I can provide a list of random elements and comment on things.
1) picks at start (may be switched to random)
a) town - shouldn't matter; I include the TOWN SPECIAL here; it's random and it may make a difference. Getting additional troops or money or a better exchange rate seems to be better than a luck bonus on defense, for example
b) hero - may make a difference in some cases, but chances to end up with a complete loser are slim while the really good ones are combinations of two heroes, like, for example Havez (who brings the goodies) and Jhora (who brings the fire power); clearly, though, depending on what your starting hero(es) come(s) equipped with and who they are the game plays differently, the higher the difficulty level is.
c) bonus; with artifacts being tradable now, at least money is not an option anymore. Since the artifact is the clearly superior pick - on all diff levels -, leaving this at random is more like a handicap.
2) map findings
a) Chests; they make a difference. On high difficulty the difference between 1000 gps and 2000 gps may make in fact all the difference when it allows a crucial building or not; on lower it may make the difference between a crucial level-up of the hero (and remember, that you don't get so much xp on low diff from fights)
b) Resource piles; on higher diff they may make all the difference, not only in terms of how many resources a pile will give, but the sort of a random pile or campfire gives as well. You'll feel the difference, of whether the two wood or ore piles at the mill/pit will give 5 rach or 9 each, and you'll smile about every find of your rarest resource.
c) Artifacts; a world of difference, as everyone should and will know; the one redeeming factor here is, that you can cash in for useless artifacts (double or triple finds or too many artifacts for the same slot or simply useless artifacts like Titans Trident for the Barbarians and so on). Of course, on lower diff the money isn't worth much - here only the quality of the artifact really counts. All in all I think that, as a map maker, artifacts are something I'd be careful with the placing.
d) joins; not much to say. Of course joins are most effective with Necropolis and Dungeon, but the Orcs and the Inferno can make good use of them as well. For the rest it depends. Still, a good join at a crucial point counts, especiall if you don't have Diplomacy. Moreover the join may be for free as well...
3) Hero development
a) Witch Huts; a skill for free ain't bad. While there are no useless skills per se, random Witch Huts may be advantageous (giving something every hero will take willingly, for example attack) to useless, for example, a magic skill for spells your guild or, in case of the Orcs, the opponent's guild don't have
b) Sylanna's, err, oldest? Tree of Knowledge, I mean; getting the level for free or not may be a crucial difference; if you play Academy, for example, you won't be too keen to pay 10 Gems for the level.
c) regular levelling; the tighter the game, the more important it is to really make the most out of your hero levelling. Of course there are certain skills that will help you more than others, especially on high diff and in the beginning. Up to a certain degree you have control over the levelling - you can make sure to get a certain perk EVENTUALLY (provided you have the skill), but you can't make sure to get a certain skill at all or a certain perk immediately. The rule of thumb on HIGHER diff is, that a new skill or perk must be useful IMMEDIATELY; if it's not it must be made so (magic skills). On lower diff it's easier to plan for the last confrontation, so hero-building is more with an eye on the opponent, if possible.
All in all this is of course a very crucial area.
d) spells; yup, make a difference. Raise Dead sucks in the guild, no matter the town. For that spell to be of use you must have losses, and while I can see the use of that spell in any last, decisive battle, it's a level 2 spell, so it would be possible to use it quite early in a game. Earthquake is the same. As a personal comment, let me add that I've suggested to make Earthquake able to destroy obstacles on any battle map to give it a use other than in siege battles, but honing on spells hasn't been too high on the priority list of fixes... Light and dark Level 5 spells may be completely useless, depending on what you and the opponent(s) are, so this is an area where you may have more luck or not. The one redeeming factor HERE is, that with all the possibilities to refine spells you clearly don't need EVERY spell to be a winner - a couple of usable ones are enough.
4) Week of
Yes. They may have a lot of effect: a plague week will benefit Necropolis, the double income week will give Haven an edge, and the double resource weeks are probably best for Academy. Moreover, the growth weeks do have a solid impact, especially in a tight game, while others will cancel skill effects or "give" everyone a (magic) skill. It's more or less like a random event (we know that from other (board) games. However, it's no different than others. If you get a week where all your moral or luck advantages are cancelled out - good for some, not good for others, but the effect lasts a week only. Sure, if you are on the brink of confronting Necropolis with Haven and your hero comes with maxed out Luck and Leadership and then the week hits you, just when you see the red in the eye of the Necro, if it would have been a tight battle you'll probably lose now. A bad case of really bad luck. But what if that week is just following the week of double income and you have made use of the additional money to train several score Marksmen or a nice squad of additional Champions?
5) Randomness in battle
a) ATB bar at start mod; everything has been said, I think.
b) Luck and moral triggers; yup, they work randomly, and getting moral or luck for your level 6 or 7 instead of 1 or 2 may make a big difference; also getting those benefits EARLY in a battle is better than getting them later on.
c) creature and hero abilities with a probability of triggering (the "Soldier's Luck" abilities); yes, they may make a difference as well.
d) Resistance effects (including Dispelling and attacking Phantoms)
e) obstacle placement
f) catapult hits
I'm sure I've missed some; the Fairie Ring, for example. Some race-specific thing like using-up resources for using a rune or not or which Runes or Battle Cries you get. The favored enemy racial. The amount of LIVING and therefore raisable troops for Necro - getting Gargoyles and Spectres only will suck for sure.
Some things depend on the map-settings, but the bottom line is that the game is based on chance.
What you can say about chance is, that the more often chance will have an opportunity to come into play the more often things will even out. The trouble is that there are SOME effects that seem to stand out:
Example: You fight Sylvans and they have Crystal Dragons. Of course they act sooner than every single stack of your troops, and OF COURSE they land a lucky hit that spreads through your ranks, having quadrupled effect on two stacks since they are favored enemies. One action, and things already look bleak.
Such a random event seems to stand out and be worth much more than everything that happened prior to that battle. In fact every random effect may HAVE evened out already and up to that point - but it may have not either. It MAY be that up to that point everything has worked in YOUR favor and the battle seemed won when you attacked.
We had a discussion about Luck (the skill and the effect) already, and the people discussing pretty much agreed that
a) halving the Luck bonus to 50%
b) nearly doubling the trigger chances by allowing Luck on retaliation
c) reducing the percentage of a luck point from 10 to something like 6 or 7
d) making a difference between Luck as a skill and Luck from bonusses that way that you can have more luck with the skill: for example,
Maximum Luck taken into account (!)
without Luck: 2
Personally I'd say that there is nothing wrong with the amount of randomness in the game, but that some aspects could have been better balanced - like Luck, for example.