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Though yes, Sonic's the fastest runner alive, not Shadow.
Also, in Sonic Generations during the rival battle with Shadow (on the console version), if you do a homing attack on Shadow and then boost or by any other means get way ahead of Shadow while boosting, Shadow can boost at much higher speeds than Sonic, catching up with him in mere seconds if Sonic did the homing attack thing. But still, Shadow doesn't run while boosting, he just... flies?
He keeps up with Sonic by using Chaos Control with an emerald (as explained in pretty much the first moment sonic ever sees him in SA2.)
So, Shadow doesn't move fast at all. He either teleports or bends time aorund him to be slower, his actual movement is no faster than Tails or Knuckles. He only SEEMS to move faster via manipulation of time and space.
I.E. He beats Sonic in a race by making Sonic move slower, NOT by moving faster than Sonic.
One, No his shoes don't help much. If they do, it's not a noteable amount. Sure, that one card from Sonic battle says they do, but Sonic battle IIRC is not canon, and that information runs in direct contradiction to information from Sonic Adventure 2, a canon main series game. SA2 info holds more weight than Battle becase of this. SA2 said it's through use of Chaos energy, thus I think that info takes priority.
Other issue, Game Theory is a ♥♥♥♥♥♥♥♥ show. It applies math to things clearly not in scale (which means the results are going to be meaningless. If you're going to use math to measure something, every single element of the equation must be in scale, otherwise all results are garbage. Game Theory is a terrible show.)
Final issue. You said that Sonic and Shadow never had a full on, no holds barred race.
This is also incorrect. The Sonic VS Shadow Race/Battle on space colony arc that served as the last boss of the Hero/Dark campaigns in Sonic Adventure 2. That battle is exactly the kind of battle you are describing. If you run full pelt without much fighting, they run at approx. the same speed. I believe that their running speeds are identical in the game code anyaway, so it's difficult to tell.
Point is, SA2 explicitly stated how Shadow moves so fast, Sonic Battle is a non-canon spin-off, and jet shoes couldn't possibly boost his speed that much. They could never generate the thrust, and a main series, canon game has already explicitly stated that his "speed" comes from the Chaos Emerald, so I don't see that as being up for debate.
Really. it seems like lore and things told to us are the only reliable sources of information.