Make card droprates more consistent

This has been prompted by an experience I had today grinding cards, but I think is reasonable in the wider scheme of things.

I was in the map Camp 3 trying to farm Officer Skeleton cards. According to the library, there are 14 officer skeletons and 6 skeleton soldiers on this map (although in practice, there looks to be a lot more of both). Despite this, I had 10 drops of skeleton soldier cards in the time it took me to farm 5 officer skeleton cards. I recall something similar happening on my bowmaster and my shadower when I farmed these cards on them, although I don't have specific numbers to back this up.

If we assume I got average luck here (which I appreciate is quite an assumption), that would mean that the drop rate for skeleton soldier cards is around 4.6 times the drop rate of officer skeleton cards. Even if I had horrible luck on the officers and the expected rate would be to get 5 of both cards at a similar speed in this map... that still puts skeleton warrior at over 2 times the drop rate of officer skeleton.

The question I have, then, is "why?"
What benefit is there to the drop rates being so wildly different from each other?

I could understand if it was balanced with something else in mind, like the values of items dropped, or the exp gained, or even just how popular the maps were to grind at before the monster book was implemented, but both of these mobs should be pretty similar in all of those ways and I fail to see a pattern like this in the wider scheme of things. It just seems random. If there is a pattern and I've just missed it, I'd love to hear what it is

To be clear, I'm not saying to make all of the card drop rates exactly the same. What I am saying is: reduce the drop rates on cards like pinboom that take 5 minutes for the full set and increase drop rates on anything that's super low (like Officer Skeleton seems to be). Would it not be more balanced and more fair to players to normalise these drops rates?

 

I'm currently grinding my third ring. My complaint isn't that card hunting is too slow, which you seem to be implying. The overall effort to reward seems about right in my experience. My complaint is that some sets take 5 minutes while others take 2 hours and this makes no sense to me

 

On the three characters I've done it on, not one of them has finished the two sets at the same time. Either way, it was just an example of a wider design choice that has been bothering me for a while. To be clear, I'm not saying this is necessarily a bad design choice, just not one I would have made. If people really enjoy the drop rates being inconsistent, then that is a valid reason to keep them this way, it just doesn't make any sense to me that people would enjoy imbalance like this. As for me being unlucky, what I'm hoping for out of this thread is that the balance team might take a look at the actual numbers for card drop rates and decide if a change needs to be made, hopefully culling the more extreme outliers (if they exist). This doesn't need to be an all or nothing thing. They could pull in the very extreme cards while still keeping a large amount of variance. Everything I'm basing this on is anecdotal or from very small sample sizes (Usually 10-15 card drops, since this is my third ring) so of course, it is possible I've just been screwed by RNG. Kind of unlikely that I've been screwed this hard on the same mob three times in a row, but definitely within the realm of possibility.

If the different tabs do have different drop rates, then that would be a... reason, at least, but not a consistent thing to go by based on my own observations (and yes, I appreciate I don't have numbers to back these claims). Pinboom, which from my experience is the fastest set to get in the game, is on the orange tab. It's drop rate is considerably higher than anything on the red tab. If this was an intended way of scaling the drop-rates, I'd be fine with it since it makes sense, even though I don't like it, but I'm not convinced this is a thing. Even if it is the case, though, I don't really see that as a good reason. Cards from higher level monsters are already harder because they're dropped by higher level monsters.

This is fine, but it's punishing players for not knowing something they have no means of knowing (given the drop rates aren't made public and have likely been changed over the years anyway). Yes, I am getting my subsequent rings faster too, by virute of skipping cards that I know are ultra slow, but other than doing actual statistical analysis on drops from multiple people, there's no way for players to know which cards are harder to farm. You can get a feel for it by farming multiple rings yourself, and this will help, but there's no concrete way to tell the difference between a lower drop rate with good luck and a higher drop rate with bad luck. Given the cards all give the same utility, you'd generally expect them to have similar drop rates. Again, maybe this is intended, it's just not a choice I would make in the design of it myself, so I am suggesting it be changed.

 

This is why I'm asking that the balance team just do a quick runthrough of the drop-rates and change anything that is excessively high or low. As I said before, for an individual, it's impossible to tell the difference between a higher drop rate with bad luck and a lower drop rate with good luck, so actual decisions need to be made by people with actual numbers.

Extreme variability seems to be a common experience from what people are saying, hell, you even said

so even if my example is just a case of bad luck, that's not super relevant to what I'm saying. It's only the nonsensical drop rates that I'm asking to be changed. If I was just unlucky (3 times in a row) at officer skeletons, then that's fine and their drop rate specifically shouldn't be changed, but you do agree that there are some drop rates that are stupidly high or low.

Do you actually disagree that the more extreme drop rates should be normalised or have I just misinterpretted what you've said as disagreement?

This relies on knowing which cards are "easy drops" which isn't reliable. There's conflicting information from different sources on this exact topic and even things said in this thread conflict with my own experience of grinding certain mobs. Drop rates on all items are subject to change without the playerbase being notified, so even if you had statistically significant data to show that x card was fast and y card was slow, that could potentially change. If there was an actual reliable pattern in game to go by for card drop rate, even if that pattern made no sense whatsoever, I would agree with the notion that you can skip bad cards, but there isn't.

I definitely don't agree with this. While it does make it harder to make concrete decisions, drop rates have always been hidden from players with good reason. What I do advocate for, however, is vague ways we can predict how likely something is going to be. We were given this for the CWK exchange, with items separated into tiers. It would be nice if we could have something like this for cards.

I... don't actually agree that it is. My second ring was a lot faster than my first because I skipped a lot of the truly heinous mobs. I expect my third ring will be faster still, since I am skipping a few mobs I suffered through on my second ring. If I ever farm a fourth ring, I expect that will be even faster because I'll at least know to skip officer skeletons and anything else I end up regretting doing for this ring.

 

Super long post. If there are typos or grammar errors, I'm not sorry.

Again, you're not replying to what anyone in this thread is actually saying. If you continue like this, I'm just not going to reply because there's no point if you just make up what I've said and argue against that instead.

I'm not saying that it takes too long to get a T10 ring. I don't think anyone in this thread is saying that. The average time for cards is fine. I'm saying there is too much variance in how long different sets take to farm.

As I explained in multiple other posts, it's impossible for an individual to come up with univerally accurate expectations of which mobs are good and bad with such small sample sizes (farming only 5 cards from each monster). It's like talking to a brick wall...

The officer skeletons, which prompted me to write my original post, took me 1 hour 45 minutes. I timed it because I only technically had 1 hour 30 minutes of free time to play the game and overshot by 15 minutes because I was frustrated at not getting a single set in all that time. I was being as efficient in my movement as I realistically could be and was either 1 or 2 shotting the mobs with avenger, 1 shotting them with lucky 7. Even if I was hindered slightly by the fact that I'm not used to having to space myself from enemies, my killing wasn't so inefficient that it would make the card take 3-6 times as long as it does for you.

Honestly, though, the "get good" argument doesn't really work here. If I just sucked at grinding, most of my card times would be high, but they're not.

Personally, I think your own account of what is going on is distorted because that you just didn't notice how much time was passing. Even if the drop rates were all the same, tailored to being around 22.5 minutes (half way in your estimate) it's insanely unlikely that you'd never take longer than 30 minutes to farm any of the 300 sets you're farming. RNG is going to screw you eventually. I've also said that if that is what happened in my example, that's fine and I can live with it, but if it's not mostly that RNG screwed me, the drop rates are too variable in my opinion.

If the following is too much to read, just skip to the next bit of large text.

Just to labour the point, I just ran two epm tests at Path of Time 3 on my BM. I'm killing all mobs in 1 hit with both hurricane and arrow rain. Each mob gives 164 exp per kill.
The results of my two epm tests were 47,736 and 51,660.
The first doesn't divide perfectly because there were a few mobs at the start that had already taken damage.
47,736/164 = 291 kills
51,660/164 = 315 kills.

You may be able to kill faster than me, maybe even a lot faster than me, but certainly not 3 times my speed. In fact, I'll wager 10m that you can't get over 900 chronos kills on Path of Time 3 in 5 minutes using attacks that hit a maximum of 6 enemies. Send me a video of you doing it and I'll pay you that money.

Assuming I'm not just trash and that is a reasonable speed at which to be killing, we can come up with a fair drop rate to aim for that 22.5 minutes. I'll use the average of the two tests: 303 kills per 5 minutes.

This gives us 60.6 kills per minute.

We're aiming for an average of 22.5 minutes for 5 cards. For this we need a card every 4.5 minutes on average, which means 1 card every 272.7 kills. We'll round that to 273.

So now we have our numbers. We have a 1/273 drop rate, killing 60.6 enemies per minute and we want to know how likely it is to take over 30 minutes for 5 cards.
This is actually a simple binomial distribution. Every time we kill a monster, we either get a card or we don't. In 30 minutes, we'd expect to kill 1818 monsters, so we just need to find the probability of taking a 1 in 273 chance 1818 times and having 4 or fewer successes overall.

I'm not going to go into the details of binomial distributions, your math teacher should have covered that when you were about 15 or 16. Here's a handy-dandy calculator for it though: https://stattrek.com/online-calculator/binomial.aspx

If you aren't clear on what any of it means, I've put the numbers in for you:

The number circled in red is the one we care about. This means theres a ~20.6% chance that you won't have your 5th card by the 30 minute mark.
This does taper off pretty quickly, but there's still a 3% chance (should happen for 9 cards per T10 ring) that you'd take 45 minutes for a card at this rate and a ~0.3% chance (ie. you'd expect this once per tier 10) at the one hour mark.

If you have genuinely got all 300 cards in under 30 minutes... enter the lottery, dude. Your luck is wasted on this mushroom game.

This all assumes that the drop rates and kill speeds are exactly the same for all mobs, too, which they obviously aren't. What this means is that if you get very bad luck on a mob that also has a low drop rate, the two compound meaning it will take exponentially longer.

If you skipped ahead, read from here

Which brings me to my final point here, which was also my first point, but I didn't have math to articulate it so well:
Even small adjustments to the drop rate will massively affect the expected times taken. Even a less than 10% reduction (I changed the 2nd significant digit from 6 to 3) in the drop rate increases the probability of having 4 or fewer cards by 30 minutes by around 25% of its original value (for clarity: it goes from ~20% to ~25%, that's a 25% increase in the likeihood of it happening).

If we take this drop rate as the mean drop rate and introduce some variability on that, taking drop rates 25% less and more than the mean we get:
0.75x mean: ~44% chance of 4 or fewer cards at 30 minutes
1.25xmean ~8% chance of 4 or fewer cards at 30 minutes

These numbers (0.75x and 1.25x) might not intuitively seem like they're too far from the average, especially if you want drop rates to be variable, but the effect is that one card has a ~92% chance of being done in 30 minutes while the other only has a 56% chance of being done in 30 minutes. This is exactly the kind of mistake I could see being made when deciding on these drop rates. If it did happen and it was a mistake, it should be fixed.

Again, I'm not necessarily saying there is a problem, but IF the drop rate of any card is even close to 1.666 (1.25 is 1.666x0.75) times the drop rate of another, those two cards should have their drop rate normalised to some extent in my opinion.

Extra numbers if they're helpful to get a picture of what I'm saying, still based on the made-up drop rate from before:
Drop rate WRT the mean : chance of having 4 or fewer cards after 30 minutes farming
0.75x: ~44%
0.8x: ~38%
0.85x: ~32%
0.9x: ~29%
0.95x: ~24%
1x: ~21%
1.05x: ~17%
1.1x: ~14%
1.15x: ~12%
1.2x: ~10%
1.25x: ~7%

staff: If you do decide to take action based on what I've said, please don't use these numbers as a basis of normalising around a mean value. These numbers are derived from made up numbers. The purpose of them is to show how quickly probabilities take off in what might intuitively seem like small increases/decreases. Take your actual mean value of drop rates and see how much variance you actually have and normalise to what you actually want.