Trial by combat was only abolished in England in 1819, after the much-publicized case of Ashford v Thornton in which the defendant successfully called for it. (No combat took place - the plaintiff withdrew rather than fight the much larger defendant.)
Could not a man with a familiar dog, perhaps a hunting animal, the property of a rival, cause it to rise against a particular person at a signal? I suspect the 'friend' of manufacturing the entire event, being the murderer himself. We have only his word on the history of the dog. He may have assumed its ownership upon the killing of the real owner; he was aware of the curious tradition of combat; he contrived a cute storey of animal loyalty to cover his vile act and misdirect attention onto another for the crime.
Depends on the dog. And the man. And the cudgel. Kidding aside, dogs weren't bred to be gentle house pets back then. Think something closer to a domesticated wolf.
The Pinterest link to the statue submitted earlier (https://news.ycombinator.com/item?id=11049681), if it's supposed to be a depiction, makes the dog look pretty damn big by today's standards. I would not fancy my chances against it with just a cudgel... :)
I don't think it's even close. 9 times out of 10, a man with a cudgel should be destroyed by a large dog (especially one much closer to its wolf ancestry).
Even now, watching my very gentle Golden Retriever have an exuberant running fit, it's clear that dogs are much more agile than humans. All it takes is one miss of that cudgel, and teeth are locked in on the human's delicate skin, cutting in with hundreds of pounds of pressure.
If you can stand a lot of pain long enough. If the dog is determined and has jaw muscles and bones enough to crush your arm you might not be able to focus even enough through the pain to hit the dog even once. My gentle mixed breed refuge (who is roughly the same size as the dog depicted for this story) dog uses his back molars through rapidly bite through bone (and he just splits the few big dog Kongs we tried in half to get the food out) and that is when he is not angry or hungry; when angered I think the splintering of your arm would be enough to make you drop your stick in the other arm's hand.
Or clever. My associate was running from the police, had an Alsatian set upon him. He let it grab his arm then picked it up and snapped its spine over his knee and then fled.
I've had a dog set on me in a street fight. It grabbed my sleeve so I ran it its owner with it attached. He fled.
As for the cudgel, poor weapon on close combat. If you find yourself with a swinging weapon, use it like a spike, not a bat.
I wouldn't necessarily call that an advantage, or a disadvantage for that matter. The kind of person who is locked up by fear in a fight likely hasn't had enough training or experience to win the fight anyway.
Judiciary combat probably wasn't that common in the late 1300s, although it still existed.