Harmonic mean

The Expected F1 (EF1) is the harmonic mean of expected Precision and Recall. Expected Precision (EP) is calculated based on the uniform utility function and the posterior probability for each spelling variation your speller generates for each query. To be more specific, suppose for query q your system generates spelling variations C(q)={ci,i=1,2,…,Nq} with posterior probabilities P(ci│q). Let S(q) denote the set of plausible spelling variations annotated by the human experts for query q, and Ip(c,q)=1 if c∈S(q),0 otherwise. Given a query set Q, the Expected Precision is defined as

Note that if |S(q)| = 1 for all q, EP reduces to the well known Mean Reciprocal Rank (MRR) metric if

Similarly, we define a utility function IR(C(q),a)=1 if a∈C(q) for a∈S(q), 0 otherwise. The Expected Recall (ER) is defined as

and 1/EF1 = 0.5*(1/EP+1/ER). 
Pasted from <http://web-ngram.research.microsoft.com/spellerchallenge/Rules.aspx>