The Real Stats
Mobafire's table above doesn't calculate additional bonuses from items (like Bloodthirster) and stat increases from masteries. Here's the real calculations for the complete build:
(These stats were calculated from LOLCrafter, a droid app)
Total Cost of Items: 15045
Attk Spd: 1.2
Crit Chance: 18%
Crit DMG: 210%
Armor Pen: 31|50%
DMG reduction against basic attacks: -10%
Heavy Armor Penetration because he's an AD champ.
Armor (static) for early game advantage.
Magic Resist (dynamic) for late game survival. I use to have Armor (static) for glyphs but 24 MR late game is a better choice.
If there was a set of points I could apply elsewhere, it would be Alacrity (attack speed) but there is no other viable option at the trunk of the tree. Havoc (damage increase) is tempting but three points for 1.5% damage is better spent in the defense tree to get that +30 health (early game pwnge). Also, Leathality (crit damage) with an 18% crit chance is equivilent to a 1.5% overall damage increase. However, you won't see that 18% until you buy your last item.
In the defense tree, that little bit of armor and magic resist are more early game adavantage. If you wanted to go three in armor and one in magic resist, it wouldn't be a terrible idea. Most AP champs are not going to be a huge threat early game and the majority of damage dealt early game is going to be from auto-attack (attack damage). The 30 health also gives you the early game edge. How many times have you gotten out of a fight with a sliver of health? It grants you that extra hit and potentially another Spear Shot.
Pantheons biggest problem early game is his mana. It runs out quickly with Spear Shot and takes forever to come back. Harassing enemies early game with Spear Shot is essential and, if you harass correctly, you should be throwing a spear every four seconds, at enemies of course. Grabbing Faerie Charm right out of the gate will keep the spears chuckin'. Plus, to execute the proper Pantheon kill combo (spear/stun/hss/chase/spear) takes 190 mana early game. A lot of people may disagree with this purchase, which is why I'm putting so much explanation into this 180g cost item, but Pantheon's Spear Shot harass is key to his success. Obviously, you build into Philosopher's Stone which grants you health regen (more lane sustainabilty) and 900 gold every 30 minutes. This increases your trickle income by approximately 39%. I usually sell this item when I build Frozen Mallet to make room.
For boots you want Ninja Tabi. The armor plus the general 10% damage decrease from basic attacks is huge against auto-attack champions like Yi. Otherwise, you can swap for Mercury treads if you're facing heavy AP. Tenacity is good in any game. However, you're going to get much more use out of Ninja's damage decrease, being that Pantheon is mid-to-close-range AD, than you would with tenacity. Ninja's will save your life more often.
For you first AD item, Last Whisper is cheaper than most common choices, has a decent AD increase, and the armor pen percentage scales throughout the game. The problem with trying to get Bloodthirster first is the BF sword. A cost of 1650g is always a hurdle and a wait and being able to buy it is dependent upon your performance which is dependent upon your build (vicious cycle). A pickaxe costs 975g, you can buy it in less time and you can start doing extra damage sooner. Last Whisper makes your build and your performce much more fluid.
Next is Bloodthirster. No one will argue against this weapon. Damage and Lifesteal that you can build up from 60AD/12LS to 100AD/20LS. This is one of Pantheons most obvious and essential purchases.
Maw of Malmortius is plain amazing. It completes Pantheon. Attack damage, magic resist, damage increase that scales to how much life you're missing (max +39 AD), and an automatic shield (400 AP absorb) from magic at 30% health remaining. I don't see many people use this item and I have no clue why. The 1 point in damage for 2.5% health is a 'cloak and dagger' and means that everytime you're hit you become stronger and it works well with your lifesteal. Enemies that are prepared to engage you 1v1 have the idea in their head that they can take you (obviously) but they aren't going to see the scaling damage until its too late. It's one more advantage and makes you an unanticipated threat. The magic shield is the other amazing game stopper. It's another unanticipated affect the enemy won't see coming. In addition, in a team fight, the enemy with the lowest health is going to be collectively targetted and, if you're that enemy, this affect will either get you the "out" you need to find safety or the time you need secure kills.
Frozen Hammer remedies Pantheon's squishiness. Pantheon's low health early game isn't too detrimental, but late game he's a target with a low swing count. You need the health to support your battle superiority and keep you in the fight longer. In addition, slowing your target's movement speed makes your stun even more powerful. Now, not only can you jump to your target and stun them - "IN YO FACE!" - you can slow them as well, thwarting their escape. "Come here, you ain't going nowhere!"
Atma's Impaler; the cherry on top. Most people here would buy Infinity edge, but I'm not as concerned with critical strikes. Even though Pantheon's spear has chance to crit, Pantheon is not an auto-attack champ. All of your damage comes from abilities which means Pantheon is not going to get as high as output with critical strikes than another champion might. Atma's grants you a decent amount of armor and damage based upon your max health which is synergetic with Frozen Mallet totalling +42.6 damage.
I don't believe in absolutes but this skill sequence is definitely absolute. Here's the order of priority:
Ultimate > Spear Shot > HSS > Stun (with the exception of level two, grab stun)
This does not mean on your third level you grab HSS because you don't have it. At level three, HSS is GARBAGE and not useful until it gets bonus damage from items anyway. The maximum damage for the first point of HSS, if you hit your target with all three strikes is a whopping 78 damage; not even a bar. For the same casting cost of 45 mana, put that point into Spear Shot to increase it to 105 from 65. You can cast Spear Shot 2.5 times in the time you can cast HSS once which totals 100 extra damage versus 78. An increase of 128%. FRACK! You only take HSS when you can't level Spear Shot anymore. Get those early game kills and sate your appetite! Nuff said.
Flash is just too good to not have with an offensive champion, especially Pantheon. You've all used it for outs and ambushes; easy peasy.
In regard to ignite, use it toward the end of a fight and not in the middle! If you use it in the middle, its just a flag to the enemy to run away with a reasonable amount of health. If you use it toward the end of a fight, it flags the enemy to run away when its too late.
Be diligent about your map awareness and ask your teammates to ping when enemy champs are at low health, so you can pick up those extra kills and allow your teammates to push lanes.
There is a two-step cast time to this ability. The first step is before the jump when you're actually casting the ability. During this time, you can choose to disengage the ability. So, if your target is moving around a lot, they're more prepared to run out of the affected area before you actually land. Pay attention and target between the enemy and their safety (tower) a little bit to maximize your chance of success. The second step is the time it takes to fall and hit. You may not know this, but during this time you can cast Spear Shot and as soon as you appear in the air it will activate, doubling the damage and allowing you to quickly follow up with stun.
Tips and Tricks
Using flash in tandem with Pantheon's mid-ranged abilities:
You just got out of a fight and your girl of a target is one Spear Shot away from death and is on the move back to base while his buddy is trailing to cover him. They stunned you during retreat leaving a huge gap between you and your target. You respond by chasing, flashing forward in range of the trailing champion, leaping and stunning that champion bringing you in Spear Shot range of your severely wounded prey. It's like using two flashes. Pure joy.
Keeping your lane enemy from leveling:
When soloing, as I said before, you should be harassing with Spear Shot. If you get your lane enemy down to a low enough hp count to where they won't come near you, you should be able to hang on the back side of their caster minions keeping the enemy champ out of experience range. Don't try to slaughter the minions so quickly either. Drag out the time they're not gaining experience by only last hitting minions. This will keep the enemy champ at low level and low maximum health. Eventually, they may come close enough for stun range for a kill. This tactic works best with non-ranged champs.
Countering stealth champs:
The nice thing about HSS is that you don't need to actually target your enemy. When they stealth out and try to run, save your HSS for that moment to get the kill.
Countering stealthed Teemo: if you're laning against Teemo, pay attention to where hes at before he stealths. You can HSS him and he can't move without revealing himself. Stay there and continue to HSS. If he decides to run, it's as easy as stun and spear shot to get the kill.
Countering stealthed Akali: Akali likes you in her stealth bubble. If you're diligent with Spear Shotting her when she appears and HSS her bubble, you can out DPS her. However, she's really good about jumping out of it and running when she knows she's losing. Pay attention and be ready to stun.
You're not going to be able to farm with HSS until late game, so save your mana for ganking. For the first half of the game, you have to focus on last hitting and Spear Shotting minions. For the last half, you can finally HSS crowds of them.