Badgers are known to surplus kill chickens and ducks when they are roosting in their pens, just like other mustelids, cats and dogs. However with the limited info available in this example it could be anything, its impossible to say without photos of the pen, bodies, field signs etc.
No offence to the OP but threads like this are impossible to answer all you can do is speculate several potential predators, a fox is most likely but that doesnt mean it wasnt a mink or a badger or an otter or cat etc....... No bodies makes it very hard to judge as you have no kill method, but could speculate more likely fox as badgers habitually feed at the kill site so you would expect some evidence. Surplus killing usually involves prey being left which is slightly odd here, although could be a fox with young returning and caching the ducks elsewhere.
Why did he think badger?