So how "random" is the game

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What you are missing is the fact that you think it isn't random when going the same thing over and over. The problem is you are forcing something. That thing is only going to work if your opponents aren't also trying to use it. If you are the only one going for it then it will work out great. If there are 2 other people trying to get the same champions as you, you are all going to lose miserably while all sitting on one star units until it is too late. IT IS 100% RANDOM so you have to look for what your best odds are. If you see 3 people started with a 2 star Vlad, don't start buying ocean units because you won't get them. The opposite is also true though. If you see someone is doing well with glacial and you are sitting pretty well yourself with resources to spare, pick up every Olaf you see. The same can be said of any comp that depends on certain units to carry. If you see first place is sitting on 3 blademasters, buy up every Yi that you come across.

It is just simple math and it straight up tells you the odds now. If you have a 15% chance to get one of the 5 cost units, that is a 15% chance that one of them shows up, not that any specific one shows up. If someone else already has 5 Nami's, you have a higher chance of getting a Taric because Nami is less likely to show up.

Let's say there are 9 of each 5 cost unit in the shared pool. (Amumu, Zed, Yi, Singed, Taric, Nami)

2 people have 3 Amumus, and one person have 3 of Zed, Yi, Singed, and Taric. This is under the assumption that most people only go for a 2 star 5 cost due to the difficulty of getting a 3 star.

If you have a 15% chance to role a 5 cost, that means you have a 15% chance to role 3 Amumus, 6 of Zed, Yi, Singed, and Taric, and 9 of Nami.

Break that down further and you have a 2.8% chance to get Amumu, 5.6% chance to get one of the 4, and 8.4% chance to get Nami. Point being that while it is up to chance if you get something, there is no point trying to get one thing when you have a higher chance to get something else.

Very detailed reply that had absolutely nothing to do with my post. I was not contesting what builds you can get. I was talking about their erratic effectiveness from game to game.

Let me clarify a bit:

There is no "what I am missing". I fully understand the issue with forcing a build. I am not talking about those moments. I am talking about the limited number of effective comps in a situation where a complete build (I would say all units present, 2 stars on all is that definition) occurs, and over the course of time, watching how that comp gets stomped super hard one entire game, but then stomp super hard in the next game (not matches, but entire games). To the point that it is about a 50% WR (defined as 4th or better).

But it's not a subtle deviation. It's stomp or get stomped. It's very extreme. It's 8th place one game and 2nd place the next. It's that that pattern is also very constant.

But, as I said, drop that bit of the question. That's where skilled people get offended because how dare you imply they just win a slot machine game instead of one they work so incredibly hard to be good at. No need for the ego drama.

Let's go back to that word you liked, "math."

Per the Brand issue, also noted on several other champs, using the same build over and over because constants, we end up with massively wild swings between effectiveness of a unit from match to match.

But in just the one scenario where something autos 7 times and ults twice, the sum of that damage should not be equal to a handful of auto attacks.

That trend in any given match makes it seem more and more like the game is a lottery-styled slot machine with a handful of variables you can play into in order to more consistently win, if by win you mean 4th-6th place.

Card counting need not apply.

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Damage to shields isn't included in stats. Once had a game with early mountain bonus which went on my tank and the enemy teams stats showed no damage dealt. Also don't quote me on this one, but armour and magic resistance lower your damage against the respective attacks and I'm pretty sure that isn't calculated in the stats.

So if your brand auto attacked the enemies tank who presumably had some armour the aa's wouldn't do much damage. If the ult then hit enemies with shields or magic resistance (aswell as through mystic bonus and items) then yes it would appear that your brand did very little damage.

That might be the case. But other than the occasional buffed to excess Braum, it seems to me impossible that any single champ (let alone the entire group) would mitigate 90% damage. You'd have to be up against a 4man mystic (which was not the case here, no Nami present) with everyone wearing defensive items to even remotely get there.

The math just doesn't work for me no matter how I do it. I frequently get matches where a buffed champ does 90 damage the entire match, still alive until the end. Makes no sense. There is not that much mitigation available in the game, I don't care how you build.

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Units have to be close enough together for the ult to bounce also. Too many games had brand/siv only hit one unit because they weren't close enough together for the bounce to work. That's why positioning is also key in this game. Unless stuff is clumped up, siv/brand aren't nearly as effective.

I can give you that point. I hadn't really thought on it. But even one hit of the ult + all the AAs should equal a bit more than what pumped out, even if everything had max mitigation. But, in this case, it turns out that the sum of warfare was waged in a clump dead center of the map, around where the element buffs were located. I did not actually count the ult to make sure it hit X targets, so it may have only hit a couple times. But I know it went off because the mana bar was fully exhausted.