I doud't very much if BA gets involved until the last stage. The whole point of outsourcing is so they don't have to commit huge amounts of resources to the whole thing. The sifting of the initial applications is a huge task.
I suspect there is an initial computer sweep through to weed out those that don't meet the min education, right to work etc. Then it will be into the schools to see what's left. The it will be human opinion if you get through to the next stage.
The schools will only be able to process through to the next stage x number of people. So the standard required through to the next stage will vary between schools depending on the quality of the bulk that apply to them.
There is so many variables which can come into personal choice with a lot to do with the person reading the application. I know that when I read a CV rugby players and military service stand out to me. Football has the opposite effect.
So there will be a base line of what they are looking for, but there will be an element of luck of who your CV lands in front of.