This is the response I sent to support regarding the compensation for incorrectly banned accounts.  Warning:  long read, full of opinions.

Ok, after getting over my nerd-rage of this debacle, I started thinking this was an interesting psycho-economic question to answer. There is widespread dis-satisfaction with the compensation being provided. Why is that? So I started noodling it from a hopefully objective perspective, and I think it's all about the perception of fairness. Not necessarily what is de-facto fair as determined by the internal exchange rates of silver and gems, for example, but what people perceive to be fair. This is how I think you (or any other company) really should have handled it, at least in my humble opinion. Let's look at the banned accounts problem; server maintenance can probably be handled by your regular estimates, albeit scaled up by some of the factors I bring up below since it was so frequent and of such long duration. (I'm not an economist, so I'm going to assign my own terminology. There's probably formally defined words for the things I'm going to describe.)

First, let's get an assumption on the field: I assert that it costs nothing for Plarium to hand out more comp. Arguments against might be:

• This causes in-game inflation. I don't really think this is a problem, as it's well known that game companies do and must manipulation in-game economies. After all, you're a business. An example of this is the faction crypts, whereby they intersect with silver currency by requiring silver to enchant artifacts. Any in-game inflation can be corrected.
• This may keep someone from spending real money on something that they otherwise got for free. I don't buy this argument as well, if people don't believe that Plarium is treating the fairly, they are already at a reduced likelihood of making in-app purchases. They're not going to give you more money because they feel like they got cheated out of what they already gave you. You need to establish trust.

So, let's operate under the assumption that Plarium minting new resources for compensation is "free" for the company.

Let's now consider compensation for primitive or foundational resources. These building blocks that are transformed into other resources. These are things energy, silver, arena tokens, and gems, and to a lesser extent, clan boss and faction keys. These are things you receive just for time passing. For easy numbers, let's assume that a given account was incorrectly banned for 1 day, and rolled back 2 days. This means that the player lost:

• 1440 energy: 24 hours * 60 minutes / 3 minutes per energy regen * 3 days
• 45 gems: 24 hours * 60 minutes / 96 minutes per gem * 3 days (assuming fully upgraded mine)
• 72 arena tokens: 24 hours * 3 days
• 72 faction keys: 12 per crypt * 2 cryptes * 3 days
• 12 clan boss keys: 4 per day * 3 days

In addition, assuming that most people complete playtime rewards, there's also:

• 82,500 silver: 5 min and 90 minutes quests * 3 days
• 3 ancient shards: 20 minute quest * 3 days
• 390 energy: 60 minutes quest * 3 days (assuming level 60)
• 3 lesser arcane potions: 40 minute quest * 3 days
• 10 arena tokens: 180 minute question * 3 days

And then, on top of that, there's the daily quests. I can't recall exactly what these are offhand, but there's at least:

• 15 arena tokens: 5 token reward * 3 days
• 390 energy: full energy * 3 days (assuming level 60)

I think there's also maybe some gems (~30, 10/day?), can't recall offhand.

So, with that we're currently at:

• 2220 energy
• 87 arena tokens
• ~45-75 gems
• 82,500 silver
• 3 ancient shards
• 72 faction keys
• 12 clan boss keys
• 3 lesser arcane potions

Look at the from the perspective of a bank account. These things being lost are something like the bank saying "oops, we accidentally removed $100 from your account." So, this is the rough shape and size of the absolute baseline of what compensation should look like. Maybe not this granular, but something roughly equivalent, like "3000 energy, 100 arena token, 400 gems, 1M silver, and 2 CB keys." I don't know what the internal conversion rates are, so take those numbers with a grain of salt, but I'm sure there's an official exchange rate internally. It might be tempting to say "well, these were given to players, it's not like they paid for them, so we don't owe them." That may or may not be true, but it's not how the user perceives it. Once the player has a given something, unjustified removal of it feels like stealing, or in other words unfair. Doesn't matter if it is, it feels like it.

However, people don't gather these resource to hoard, they gather them to transform them. They use them to upgrade artifacts, acquire and level champs, etc. Some of this involves luck. So, only returning the absolute baseline of comp is like the bank saying "we're crediting back the $100, but not the interest you would have received on it." So, how to account for the "interest"?

The best approximation is probably to look at something like the environment at the time of the ban/outage. What events, tournaments, and other things were going on? If you have the data analytics tools (and I really hope you do), you should look back at each affected users' completion rates of events that were in-progress or recently completed. If they generally get, say, 6 of the 10 reward levels of a spider event, you should give whatever those first 6 levels were. But, you also have no context on recent changes, e.g., level upgrades or timing of the event, to say that's as far as they would have gotten, or if they were off work that day and planning full-day grind fest. So you should them, say, up through levels 8. Why? If you fall short at all, it is perceived as unfair in total, and if you go a bit over, you generate a very small amount of goodwill. Not much, but a little, since you're still very close to the "only returning what I lost" perception. 

Given this, you can approximate some of the rewards you can expect the user to have achieved. But in addition to the goodwill generated by going a bit over, you need to go a bit more over that. Why? we still haven't taken into account the transformed resources like cruel/immortal artifacts, potions, books, silver, XP brews, and gems from the clan boss engagements, nor medals from the arena, or maybe awesome artifacts from farming for 3 days. Nor have we taken into account things like lucky artifact improvements or lucky shard pulls. How to handle this? I would propose adding in some worthy artifacts. Not randomly-generated artifacts (risk of flat-rate stats generating ire rather than goodwill), but something decent: offense crit rate gloves, speed boots of speed, immortal HP% chestplate, or some relentless gear, something like that. Something you know people would value. Maybe two of each superior potion, or of each XP brew.

So, if you went this far, the sum of all these things (or equivalent) is roughly what people believe they have lost. Hence, this becomes the new bare minimum of what people might consider fair. Note, however, that there is little to no goodwill generated toward Plarium. People don't want to feel like a dollar sign, and don't want to re-grind those 3 days worth of time. So, how to get back that goodwill, that manifest is high app reviews, recommendations to friends, and changing the engagement model of current users from "meh" to "excited and having fun" (as a game should be) -- and by extension, more willing to spend more money on more in-app purchases.

The knee-jerk reaction here might be "give them a sacred and maybe some void shards". However, think about the psychology behind shards. Opening shards, and to a lesser extent artifact upgrades, act on the brain in a similar way as gambling. Normally, this acts in Plarium's favor: if you get a good result, you get the "high" from beating the odds, and it's "I am so lucky!". If you don't, it's "meh", and the fault of the "stupid RNG." But, during standard gameplay where you trust the company, you want to work to get more shards to do it again, or buys some shard packs, or gems, or whatever. This is good for Plarium's bottom line.

Notice, however, that in the positive reinforcement response, it's the user that is responsible ("I was lucky"), and the in the negative reinforcement case, it's Plarium that is responsible ("crappy RNG/drop rates"). This quirk of human response is well documented: we tend to attribute success to ourselves, and to blame our failures on others. It's like someone giving you lottery tickets; it's either garbage pieces of paper or you were lucky. Shards will not generate goodwill toward Plarium unless you give enough that that statistics will yield a positive result for most people, i.e., "Plarium did right by me by providing these opportunities". However, this is likely over-compensation. So, I am actually advocating not using shards as compensation. Or at least, not as the "big ticket" items that are supposed to indicate you're really sorry. What you're looking for is something to get people to re-engage with the game on a long term basis.

Think about casinos: how do they pull you in? One answer might be "a free pull on the big jackpot slot machine". But that doesn't get you to stay. If you didn't win, you'll probably walk to the next casino -- because they have one free pull of their big jackpot slot as well. Casinos get you to stay by providing buffets, free hotel rooms, etc. You need to provide something durable. What is durable? I would propose that a desperately needed champion is durable. Something that requires continued engagement; grinding out levels, ascension, gear, etc. Something that makes you want to keep logging in. But here's the two most important aspects: it needs to be (a) a good champ, and (b) a champ that is not one they already have. Re-level'ing a duplicate champ doesn't provide the same entertainment and playing around with a new one.

If this is the case, the question becomes, which champ? There's a few avenues here. The quickest and easiest answer is "a new champ no one has". That's definitely an option. Another easy option would be, out of a list of, say 10 good epics and/or legendaries, select one the user doesn't have. With this strategy, you'll probably get people complaining that they didn't get as good of a comp champ as someone else, but it's not a bad option. If you really want to make it look like you care about the users, leverage data analytics. I'm just going to assume you have some sort of analytics you use when rebalancing the game, QA testing, or, adding new champs/quests, etc. Run those against each affected user. Give them a champ that they would appreciate. E.g., do they not have a good rezzer, or tank? No one with HP burn AoE? Maybe something nothing that has speed aura for all battles? Are they stuck on spider 13 without a good HP nuker? Find something that would make the user happy and that will generate goodwill.

Now, if you did all this, there would still be a percentage of haters out there; and you will never satisfy them. But, I would hazard a guess that a huge majority of people that are currently complaining would be willing to pivot to "wow, Plarium really owned this mess, thank you! I'm going to keep playing with confidence that if something like this ever happens again, it will be made right! Maybe I will buy that Battle Pass after all...."