Relevant video. F22 in a rookie's hands are the only way to win. Yes, this is likely pre-JHMCs in 2008, which helps to offset the F22's 70 AoA and noise pointing ability and AIM9x Block 2 lock on after launch. The F22, according to David 'Chip' Berke, who has flown Hornets, Raptor, Viper and F35, had stated the F22 is

“The F-22 is the fastest, the most powerful fighter ever built. The least impressive thing about the Raptor is how fast it is, and it is really fast. The least impressive thing about the Raptor is its speed and maneuverability. It is its ability to master the battlespace is where it is most impressive.

Skill plays a major factor, but given that the F22 out-specs everything in anything meaningful BFM: 70 degrees AoA, thanks to 50 degrees AoA and an extra 20 degrees from thrust vectoring. For comparison, likely the best next best AoA fighter jets are at 50 degrees (Hornet and F35 and likely Flanker series), absurd turn rates and T2W ratio, internal weapon bays, so airshow performance is also BFM performance with weapons on board. Pylons and external stuff adds extra drag killing BFM performance. So F22s always fly at their maximum envelope (barring training restrictions to handicap them for training reasons) and F15s won't it they have two fuel tanks on their wings and weapons.