Item Updates & Jax
TL;DR: I made a spreadsheet detailing a level 13 Jax's damage and survivability with the item changes in two different builds: Triforce and BORK, and Gunblade and Rageblade
Introduction: Trinity Force and Blade of the Ruined King have been the dominant two damage items on Jax for a long time now, with Blade of the Ruined King being replaced by Hextech Gunblade in certain situations. There are several changes detailed in the preseason to these items, and after having done similar calculations previously, I have decided to once again discover the effective strengths and weaknesses of these items. The main things I was interested in were Damage Per Second, or how much damage a Jax with these items would do continuously attacking, and survivability, or how much damage a Jax with these items could take with his ultimate active, either over 8 seconds (the duration of his ultimate), or instantaneously, as in if an assassin tried to 100-0 him. I have attached a spreadsheet with my findings. Below are answers to some questions I expect people will have. At the very bottom are my conclusions based on the information.
Why Two Items, and Why These Items?: Proper building on Jax generally dictates that two damage are bought, then full tank, with the sixth item occasionally being used for more damage. A cursory glance into probuilds.net demonstrates the widespread use of this build, at least among high level players. Therefore, except in rare cases, DPS is maximized once the two item threshold is reached. For most of this Season, it has been standard to buy Trinity Force and Blade of the Ruined King (not necessarily in that order) both in order to maximize damage, and because the additional effects of the two items are very potent. In the preseason, however, both items are being nerfed (Trinity Force is more of a power shift, but it is mostly a nerf in regards to Jax), while Hextech Gunblade and Guinsoo's Rageblade, two items which Jax can make extremely effective use of all of their stats, are being buffed.
Why Level 13?: In addition to being the average level I estimate I am upon completion of these two items, this zone of levels is the best for testing any build not consisting of more than a few items because there are many games which do not last long enough to hit higher levels, and many decisive things happen at this point due to it (generally) being in the mid-game, meaning that it is extremely important to know effectiveness at this point.
Where did you get the information used?: All raw data was taken from the wiki, which (I have checked) is an accurate source for information such as stats and ability damage. Various formulas used, such as the calculation of attack speed and damage reduction due to armor, have also been taken from there. The only information not taken from the wiki, the new stats of the items, was taken from the patch notes, which you can read here.
Assumptions: These calculations assumed the Jax in question is continuously attacking a target, has full stacks of both his passive and Guinsoo's Rageblade where applicable, he is using all of his abilities on cooldown, and (I don't actually know if this is theoretically possible) he is proccing Sheen every time it is available. I do not factor in how quickly he will ramp up to full stacks because due to his W resetting his auto-attack he can do it in a very short amount of time, and because against a tanky champion the fight will last long enough so as not to matter, and against a squishy champion he will either burst them out or get kited, so it does not matter in that scenario either.
How did you calculate the damage of Blade of the Ruined King's Passive and Active?: I assumed they were being used against a target with 2000 health, since this is a good estimate of the health of most champions at that point in the game. DPS increases by 1 for every 33 more health the enemy has, so keep that in mind if you think it would make more sense for the value to be higher or lower. Since the passive is based on current health, I just halved it, as you will usually be taking someone down from 100% health to 0% health, resulting in a gradual, and almost perfectly mirrored, reduction of the bonus damage from 6% to 0%.
Your 'Survivability Over 8 Seconds' Values Look Way Too High: For survivability over 8 seconds, I took the heals per second value and multiplied it by 8 and added it to the health. This is obviously unrealistic since in a fight healing is going to be reduced by the opponent's resistances, and the Jax in question may be stunned for a few seconds, but it also doesn't factor in the invulnerability from E's dodge and stun (as for AP, keep in mind the dodge also avoids 25% of all AoE damage). This of course does not perfectly balance it out, far from it, but the over 8 seconds section was merely meant to demonstrate how much more powerful Hextech Gunblade and Guinsoo's Rageblade are in a prolonged fight compared to Trinity Force and Blade of the Ruined King, as far as surviving goes.
Conclusions: If these changes go through, based on raw numbers Hextech Gunblade and Guinsoo's Rageblade should be the optimal build on Jax because of how much they increase his survivability, at the cost of only a relatively small amount of DPS. These items would allow Jax to last much longer in fights, and after a fight he can heal up twice as fast than he would be able to with the other build. The builds would do comparable burst damage against a squishy due to the decreased damage Blade of the Ruined King's passive would deal, and against a tankier target the benefit of the sustain would outweigh the lack of the passive's damage. The only other things these items would lack would be movespeed from Phage and Blade of the Ruined King active, but due to the nature of Jax's burst (stunning a squishy as soon as he is on top of them) this is not exceptionally important. As far as chasing down champions with more limited mobility goes, Hextech Gunblade's active should be more than enough.
About the Author: I have been playing League of Legends since June of 2010 and played Jax more often than other champions. After the Jax rework, I fell in love with the champion and mained him through much of Season 3 and Season 4. I have played him less this season due to the shfting meta. As far as my rankings go, I was unranked in Season 1, Bronze in Season 2, Gold in Season 3, Platinum in Season 4, and Diamond this Season.
If you find any errors in my calculations, don't hesitate to let me know. Politeness is preferred obviously. Thank you!
Edit Log: Changed title for clarity.