Just to add to what Celtie said: don't just look at the minimum requirements - also look at the "usual offer" per subject.
Ds met (and exceeded, but not by much) the minimum requirements for Edinburgh and will exceed by a long way the "usual offer" once you add in the AHs and extra Higher (which ironically is the only one that is relevant to although not compulsory the subject
) (And will have got an excellent reference and predictions from the school).
The positive is that they were very late in responding, so ds, who already had two Unconditionals (from Aberdeen and Strathclyde) and was expecting, if he got an offer from Edinburgh, it to be a Conditional, kept working hard at school. So by the time he got the rejection (and went to the Offer Holders Day at Aberdeen which made him really happy about choosing there over Strathclyde), he'd already done most of the work for the year and didn't see the point of wasting the effort. He therefore never suffered from the dreaded disease "Unconditionalitis" 
....Although he has taken his foot off the gas for his AH Physics
as it's the day before his (crashed) Modern Studies Higher (the former no longer relevant for his degree and the latter the subject he is passionate about and which is relevant to his degree)
(For context, ds changed his mind about what he wanted to do over last summer: from Maths/Physics/Astrophysics, with last year's Highers and this year's AHs structured around that, to International Relations
Fortunately he'd already starting crashing Modern Studies Higher
)