saving my time a bit and not reading this entire thread, i will say that this method is flawed. the problem arises regarding the fact that a good 60% of the cast is unplayed because of their matchups vs the played characters. Sheik is not the best character in the game, but she is the counter to all those unplayed characters.
Once you start looking at the played characters you start seeing that sheik's matchups arent all that great. in the top tiers (Fox Marth Falco Sheik Peach) you see sheik's matchups are decent. fox and falco beat sheik, marth and sheik is fairly even though very slightly to sheik. sheik vs peach is a matchup i dont know too well. my only experience are sets between rob$ and wife and BigC vs Kels. both sets seemed very even. If you add in sheik's worst matchup, ice climbers, which have become one of the most popular characters recently, you see that sheik's overall tier ranking shouldn't be #1.
Fox on the other hand has no bad matchups. his worst two are marth and falco, which are both fairly even. Fox is the other reason that that 60% or so of the cast isnt being played. fox combos like mad and all aspects of his game (edge game, sheild pressure, control, ect ect) are all the best or one of the best.
Marth, who has the best range and priority in the game, is another character that comes to mind when you think of the best. His control and spacing can be the best in the game if used properly. His combos are also very good, which get led into by his defensive fair spacing and lead into kill moves (fsmash, dair, sheildbreaker) or edgeguarding. His biggest weakness is when you get in close on him, which is what sheik is very good at and why she was considered a bad matchup for him. the problem is, marth also combos sheik like mad and with moderate mindgames you can beat her approach.
Falco is the more recently popular character. In the last official tier list people greatly overestimated falco as being the 2nd best character. Falco is good, however he instantly became as king i think it was described it, the new sheik. everybody instantly learned how to beat falco in every way because he was instantly so popular. what happened was that he was really good for a short period of time then really bad. he is still definitely in the top few at least though. His combos are fairly good, a shine gets most characters instantly up to 50%+. his biggest downfall is just about any time he is off the stage is will probably die, not only due to the fact that his recovery is short, but also that it doesnt defend him at all (so he has to be near to the stage but completely unprotected). if he sideb's you can jab or simply punish the lag. sweetspot sideb gets dsmash/fsmash/whatever. any time he upb's he should die.
the last one is peach, but because this is taking a long time and i figure nobody is even reading this far, ill shorten it up. peach is good. dsmash, FC. nuff said.
basically, what im trying to say is that your method is flawed due to the fact that you are assuming every character gets played evenly. the fact is that there isnt as many YL Pikachus and roys as there are sheiks marths and foxs. to assume that gives the characters that dominate them and make them unreasonable tournament characters an unrealistic teir listing.