This is my first build on this site and I still don't understand how this site even works so please don't bash me for anything stupid.

Boots : Anything you like

Why this over Mathematically Correct Pantheon?
I wanted a good mix of Mathematically Correct Pantheon and your usual Bruiser Pantheon. So I came up with this.

Can this build even compete with Mathematically Correct Pantheon in terms of damage?

Generally, yes it can. Here are some test results

vs no armor (yeah I know it isn't the best comparison for a vs ADC)

MC pantheon - 4.2k damage (no crit)
- 5.3k damage (crit)

This build - 4.5k

vs 3.5k hp 120 armor (more realistic to an average bruiser who opted for some/no armor)

MC pantheon - 3.9k (no crit)
- 4.8k (crit)
This build - 3.5k

vs 10k hp, 300 armor

MC Pantheon - 3k (no crit)
- 3.2k (crit)

This build - 3.3k

Now, you may see the number and go 'Yeah your build has lower damage'. Yes, even into no armor, you deal lesser amount of max damage. But the build isn't about that. Also, Mathematically Correct pantheon, in my opinion suffers from not being able to crit consistently. After some rough testing, I figured you would only crit about 1 out of 20 times. This, blocks the build from reaching maximum damage.

Now, in case of bruisers, you might get the feel that 'Mathematically Correct pantheon is inarguably better'.
In terms of damage, yes it is. But think about your average bruiser/skirmisher. Most of them have some sort of way to reduce/block damage. Camillie passive, Irelia W, Renekton/Nasus ult, Jax E/R... the list goes on.

Into these champions, prioritizing survivability over damage is essential to land the 1v1s against them. Having 850 more HP can easily make a huge difference, whereas on Mathematically Correct Pantheon, you might suffer by comboing at the wrong time and busting your load when these champions are at the pinnacle of their forms. This build is more forgiving.

Now, you may argue that 'Pantheon E solves that problem entirely'.
Yes I get that, but smart players will wait out your E until they unleash their damage on you. So having this extra HP can easily make a huge difference and give you the time to wait off their buffs and simply outdps them.

Against tanks, both the builds start scaling off, but this builds ends up with more damage and survivability. This build will be better into someone who builds more than 170 armor(that number is a wild guess but its a good approx.).

Also with MC pantheon you just outright overkill people so why not use that damage somewhere else, while maintaining the 'haha 1 shot funi' aspect of the build.

Well this is all I had to say. I hope you have fun with the build.

Edit : Eclipse is equally good in the build, just that it does a little bit less damage, but with more defensive stats(around 300 armor), eclipse is simply the better option.

Generally, eclipse is better as it provides more utility on pantheon than anything else. But Prowlers damage is high, almost being able to one shot everyone other than big health and armor heavy tanks, against which only eclipse can compete. Eclipse in general is lesser amount of damage, but if you are overkilling almost everything, it isn't as bad as prowlers in terms of damage.

It should be obvious, you shouldn't build any sort of armor pen as your ult passive already gives 30% pen. But armor reduction like Black Cleaver isn't bad as it stacks one after another and provides about 50% net armor penetration. It also gives so many valuable stats, which is the main reason you even purchase this item.

Well, that's it. hope you enjoy the build!