I thought by "blue build" meant all items from the blue color, and "purple build" meant all items from the purple color.

I'm gonna make other small guide about champions and write more in this guide after.

the reason i( and actually most people) prefer blade of the ruined king on jax is that the current meta has made health stacking cheaper and BOTrk counters health.

On varus now, an AS/AP build was viable in season 2, i haven't tried it in S3, though. In any case, he is not as strong as a pure adc now.

Now on what hybrid means...i consider hybrid any champ that goes AS/AP/AD stacking items like Nashor's Tooth, Hextech Gunblade and Guinsoo's Rageblade.
The reason that i don't think it's any champ that benefits from more than one source of stats is that almost any champ will buy a defense item. Even adcs/marksmen could be called hybrids this way beause of the one defense item they often rush...but they're called marksmen/adcs.

What is a hybrid can be discussed and subject to debate maybe? In my point of view, it's only a character which will benefit's from more than only one source of damage. In this case, Katarina is maybe not a real hybrid because boosting her ad still boost mainly her spell's?

Jax benefit's from Blade of the Ruined King (which give him a nice physical damage boost), but he deal also a great amount of magical damage with his skills and passive. An other exemple is Varus which deal great physical damage while being able to deal good magical damage too. Blade of the Ruined King will boost his auto-attack a lot. Maybe a Liandry's Torment could possibly give him a nice boost to the proc of his Blighted Quiver? This boost his Magical damage with an on hit effect, that's true. But it will still result in boosting his magical damage and maybe making him hybrid?

the hybrid is a role/build that doesn't fit in the current meta- and with hybrid i mean the classic AP/AS and maybe also AD build with items like Nashor's Tooth and Hextech Gunblade. The reason is that most champions who in paper seem to benefit from these stats, in game have really better choices. A Jax for example might have lots of AP ratios and scale with AS but Blade of the Ruined King is simply better on him than Hextech Gunblade since it counters hp and it gives overall more damage output due to ASPD on which he really relies on. Almost same yields for Kayle where on hit items like Wit's End or Blade of the Ruined King have great impact on her. She can follow a hybrid build however and teemo does so as well, but they are possibly the only exceptions.
Hybrid builds are limited nowadays.

1. In the chapter with the comparison between tankiness + damage built vs ad/ap hybrid, the point is than both want to be "versatile". I will rewrite this chapter, I'm shooting idea and brain-storming for now.

2. yea... That will be great if you can talk about which set than I talk you don't find effective. Otherwise, tell why this isn't effective anymore? (I agree than it's really treaky to build pure hybrid).

1. tankiness + damage built champions are called offtanks/ bruisers/ tanky dps etc. depending on how the deal the damage and how you approach the whole thing.

2. THE REAL HYBRID IS LOST... On-hit builds are still good but this isn't hybrid- the time when one played jax, nidalee , teemo , kayle hybrid are over- the builds might look similar with some old- school hybrid builds but they're just on-hit ones.