Impact of the Pity system on Special Valiant crystals
DNA3000
Member, Guardian Guardian › Posts: 20,271 Guardian
According to the latest stream, Kabam is experimenting with a form of pity system in the context of special Valiant featured crystals. According to the stream, the system will work as follows:
If you pull four crystals in a row that are not 6* rarity or higher, the next one will be at least a 6* champ
If you pull 29 crystals in a row that are not 7* rarity, the next one will be a 7* champ
If you pull 199 crystals in a row that are not the 7* featured champ, the next one will be the 7* featured champ
This is not precisely how it was explained, but I believe this more clearly represents the intent Kabam was describing. If you miss four in a row, the game still rolls the next one, but if that fifth roll is a 5* champ it "forces" it to be a 6* champ to break the streak of misses, it doesn't just automatically make the fifth drop a 6* (because if it did, that might cost you a 7* champ if that roll just happened to be a lucky pull).
Given those mechanics, how does the pity system alter the effective drop rates of the crystals? Since every time the pity system triggers the crystal drops more 6s, 7s, and 7* featured champs than the drop odds would ordinarily produce, the average number of those drops goes up. By how much?
There's two ways to calculate this: solve a bunch of recursive equations, or ask a computer to do it. Computer?
Measured drop rates:
5* rarity: 67.06 %
6* rarity: 27.82 %
7* rarity (not featured): 4.42 %
7* featured rarity: 0.7 %
Compared to the published odds of the Featured Valiant:
5* rarity: 73 %
6* rarity: 24 %
7* rarity (not featured): 2.64 %
7* featured rarity: 0.36 %
(Note: the published odds lists 7* drop rates as 3% but that includes the 7* featured champ odds of 0.36%, so I've separated them here for comparison purposes).
Because almost one in four drops is a 6* anyway, implementing a miss streakbreaker of five doesn't improve those odds dramatically, but it does improve them slightly. The bigger changes are with 7* rarity and 7* featured drops. On average, ordinarily about 38 drops are 7* champs (not featured) so breaking miss streaks at 30 has a substantial impact on the overall rate of return of the crystal: the crystal will drop about 67% more 7* champs with the pity system than without it. And the largest impact is on the featured 7* champion drop rate. About one in 278 crystals drops the featured 7* champ, and a pity system that streakbreaks at 200 increases the drop rate to almost double its initial rate.
Now, this is all separate from the fact that these streakbreaking pity drops are *predictable*. In theory if you keep track of all of your drops, you can actually predict in some cases when your next drop is guaranteed to be a 6*, a 7*, or even a 7* featured champ. If you open 199 crystals and none of them are the 7* featured, the next one will be. And since the pity system is (according to the stream) global across all special featured valiant crystals, if there's a featured you want among the special valiants that are announced, you could simply stop opening those crystals until the champ you want is released, and then the first crystal of that champion you open will be guaranteed to drop the featured champ.
As far as I am aware, you don't have to stop buying crystals, you just have to stop opening them. So if you really want a particular champ and you keep track of your openings and you know #200 is coming up, you can continue to buy featured Valiants and just hold them until the champ you want gets released, open that one, then go back and open all the other crystals you've stockpiled. I'm not sure to what degree anyone intends to play those kinds of games, but it is theoretically possible.
For everyone else, the above numbers estimate how the pity system alters the effective rate of return on the crystals. You obviously need to buy at least 30 to see the drop rate improvements on 7* champs and 200 to see the improvement for 7* featured, but for anyone thinking about buying that many, that's the overall drop rate improvements you're statistically going to see (random being random, everyone will see different overall rates of return).
If you pull four crystals in a row that are not 6* rarity or higher, the next one will be at least a 6* champ
If you pull 29 crystals in a row that are not 7* rarity, the next one will be a 7* champ
If you pull 199 crystals in a row that are not the 7* featured champ, the next one will be the 7* featured champ
This is not precisely how it was explained, but I believe this more clearly represents the intent Kabam was describing. If you miss four in a row, the game still rolls the next one, but if that fifth roll is a 5* champ it "forces" it to be a 6* champ to break the streak of misses, it doesn't just automatically make the fifth drop a 6* (because if it did, that might cost you a 7* champ if that roll just happened to be a lucky pull).
Given those mechanics, how does the pity system alter the effective drop rates of the crystals? Since every time the pity system triggers the crystal drops more 6s, 7s, and 7* featured champs than the drop odds would ordinarily produce, the average number of those drops goes up. By how much?
There's two ways to calculate this: solve a bunch of recursive equations, or ask a computer to do it. Computer?
Measured drop rates:
5* rarity: 67.06 %
6* rarity: 27.82 %
7* rarity (not featured): 4.42 %
7* featured rarity: 0.7 %
Compared to the published odds of the Featured Valiant:
5* rarity: 73 %
6* rarity: 24 %
7* rarity (not featured): 2.64 %
7* featured rarity: 0.36 %
(Note: the published odds lists 7* drop rates as 3% but that includes the 7* featured champ odds of 0.36%, so I've separated them here for comparison purposes).
Because almost one in four drops is a 6* anyway, implementing a miss streakbreaker of five doesn't improve those odds dramatically, but it does improve them slightly. The bigger changes are with 7* rarity and 7* featured drops. On average, ordinarily about 38 drops are 7* champs (not featured) so breaking miss streaks at 30 has a substantial impact on the overall rate of return of the crystal: the crystal will drop about 67% more 7* champs with the pity system than without it. And the largest impact is on the featured 7* champion drop rate. About one in 278 crystals drops the featured 7* champ, and a pity system that streakbreaks at 200 increases the drop rate to almost double its initial rate.
Now, this is all separate from the fact that these streakbreaking pity drops are *predictable*. In theory if you keep track of all of your drops, you can actually predict in some cases when your next drop is guaranteed to be a 6*, a 7*, or even a 7* featured champ. If you open 199 crystals and none of them are the 7* featured, the next one will be. And since the pity system is (according to the stream) global across all special featured valiant crystals, if there's a featured you want among the special valiants that are announced, you could simply stop opening those crystals until the champ you want is released, and then the first crystal of that champion you open will be guaranteed to drop the featured champ.
As far as I am aware, you don't have to stop buying crystals, you just have to stop opening them. So if you really want a particular champ and you keep track of your openings and you know #200 is coming up, you can continue to buy featured Valiants and just hold them until the champ you want gets released, open that one, then go back and open all the other crystals you've stockpiled. I'm not sure to what degree anyone intends to play those kinds of games, but it is theoretically possible.
For everyone else, the above numbers estimate how the pity system alters the effective rate of return on the crystals. You obviously need to buy at least 30 to see the drop rate improvements on 7* champs and 200 to see the improvement for 7* featured, but for anyone thinking about buying that many, that's the overall drop rate improvements you're statistically going to see (random being random, everyone will see different overall rates of return).
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Comments
What happen to milestone store offer? That was better value wise…
When nafaria came out on web store he was I believe $500,600 spending in the store to get him?
And $400,$500 for 7* jacko lantern in webstore also..
So why have this system in first place?
I feel like this pity crystal is a disguise to make you spend more because people thought spending that much for 7* nefaria and jack was a lot…
Not we have these.
I just totally stopped buying these crystals and just use my money and units for big sales for 4th and cyber.
200 featured crystal’s is just way to much.
I believe the last 7* I went for was for werewolf by night and got incredibly lucky
Crazy how werewolf is not even talked about much nowadays.
If you open three hundred crystals and do not get the 7* featured, you are literally no closer to getting it than when you started. Statistically speaking, you're still approximately 280 crystals away, because that's how independent odds work. You never get closer with more crystals. With the pity system, that's no longer true. You *might* get lucky and get them sooner, but it is now impossible to go 300, 500, or even a thousand crystals deep and have bad luck mean you still didn't get the champ you're chasing, and are still potentially hundreds of crystals away from getting it.
Presumably, this change is intended to make the crystal more attractive to players already buying them, and act to convince players who are on the fence about them to give them a try. This change is unlikely to change the opinions of players who have no intention of buying them and expect much larger returns on their investment than that. Kabam is not chasing after those players, nor should they.
However, I'm intrigued, and I know it's been requested. I'll keep an open mind.
you sure it works this way?
I think this system reset for every featured set.