0.40%
      •   1 to 5 pts - 14.00%
      •   6 to 9 pts - 32.83%
      •   10 to 11 pts - 18.35%

Opening Count (12 to 21 HCPs) - 34.39%
      •   12 to 14 pts - 20.63%
      •   15 to 17 pts - 10.10%
      •   18 to 19 pts - 2.64%
      •   20 to 21 pts - 1.02%

Strong Count (22+ HCPs) - 0.42%
        •   22 to 24 pts - 0.38%
        •   25 to 27 pts - 0.04%

Hand Shape

The shape of a hand is generally described as X-X-X-X (i.e. the number of cards in each suit). The accompanying table lists the 10 most frequent hand shapes and their frequency of occurrence.

These 10 hand shapes account for 91.1% of all hands.

Note that 3 of the top 5 hand shapes (with yellow background) are described as "balanced hands", and account for 47.6% of hand distributions.

Suit Length

The accompanying table lists the longest suit lengths and their frequency of occurrence. These 5 maximum suit lengths account for 99.97% of all hands.
   •  Note: a 5-card suit is more frequent than a 4-card suit.
   •  Note: a 6-card suit (used in "weak 2" bids) is almost 5 times more frequent than a 7-card suit (used in "pre-empt bids).