Trump's statement could have been interpreted in two different ways. One, Politifact's interpretation, is that he draws bigger crowds than Beyonce and Jay-Z at their concerts and another is that his rallies are bigger than Hillary's rallies where Beyonce/Jay-Z performed. I don't know if the second interpretation is true or not (as I haven't done the research), but the whichever one you choose to analyze shows your bias. Probably most Clinton-leaning folks would pick the first interpretation of Trump's statement and most Trump-leaning folks would pick the second. So from the perspective of a Trump supporter Politifact looks biased, but from your perspective they're an impartial fact checker.

The point is THEY CITE THEIR SOURCES and lay out their analysis showing you exactly how they came to their conclusions. So the end result is the reader is more informed than before.

Also, Politifact sanely sticks to the common sense meanings of English words. Your interpretation of "bigger crowds than Beyonce and Jay-Z at Hillary's rallies" adds a qualifier beyond what was in the original quote.

Except that what Trump originally said was: "She's not getting any crowds so she gets Beyoncé and Jay Z, I like them, I like them and you know that they do, I get bigger crowds then they do. It's true. I get far bigger crowds," referring to a Clinton rally a couple of days earlier headlined by them. It was Politifact that edited out this reference to Clinton's rallies, starting their clip from his speech not just in the middle of a sentence but the middle of a word. They don't give readers an easy way to find the uncut version either - I'd have to find and dig through a video of the entire speech to link it here.

NBC's fact check provides better context despite being far shorter and not citing a single source: http://www.nbcnews.com/card/not-even-close-trump-said-he-dra... The stuff Politifact cited is easy to check even without the citations, but their omissions are much harder to spot.

Bias can appear both in what facts they decide to cover and in how they cover it. The first part is the one people usually ignore and the easiest to hide. You can just fact check one person on their every sentence and not fact check the opponent on their every sentence. You can also decide to only fact check mostly true or true statements for one person and mostly false or false statements for the other person. You'd be performing proper fact checking most of the time, but you'd be helping one person more than the other.