Did you go and see?
with a bit ( Biiig!!!) of luck all directories may still be intact, that is their content still bear their names... only you have to guess what directory it was and give back its correct name and do the next one...
for the files directly in /var its less obvious...
(I happen to have been through such a mess (was /usr) many years ago and I had backups but without /usr it wasnt of much help... and yes I managed to get enough things right to use the box but unlucky the restore command and out of order (one of those tricky corrupted files in lost+found I could not get back) but copied later from another box finally managed to restore...
Well it has learnt you that under UX you cannot live without backups...

Good luck
&All the best