Actually doing a BLAST search in the human genome for a 100 bp perfect match, I get a bit score of 194 bits (calculating from the E score and assuming a target genome size of 3e9). For this scenario, the bit score is clearly not a good estimator of the FI as you have defined it. It’s not because the two are measuring fundamentally different things. The bit score assesses the probability of a specific sequence by chance, with no reference to the other sequences that could perform the same function, while FI represents the probability of finding a sequence with equivalent function.
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