2000 Uncollected Arena Crystals
DNA3000
Member, Guardian Guardian › Posts: 19,841 Guardian
It is time for another Deluge of Numbers in the Arena post.
A while back I did an analysis comparing standard and uncollected arena crystals. Based on that analysis I concluded that the data supported the notion that the value of the two crystals, exempting the Punisher rarity, was identical: the UC crystal cost five times as much and dropped rewards that were scaled up by five times. However, that was not enough data to do more than estimate what that actual value was. The crystal states the drop rates for the different types of drops - gold, units, etc - but does not state the breakdown for the different values of each - how often the low gold drop vs the high gold drop occurs. To do that requires a lot more data.
Since February of 2020 I've been recording UC crystal openings individually and I now have 2000 individual drops recorded (this does not include any of the 2019 data, by the way, for technical reasons), which let me estimate the internal drop rates of the different types to moderately better accuracy. Here's a summary of that data:
2000 UC crystals
1685 Gold drops
300 Unit drops
8 Punisher drops
7 Energy Refill (x5) drops
The crystal states its drop rates as:
Gold: 83.98%
Units: 15%
Energy: 0.35%
4* Punisher: 0.65%
5* Punisher: 0.02%
My data is pretty close to this and within the margin for error: 84.25% gold, 15% units, 0.4% 4* Punisher, 0.35% Energy. Here's the deeper breakdown not listed by the crystal:
Gold:
15k: 985/1685 (58.46%)
25k: 419/1685 (24.87%)
50k: 281/1685 (16.68%)
Average Gold per Gold drop: 23,323 gold
Units:
75: 194/300 (64.67%)
225: 106/300 (35.33%)
Average Units per Unit drop: 128 Units
If we accept the Kabam stated drop rates for the crystal, we can then use the breakdown numbers to calculate the average value per crystal. It is 83.98% x 23323 gold + 15% x 128 units = 19587 gold + 19.2 units. This is pretty close to my original estimates for gold, and slightly higher for units, which is not too surprising as most of the drops are gold, so the earlier gold numbers would have been more accurate than the unit numbers. If we divide these by five, we get the average value of the standard arena crystal: 3917 gold and 3.8 units.
Some trivia:
Longest streak of just gold drops: 28
Longest streak of just unit drops: 4
Highest non-trivial density of unit drops: six of eight and eight of thirteen drops
Best batch of 100 openings for gold: 2,586000 (with 20% gold boost)
Best batch of 100 openings for gold: 2,235,000 (without 20% gold boost)
Worst batch of 100 openings for gold: 1,520,000
Best batch of 100 openings for units: 2850
Worst batch of 100 openings for units: 900
Average gold drops per 100 during 20% gold boost (normalized to remove 20% boost): 1,961,415
Average gold drops per 100 outside 20% gold boosts: 1,967,201 (so, basically the same)
Maximum "rare drops" per 100: 3 (one 4* Punisher and two energy in one batch, three 4* Punisher drops in another)
Number of drops to go before odds of 5* Punisher showing up at least once would have been 50%: 1465
What does 2000 Uncollected Arena Crystal openings look like?
Something like that.
A while back I did an analysis comparing standard and uncollected arena crystals. Based on that analysis I concluded that the data supported the notion that the value of the two crystals, exempting the Punisher rarity, was identical: the UC crystal cost five times as much and dropped rewards that were scaled up by five times. However, that was not enough data to do more than estimate what that actual value was. The crystal states the drop rates for the different types of drops - gold, units, etc - but does not state the breakdown for the different values of each - how often the low gold drop vs the high gold drop occurs. To do that requires a lot more data.
Since February of 2020 I've been recording UC crystal openings individually and I now have 2000 individual drops recorded (this does not include any of the 2019 data, by the way, for technical reasons), which let me estimate the internal drop rates of the different types to moderately better accuracy. Here's a summary of that data:
2000 UC crystals
1685 Gold drops
300 Unit drops
8 Punisher drops
7 Energy Refill (x5) drops
The crystal states its drop rates as:
Gold: 83.98%
Units: 15%
Energy: 0.35%
4* Punisher: 0.65%
5* Punisher: 0.02%
My data is pretty close to this and within the margin for error: 84.25% gold, 15% units, 0.4% 4* Punisher, 0.35% Energy. Here's the deeper breakdown not listed by the crystal:
Gold:
15k: 985/1685 (58.46%)
25k: 419/1685 (24.87%)
50k: 281/1685 (16.68%)
Average Gold per Gold drop: 23,323 gold
Units:
75: 194/300 (64.67%)
225: 106/300 (35.33%)
Average Units per Unit drop: 128 Units
If we accept the Kabam stated drop rates for the crystal, we can then use the breakdown numbers to calculate the average value per crystal. It is 83.98% x 23323 gold + 15% x 128 units = 19587 gold + 19.2 units. This is pretty close to my original estimates for gold, and slightly higher for units, which is not too surprising as most of the drops are gold, so the earlier gold numbers would have been more accurate than the unit numbers. If we divide these by five, we get the average value of the standard arena crystal: 3917 gold and 3.8 units.
Some trivia:
Longest streak of just gold drops: 28
Longest streak of just unit drops: 4
Highest non-trivial density of unit drops: six of eight and eight of thirteen drops
Best batch of 100 openings for gold: 2,586000 (with 20% gold boost)
Best batch of 100 openings for gold: 2,235,000 (without 20% gold boost)
Worst batch of 100 openings for gold: 1,520,000
Best batch of 100 openings for units: 2850
Worst batch of 100 openings for units: 900
Average gold drops per 100 during 20% gold boost (normalized to remove 20% boost): 1,961,415
Average gold drops per 100 outside 20% gold boosts: 1,967,201 (so, basically the same)
Maximum "rare drops" per 100: 3 (one 4* Punisher and two energy in one batch, three 4* Punisher drops in another)
Number of drops to go before odds of 5* Punisher showing up at least once would have been 50%: 1465
What does 2000 Uncollected Arena Crystal openings look like?
Something like that.
24
Comments
In other words, you got unlucky.
Having a patent does not mean it is being used. Believing that it is, is conspiratorial and against the forum rules.
Nice data DNA!
Fyi, here's DNA's original analysis set from a while back that he mentioned...
https://forums.playcontestofchampions.com/en/discussion/173631/arena-crystal-drop-odds-analysis#latest
You might be one of those people who thinks that Kabam has a patent that lets them adjust the drop rates of crystals whenever they want. But that's not true, because that's not even patentable. Patents must be specific and novel, and all of Kabam's loobox related patents specifically patent very specific things. I know because I've read them all, multiple times, and analyzed them all when this first came out, and the second time this was brought up, and two years ago when this was all brought up again.
For example, there's this patent: Mystery boxes that adjust due to past spending behavior. That doesn't seem relevant here. Also, COWhale's channel pretty much destroys the notion that this patent was used for any high value crystal in MCOC (I know because I used his videos to do exactly that).
People like to point out this one also: System and method for rotating drop rates in a mystery box. If you read that one, this is a patent for using spending data to periodically change the drop rates of old lootboxes to increase their perceived value so people will become more interested in buying them again. Which, you know, requires Kabam to actually inform the players when they do this for it to actually work.
This one just blows my mind every time someone mentions it: Dynamic item obtain rate based on player progression, action, and other in-game behavior. People read only the title and see "dynamic item obtain rate" and think "lootbox manipulation." However, if you read the patent it doesn't describe that at all: it actually describes a method for applying handicap bonuses to players of lower progress level to make it easier for them to complete content to obtain progressional rewards.
If your knowledge of this comes from Youtube videos, all of the ones I've seen have been uniformly uninformed. If your knowledge of this comes from Reddit, as far as I'm aware this particular tin foil hattery seems to have fallen out of favor there in the last couple years. Here on these forums, I haven't had to break down one of these in quite a while now.
They could have added it later you say? They swapped one version of Unity for another newer version of Unity back in 2017 and broke well-timed blocks for months. That seems unlikely.
“(18) In exemplary implementations, the system and method provides for drop rates associated with virtual items to be modified based on one or more "triggers" associated with a specific player, set of players or across all players of the game. When these triggers are met, the system then makes a change to drop rates associated with one or more virtual items which are available for purchase. (19) In some implementations, triggers may include an individual player purchasing a threshold number of mystery boxes in general or an individual purchasing a threshold number of a specific mystery box. In other implementations, a trigger may require a player to hold a threshold number of mystery boxes in that player's virtual goods inventory, or alternatively, hold a threshold number of a specific mystery box or set of mystery boxes in the player's virtual goods inventory. In these cases, if the trigger is met, when the specific player makes a purchase of an applicable mystery box, that player will obtain a different drop rate for one or more of the virtual items in the mystery box. Typically, the different drop rate will comprise an enhanced drop rate such that the player is more likely to obtain a high value virtual item although this is not required.”
First off I don’t necessarily agree with _sham_, but I disagree with the idea that Kabam wouldn’t use their shady patents because other companies don’t. The patent I linked is certainly applicable and this would be impossible to detect without lots and lots of data. This patent is about changing drop rates based on triggers(“triggers may include an individual player purchasing a threshold number of mystery boxes in general or an individual purchasing a threshold number of a specific mystery box”) which is states can include spending habits. I don’t have proof that this patent is being implemented but you also don’t have proof that it isn’t being implemented. I also don’t believe it’s as simple as, “can I personally detect the use of this patent”? Unless you have access to all of kabam’s user data, it would be impossible to detect something like this. The only factual things in this conversation is that Kabam owns a couple questionable patents and they’ve done shady things in the past(bait and switch with that 12.0 update/refusing to show drop rates until being it became mandatory). Like I said, I’m not saying Kabam is actually using these patents but I’m also not going to vindicate them when their is no justifiable reason to own such questionable patents.
System and method for providing a quest from a probability item bundle in an online game
Why aren't people coming to the forums demanding to know why they aren't getting those quest keys? Also, a lot of people probably wish they implemented this one:
System and method for implementing a refund calculator in a game.
And I'm not sure how you'd force it into this game:
System and method for providing separate drift and steering controls
but it would probably make playing MODOK ten times more awesome.
Anyone can read the patent here: https://patents.justia.com/patent/10307666. But if anyone is actually going to take the time to read it, I would recommend jumping straight to the section called "Claims." That section is the meat of the patent. I will quote a section of it to point out something that I keep pointing out, but no one seems to figure out on their own: Notice it says over and over gain: "a system blah blah blah where the probability adjustment is higher based on blah blah." Repeatedly: a system where we look at this, and then adjust the probabilities UPWARD to reflect that. Why does it always say upward and never downward?
Because the patent explicitly states that its purpose is to ENHANCE the probabilities of the lootboxes to make them MORE ATTRACTIVE when interest in them wanes.
Now, how many people believe that Kabam does this? Makes crystals better so people buy more of them? Anyone?
Now, what about the statement "Typically, the different drop rate will comprise an enhanced drop rate such that the player is more likely to obtain a high value virtual item although this is not required." Doesn't this mean it isn't required to increase the value of the lootbox? No: it refers specifically to "high value items." You don't have to explicitly tweak the drop odds of high value items to make a lootbox more attractive, and the patent is careful to state that this is not necessary to prevent alternate patents from attempting to interpret this one narrowly.
There's also a smoking gun in the patent that ensures beyond any shadow of a doubt this patent specifically is not in use in MCOC: The patent explicitly states that one of the features of the invention is a method for notifying players of the change in odds. Why? Because how else are you going to encourage people to buy more of them if you don't TELL them that you've made the odds better? This would be obvious to anyone who read the patent in its entirety and understood the stated purpose of the invention: to encourage people to buy older lootboxes that had become less attractive over time.
So it’s always assumed innocent until proven guilty.
There's no way to prove the negative. However, at some point the default position has to be that the burden of proof is on those attempting to make the claim, because once you've looked at all the different crystals I have across all the different players of different types that I have and failed to find an odds discrepancy large enough to matter (if it was tiny and undetectable by me, what possible benefit could Kabam be getting from such small deviations from normal probability), the probability that there is such things going on in the game but they exist in a way that just happens to be unnoticable by me or anyone else who has done a credible data analysis becomes vanishingly small.
To put it another way, if you believe the game manipulates crystal odds based on player profiles, why am I immune? I've been looking at crystals for a very long time. I'm not a famous Youtuber and four years ago when I started analyzing PHC drops Kabam had no idea who I was. Even if you think they are playing four dimensional chess and are specifically freezing random crystals for anyone who measures them carefully and anyone who streams crystal openings (which would preserve any data of tampering) and anyone else they happen to think would be dangerous to manipulate, how did I evade manipulation from the beginning?
This game makes a ton of money. The incremental revenue increase from tiny random manipulation so small no one can detect it objectively seems to be not worth the risk associated with hidden tampering of RNG crystals.
Or Kabam could just clean this one up.
You could argue that *everything* they do serves to ultimately make more money, even giving things away. But then all that says is if they aren't using the patented techniques, that's just because they know it won't make more money. In other words it says nothing about what they are or are not doing.
I've been posting data and analyses for a very long time now, and will continue to do so. I cannot control what people do with any of it. Some people will use that data objectively, and some will let their own subjective biases override them. A while ago I decided that the best path forward was not to focus on disproving the subjective stuff, but to strengthen the objective stuff instead. Over very long periods of time, this seems to have had a net positive effect.
I will say this about battlechips specifically. Anyone claiming that arena battlechips contain evidence of Kabam being greedy knows nothing about mobile game monetization. The arena is an almost broken source for grindable resources that you simply do not find in hardly any F2P mobile games. On a relative basis it is a ludicrous amount of rewards, especially virtual currency (units). I have never played any F2P game mobile or PC where it is extremely easy to grind several hundred dollars of virtual currency by just playing a casual game mode for a couple hours a day max. If Kabam's motives were what some people ascribe to them, arena milestones wouldn't be handing out the gigantic amount of rewards they currently do.
Anything that discusses crystal odds is likely to stray into meta discussion. I try to make sure that discussion is generally civil, so the mods don't have to take corrective action. But it is ultimately their call.
The bottom line is there are many Patents that are applied for when starting a game that are never used. There is no correlation to what content you're doing and the outcomes of the Crystals. The server doesn't even register what you're doing. You open the Crystal and an outcome is generated.
You state that, “In other words, if it says they can adjust drop rates based on player actions, they've invented and patented the ability to do that. That's legally false.” I don’t know what you’re basing this statement off of. Kabam have patented and invented this, which is evident by this patent existing. Daniel L. King even references Kabam in his paper Video Game Monetization: A Blueprint for Practical Social Responsibility Measure in the International Journal of Mental Health and Addiction. King states:
“Some registered game patents appear to indicate that some game companies employ microtransaction systems that adjust the reward payout so that it is determined largely by player behaviors rather than by random chance. A patent by McClellan et al. (2017) for Kabam refers to ‘mystery boxes’ where the payout is influenced by player statistics, including (but not limited to) how much time or money the player has already spent in the game. Knowledge about the player’s behavior may be exploited, for example, in a scenario where a novice player receives better rewards at the beginning of the game, but then the odds of receiving the desired rewards reduce over time and thereby encourage more persistent play.”
Claims 4-9 clearly states that spending habits and the player’s inventory contents can have an effect on the drop rates. You then state, “Now, how many people believe that Kabam does this? Makes crystals better so people buy more of them? Anyone?”. This statement is anecdotal evidence that’s based on your own experiences. This statement is just as meaningless as @_Sham_ saying he thinks they use this patent based on his personal experience. You would need access to user data to determine if this true or not.
“Doesn't this mean it isn't required to increase the value of the lootbox? No: it refers specifically to ‘high value items.’ You don't have to explicitly tweak the drop odds of high value items to make a lootbox more attractive, and the patent is careful to state that this is not necessary to prevent alternate patents from attempting to interpret this one narrowly.”
I’m sorry but this interpretation is such a stretch. How did you reach that conclusion? It’s literally just stating that when a different drop rate is implemented, it can increase your odds of getting a high value item. I agree the last part is to protect themselves but it doesn’t say anywhere in that quote that “ You don't have to explicitly tweak the drop odds of high value items to make a lootbox more attractive”. That’s conjecture based on your interpretation.
“The method of the present invention may also include adjusting distribution probabilities associated with individual awards included in sets of potential awards in a predetermined manner in response to predetermined triggering criteria being met such that, in response to the predetermined triggering criteria being met subsequent to purchase of the first probability item bundle being purchased by the first user, one or both of the first distribution probability and/or the second distribution probability are adjusted in a predetermined manner.”
“By way of example, presuming the applicable trigger is met, and presuming that a specific collection of virtual items potentially contains items A, B, C and D. Prior to adjustment, the probabilities of receiving the items might be as follows: A—30%, B—50%, C—2%, and D—75%. In this example, it may be that item C is a highly coveted item and thus the chances for obtaining it are purposely kept low so as to maintain the actual and/or perceived value of the item. If a trigger is met, (e.g. a player purchases the third instance of this collection), the system may adjust probabilities, by way of example, to A—30%, B—50%, C—10%, and D—75%. This adjustment may apply to all three of the purchased collections or only one of the collections (e.g. the last/third purchased collection) as determined by the game operator. In this example, this represents a reward to a player that has purchased multiple of the same collections by giving that person an increased chance of obtaining the desired item.“
Both of these paragraphs clearly contradict what you state to be the intent of this patent. These paragraphs aren’t about making old crystals more desirable but changing the odds based on predetermined “triggers”(spending). This second paragraph makes a crystal clear example where the purchasing of the bundle a 3rd time increases the chances of getting item C from 2% to %10. It has nothing to do with the age of the crystal but rather the number of times the crystal is purchased(the trigger).
Obviously I have no clue whether or not they use this patent. However, I do disagree with how you smugly dismiss the possible use of this patent with such a flimsy, subjective argument. Maybe you need to read the patent a couple more times.