Originally Posted by
orbitmic
No actually, that probability of someone not getting their first choice will increase. The key is that not getting your first choice is not random error but sampling error, ie BA actually know what proportion of people tend to choose the beef, chicken, etc dishes and organise loads accordingly (they don't just take, say, 5 of each, but maybe 7 beef, 4 chicken, 2 salads, etc).
If all BA F customers were flying on one gigantic first class flight at the same time, BA's prediction would thus be extremely accurate and the proportion not getting their choice would be extremely low. However, as you reduce the sample size (which is what you do when most people have chosen their main through pre-order and you only cater for the rest), sampling error increases and so does the 'risk' that the sample will not be representative of the whole will increase accordingly.
Good point orbitmic. I admit I used an oversimplified assumption to make my argument short. But my original point still holds. The sampling error
difference between 20 and 40 people (assume 20 out of 40 people in CW pre-order) is negligible. In fact sampling error is precisely an argument why airline should make people pre-order because that is only way for them to accurately making predictions for a small sample size (a CW cabin of 40 for example). As you said, if it's just one large premium cabin per year, then all the airline analytics would be right on the mark.