Randy Quaid's character in ID4 is an unlikely hero. Will Smith's, not so much.
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An unlikely hero is someone who doesn't want to be or isn't someone you'd think of being a hero who becomes a hero in spite of that. Will Smith's character in ID4 is an Air Force pilot, alone already a pretty heroic thing. Will Smith is not an unlikely heron in ID4. That probably better describes Jeff Goldblum's character who isn't representative as a hero, isn't heroic but ends up doing a heroic thing.
An unlikely hero isn't someone who ends up being a hero in spite of the odds against him or his original lot in life, since that would pretty much describe every movie hero ever.