The core items on Singed, as echoed, are Rylai's and Rod of Ages. The Rod just is *** on him. HP, mana, hp from mana, and his poison scales ridiculously well from the AP. Rylai's buffs your HP even further (setting you up for powerful EHP from armor/MR stacking), powers that AP up even more, and then turns your poison trail into a doom trail via slowing.
Most games I'll rush a Philospher's Stone (way better due to the low cost now) which along with mana regen runes means I'm set for mana recovery. Obviously gets sold later.
If I am kicking ass and taking names early game, I rush Rylai's immediately after my Rod of Ages and boots. However, in more typical games it is far more important to grab a Chain Vest and Negatron Cloak to make your EHP viable. These two items, plus Mercury Treads, mean you will have over 100 armor and MR, which is enough to keep your armor/MR at 50+ after penetration, except in rare cases (ie Black Cleaver) or vs % penetration stacked with 20+ normal penetration.
Rushing the Rylai's serves two main purposes. The obvious main one is the slow. With cleanse, a trail of slow, 7.5% move speed bonus (Quints + Mastery), boots 2, and base 320, you are insanely tough to catch up to. If you pop Ghost, it's virtually impossible. Once you add on Force of Nature and possibly Lich Bane... well good luck being caught.
After finishing Rylai's, you want to focus on tanking. Guardian Angel, Randuin's Omen, Thornmail, Banshee's Veil, Abyssal Scepter, and Force of Nature are all viable choices. You should pick based on the enemy team of course, and versus a balanced team, you'll want 1 armor item (I count GA as armor, not MR) and 1 MR item. Against a lobsided team, you'll want 2 of one (and don't get both resist items earlier).
This leaves you with 1 item slot left to play with. Generally I will get another tanky item if I am the initiator on the team (often Guardian Angel, but any prior listed item, or Warmogs/Leviathan work for me). Leviathan is my favorite tank item if they aren't ever killing me unless my entire team dies. However, I tend to play on teams that have another tank who initiates better than me, or at least another tank to share duties with, which allows me to pick up additional AP. Zhonya's brings you to 325 AP. Archangel, unstacked, gives you +100 hp (another 250 if you somehow got it stacked up), infinite mana, and 272 AP (another 32 AP fully charged). Void Staff nets you only 230 AP, but nets more damage against high MR teams (and is a lot cheaper). Lichbane nets you 240 AP, an extra 91.8 hp (and some health regen via the mastery), a bit of burst damage, and sexy movement speed.
As a side note, especially due to how late you pick it up, getting Warmogs this late is ONLY good if you also have a Force of Nature. The result is that even before any stacks, you are netting 1920 raw hp from Rylai's/Rod/Warmogs. If I'm planning on this route, I'll usually grab Randuin's Omen for my armor, bringing the total up to 2220 raw hp. Additionally, you net 459 hp from his passive (including the 5% mana from the mastery), and he has a base hp of 1755. This nets you 4434 hp pre-warmog-stacks. Additionally your regeneration numbers are 17/5 (base), 55.1/5 (3% of max mana, mastery), +4% (mastery), 117.6/5 (40 + 1.75% max hp/5: FoN), 30/5 (warmogs), and 25/5 (omen). At 0 stacks, this is netting you 252.9 hp/5, or 50.5 hp/second. Fully stacked, you receive an additional 450 hp and 62.5 hp/5. The hp increase nets you another 7.9 hp/5 from FoN, giving you 72.4 hp/5, then 4% from the mastery increases it to 75.3 hp/5. This nets you, with a fully stacked Warmogs in the build, 4884 health and 328.8 hp/5 (65.76 hp/second). Considering you have 198 armor (93.6 base, 6 mastery, 99 omen) and 142 MR (35 base, 6 mastery, 76 FoN, 25 boots), you are looking at some ridiculous EHP regen. Even if they have 49% reduction (mastery + void staff), plus a runebook dedicated to penetration (15), AND you have -20 reduction (which can happen from several sources), you have 54.5 MR left, or a 35.3% reduction, meaning in the WORST CASE SCENARIO, you are recovering 508 EHP/second. And if it's a carry trying to kill you as they follow you through your poison as you flee (last whisper + 30 armor pen runes), you have 100.8 armor, which means 50.2% mitigation, or a whopping 657.6 EHP/second. Plus they are chasing you which hurts them and slows them. Plus a 20% chance each hit to slow their movement *and* attack speed by 25% for 3 seconds. End result is that it's hard to even die to a 5man gank unless they have multiple ignites. And all these numbers are before you even bother to activate your ultimate (which is only a 10% boost to your regeneration speed at that point).
Figured I'd double post to comment on a couple other specifics:
Never rush an Archangels. On ANYONE. Rush the tear, then chill. The 1000g recipe cost isn't worth it until you have at LEAST 50 AP off the passive or are in dire need of the mana regen. You should pick up mana regen scaling seals. That plus a tear (or philosopher stone) would solve your mana issues for the most part. Getting 50 AP from the passive means 1666 mana, which you won't have til level 18 really.
Your runes are totally random, probably due to not having fleshed the page out properly yet. My preference is scaling MR glyphs, scaling mana regen seals, magic penetration marks, and move speed quints. See my prior post (and the fact that MR is lower than armor) for an idea why I like the extra 24.3 MR at level 18.
Generally I prefer Cleanse over Flash on Singed. But I play very aggressive, and spend a lot of time pushing lanes (baiting). If both spells are ready, it is pretty much impossible to get a gank on Singed to work, which then means they have to chase through a slowing trail of poison to keep doing their damage, while your team moves in, ready to jump on them when they wind up down to half health just trying to kill you.
I used your masteries for a long time, but have truly fell in love with 0/9/21 instead. Again, it is because I bait. 15% penetration and 10 AP just isn't worth much, and Singed has very little need for CDR. 90% of his utility is from his poison and just soaking up hits. Poison stays on all teamfight, so cdr doesn't matter. Conversely, stacking the extra 3% mana as hp/5 means 11 health per second. That adds up pretty fast.
I have recently started playing some Singed in Ranked matches. I usually try to bring a friend with me in my solo ranked games, and bring them up to the lane. One of my favorite is Vlad + Singed, with the ultimate aoe slows and the awesome damage from both.
Currently incomplete, i still am working on them.
9x Mpene Marks
9x Hp/lvl Yellow --- 9x Mp5/lvl ---- 9x Dodge
9x Flat Cdr Blue
3x Mov. Speed ---- 3x Flat Hp Quints
9 offensive : Gotta get that 15 % Spell penetration !
17 Defensive : +6 to both types of Armor, 2% Dodge, Nimbleness (Omg pro with dodge runes) 60 Flat hp boost and improved Cleanse, also the needed -1 damage just to get down in the tree.
4 utility : Imp. Ghost and 10% Reduced Death time (You're a tank, you MAY die, even though i really don't die often with Singed.
Ghost : 40 % increased speed while moving through units. Do i need to say more?
Cleanse : As a tank, and one that needs to get straight to the carries to be allowed to fling them, i think cleanse has to be one of the most useful spells you can get as the cooldown is some sort of low.
Flash -- Exhaust : Could be useful for flings and slows, but... situational.
Fling, trail, trail, adhesive, trail, ulty, trail, fling, trail, fling, ulty, fling fling, adhesive, ulty, adh, adh.
I just love fling at level 1. Trail can get you that little damage needed on the minions, and adhesive needs to be there quickly enough, but does not really need to get maxed IMO.
I simply try to get people close enough to the tower, fling them in and slow the path in front of them. Never seems to fail with a decent partner in your lane.
Mana crystal + 1 of each potions
Catalyst + boots
Either get swift boots if the farming is slow or get RoA (Swift is a lot more useful than the simple rod)
Sunfire or Rylay
Force of Nature
Omens or Thornmail or Xtra Sunfire or even Banshee's if they are CC heavy
ELIXIRS O M G GET THEM SO GOOD
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