I take it that means the quarterstaff is right out? (Well, either that or it’s limited to guys who keep shouting NOT GOOD, NOT GOOD, NOT GOOD, NOT GOOD!)
They’re disallowed for a bunch of reasons, actually… you can’t trip people, for one, and a quarterstaff is basically a giant crowbar. For a while, you couldn’t swing a two-handed weapon through a greater than 45 degree arc. And people felt for a long time that they were recreating honorable knightly combat, and the quarterstaff seemed a bit pedestrian.
I read this the wrong way round the first time (I thought you were saying that the person who is struck can declare it “not sufficient”) and was imagining the Black Knight:
“Oof! Not sufficient!”
“Ow! Still not sufficient!”
“URGH! NOT…[gasp]… SUFFICIENT!”
“ARRRRGH! What do you mean, “sufficient”? I still have my other arm!”
etc.
As to the OP, snooker has already been mentioned where players certainly do call fouls on themselves if the referee doesn’t spot it - in fact, there was a bit of controversy recently when a player apparently failed to do so and “got away with it”. Another example, though it (also) stretches the definition of “sport”, is croquet, where both players are designated by the laws as joint referees of the game, and even if an independent referee is called to watch a particular shot (it’s rare for the referee to be present for the whole game), this does not absolve the striker from declaring what they believe to be a fault they have committed.
Translation: Ball was caught before it hit the ground, so batter is out if it came off his bat, but not if off his body. Though it’s hard for others to tell, batter knows he just barely “tipped” the ball with his bat - he should thus declare himself out.
Occasionally, a cricket fielder who appears to have made a catch will declare that he didn’t quite - e.g. the ball touched the ground before it was fully controlled. But this seems far from universal.
IIRC, in the earliest days of professional beach volleyball, players called fouls (like touching the net) on themselves.
That, or THANK YOU SIR MAY I HAVE ANOTHER!
In pickup games of basketball, you’re traditionally supposed to call your own fouls.
Actually, yeah, that is how it works: blows are counted by the person struck, and if he thinks it’s light, he says so.
His opponent will then hit him harder.
For most people, there’s a point of diminishing returns here.