It's been speculated on some Trek web sites that the Enterprise under Pike's command was somewhat smaller then it would be during Kirk's command.yeah ur right I was just thinking about those on watch. didn't think about the sections. so yeah that could be a Pike era crew make up.
The Connie has 14 different labs on board, so you could estimate 1 "officer" and, say, 2 "techs" per lab/shift, so an additional 42/shift x 4 shifts = 168 crew...which is problematic for a Pike era ship that is supposed to only have ~230 crew total.
You mixed up your numbers d_d1, it's 203.
James