Accelerating Discovery

Orthogonal Comparison ◾ 113

Recall(BH)

=

BHr/t

(9.6)

Another way to think of recall(BH) is as the reduction of recall(B) by

the amount of recall(H):

Recall(BH)

=

Recall(B)* Recall(H)

= (Br/t)*(Hr/t)

= Br * Hr/(t * t)

(9.7)

Combining Equation9.6 with Equation9.7 yields:

BHr/t = Br * Hr/( t * t)

(9.8)

which becomes

BHr = Br * Hr/t

(9.9)

Precision(BH) = BHr/BH

(9.10)

Combining Equations9.9 and 9.5 with Equation9.10 produces

Precision(BH)

=

Br * Hr * N/(t *B* H)

(9.11)

Note that in the special case where t = B*H/N (the expected value),

Precision = Br * Hr/t * t = Recall

As an example of the power of this approach to increase precision

without causing serious degradation in recall, suppose B and H queries

both have 90% recall, but only 10% precisio ...