TailWag,

Anyone uncertain what a weighted harmonic mean is can easily look it up. Whereupon they will note that your formulas are not weighted.

The well-known fact that Betfair choose to inflate its matched bets figure by doubling them, will not alter the end result - as you yourself noted.

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Meanwhile anyone troubling to study the above might find this paradox about weighting cute:

http://en.wikipedia.org/wiki/Simpson%27s_paradox