With blade of the serpent, you can spend money on health gear instead of buying 4 hats.
I think it was you who posted in another thread somewhere that your main problem with demigod right now is that you don't know what else there is to learn to make yourself better? If that's true then here is my suggestion for something you can put some time into: meta game calculations.
Before I get into that I'll say this:
1) buying hats caps at 4200g. You never need more than this. Buying hp/armor never caps as you always need more because the point of buying it is so you can be risky and run around trying to melee and everyones damage is always increasing and they are always buying better hp/armor gear too. Eventually you'll be selling nimoth/unbreakables for groffling, etc. In the long term the thousands of gold you would have put into your bad reg character trying to survive a melee with a beast you could have easily avoided in the first place (that's his main strength btw, avoiding melee) would have been much better used as 2 additional levels for everyone on your team because you bought xp1 2 and 3 early on.
2) blade of the serpent is absolutely awful compared to staff of renewal for reg. First, you're still going to need to buy a hat because you'll only have enough mana for 3 total abilities otherwise. Second, it assumes you are already being a bad teammate because the cooldown on serpent (what is it 60s? even if it's 45...) means that even if you get full mana from it every time you are out of mana and you never have to wait for a creep wave (which you almost always will) half the time you won't have enough mana to spam your abilities. You will be holding back snipes or not mining towers for half your game.
Regulas has one thing he can do better than any demigod in the game, deal damage safely from range. If you want to go toe to toe with any character dropping mines, motb, snares, wanding etc trying to get the kill for yourself, for the love of god just play antoher character who class strengths are better suited for that as just about everyones are.
Now as for the meta game stuff. Unless you are increadibly good with spatial analysis (and almost no one is) this is hard to understand. The easiest way to grasp it as it applies to reg builds would be to watch two replays at the same time, one AF/whatever the other SoR 4 hat spammy mcspamsalot build. Watch how, while you don't get kills SoR allow your teammates to hold the hp flag almost the entire game because every 8s there was a snipe in their oppsitions face. Watch how you tear a tower down in <30s (before anyone can react) from full health with mines. Watch how your entire team is +1 levels by level 8 because of your cit upgrades and count how many times your team lived with <10% health or got an extra kill because they had 10% extra health because they outgeared the enemy and held hp flag all game.
The AF build game is going to be back and forth assuming equal skill of all players. Unfortunately no 2 games are alike so it's hard to directly compare 2 replays but put 400 games into your brain and compare the outcomes of all of those and you'll see what I'm saying above is accurate.
Here is a pro tip for anyone who tries a 2k hp reg@lvl10 build: totems. The simple fact is that anyone who can get to you, WILL kill you. So you have to see them first (especially erebus@10). This is easily accomplished by having totems down well in advance of your position so you are never taken by surprise. In the early game I often have 3 totems down at all times. One in the mid and one on either side of the enemy tower. They last nearly forever and cost 50g each. Easy way to never get caught. You should never, ever die with a few 50g totems down unless you just don't look at the map or make a bad judgement call.
Another cool feature of SoR on cataract is that you can get 2 snipes in on someone if they are at a flag and turn to run to their crystal the second you hit them the first time. Without SoR they will make it to the crystal before you can even start the second snipe. Again this only works on noobs but many a pro gets tricked once by the shorter cd, they won't be tricked twice though.