Wait you failed to mention a few core aspects to the sheer numbers.
HP is more effective against mages than it is against AD's.
You fail to mention that EVERY one of those MR items give HP as well.
The only one of those three AD items that gives HP is Randuins.
Now if you are wondering why HP + MR more effective than HP + Armor
AD's can auto you for the AD that they have (minus the Armor Reduction %)
While Mages can Auto You (Unless it is Ziggs, Ori, or Zoe. With special cases of Spell Procs such as Viktor Q) They have the base amount of AD they normally would have had Reduced by Armor Reduction % with no armor pen.
Any mage Aside from Azir, Cass, Karthus, and Ryze. Have a set number of damage that they can do. For Any Given timeframe.
So a full build Syndra can only do Q W E R Auto Damage In the time frame of 4 Seconds.
Meanwhile any AD champion can do Q W E R Auto Damage in the same time frame. But if that AD has more than 1.5 Attack Speed. Its more of Q W E R Auto Auto. Before any bonus auto attack resets (such as Jax W or Trundle Q).
So the fact that you are not mentioning that MR + HP is more effective against mages is bullshit. A mage isn't suddenly going to get another 300-500 damage in that time frame from another auto or crit.
That is why mages are Front Loaded with damage now. Because if they don't get all of their damage out first they won't be able to get any of their damage out at all before a ADC or Zed or Talon or Rengar or Kha or Jax or Anyone that has burst can 1 shot them. Its problematic in itself.
ADC get deleted by Assassins and mages, mages get deleted by ADCs Assassins. Assassins get deleted by Mages and ADCs. Its just whenever Riot feels like this it the flavor of the patch. They stopped following the traditional Assassins > Mages > ADC > Tank > Assassin.