Why these blast bitscores are low?

Question

[utsafar]

Hello. I have pBlasted a data set of peptide sequences of Arabidopsis thaliana vs it self. I have two issues about bitscore: 1. Considering BitRank = ( bitscore ) / ( 2 * ( length of alignment - gaps ) ), For hits that query and subject are the same (I call it Self hits) I expect that BitRank be higher than 1, but in almost 10% of Self hits BitRank is lower than 1. Why?
2. In Self hits I expect that longer sequences have higher bitscore. but as you see in the table, for example bitscore of Self hit of a protein with length 81 is higher than bitscore of Self hit of a protein with length 115. Why?

[Andrzej Zielezinski]

Bitscore in sequence alignment is calculated based on substitution scoring matrix. In BLASTp, the default matrix is BLOSUM62. You can see that different amino acid matches have different scores - for example, bitscore for the W-W match is 11 and bitscore for G-G is 6. That's way, it is possible that shorter sequence (e.g. WWW) will have larger bitscore than some longer sequences (e.g, GGGGG). You should now see that the formula you presented won't work.