Risk of Rain 2 – How bad is Purity?: the Actual Numbers

Purity

All skill cooldowns are reduced by 2 (+1 per stack) seconds. All random effects are rolled +1 (+1 per stack) times for an unfavorable outcome.
Reducing all skill cooldowns by 2 seconds is obviously pretty good.
But as you probably already know, there is a payoff. Purity makes you unlucky.

It works just like the 57 Leaf Clover and effects the same things (see 57 Leaf Clover guide) but in the opposite way. The 57 Leaf Clover re-rolls random effects for a favorable outcome while Purity re-rolls random effects for an unfavorable outcome.

Sounds similar enough right?
Well, the maths works a bit differently.

The Maths

Time to look at some probability trees again.

Okay let’s say you’re using AtG Missiles.
They have a 10% chance to activate.

The probability tree would look like this:

1 out of 10 chance that it will activate and 9 out of 10 that it won’t.

If you have a 57 Leaf Clover then every time that your AtG Missiles don’t activate, you’ll have another 1 in 10 chance to activate them.

1/10 + 9/10 * 1/10 = 19/100 or 19%
So with one 57 Leaf Clover your chance to activate AtG Missiles becomes 19%

Purity does the opposite:

If you get the 1 in 10 chance to activate your AtG Missiles, the Purity will try to re-roll the outcome so you’ll have to get the 1 in 10 chance again to activate the AtG Missiles.

1/10 * 1/10 = 1/100 or 1%
Which means that having a Purity reduces your chance from 10% to 1%

Okay so a 57 Leaf Clover doesn’t even double your luck while a Purity makes it 10 times worse.
So it seems like Purity makes you much unluckier than a Clover makes you luckier.
But why?

Imagine you’re throwing dice. And to activate your item you need to roll a 6.
If you have a Purity, now suddenly you have to roll 6 twice in a row to activate it.

Usually your chance to roll a 6 is 1 out of 6.
Rolling 6 twice in a row is 1 out of 6 times 1 out of 6.
1/6 * 1/6 = 1/36

Having to roll 6 twice instead of just once makes it significantly harder to activate items.
This is what Purity does. You’ll have to roll every effect twice in a row to activate it.

So how bad is it?

Well… if you pick up a Purity, you’re not going to be activating stuff like AtG Missiles, Ukuleles, Molten Perforators, Sentient Meat Hooks, etc.

It’s not really “oh I’m going to activate my items less often if I pick this up” but more like “i’m basically not going to activate my items at all”
Even if you just pick up one, the chance to activate most items just gets too low.

However, if your activation chance for an item is very high initially then it’s not that bad.
Let’s say you have 6 Tri-Tip Daggers with 15% chance to activate each, which adds up to 90%
9/10 * 9/10 = 81/100 or 81%

This is… not that big of a decrease honestly.

Generally, the higher the initial activation chance the smaller the decrease.
And if you manage to reach 100% chance to activate something then Purity doesn’t have an impact.

So if you have high Critical Strike chance, Tri-Tip Daggers, Sticky Bomb, etc. then it’s not that bad.
For those items obviously. Because your AtG’s and Ukuleles are still going to be useless.

Aditionally, cooldowns can only be reduced to a minimum of 0.5 seconds.
So you won’t even be able to just spam abilities with Purity.

One more thing that could be done is to have both a 57 Leaf Clover and a Purity.
Having an equal amount of Clovers and Purities will cancel out their effects.

But if you have good items you want to be activating then wouldn’t it just be better to use the effect of the 57 Leaf Clover and activating your items more instead of having a skill cooldown reduction?

Overall, Purity is just really bad except in some specific cases (which i’ll get into in a moment).

The Numbers

I’m not going to go as in-depth with the numbers as in my 57 Leaf Clover guide.

I think that calculating every item with just one Purity is more than enough because if you have multiple Purities, I don’t think you’re planning to activate any items anyway.

AtG Missile Mk. 1:
10. → 1%

Ukulele:
25. → 6.25%

Molten Perforator:
10. → 1%

Happiest Mask:
7. → 0.49%

Brittle Crown:
30. → 9%

Tri-Tip Dagger:
15. → 2.25%
30. → 9%
45. → 20.25%
60. → 36%
75. → 56.25%
90. → 81%
100. → 100%

Sticky Bomb:
5. → 0.25%
10. → 1%
15. → 2.25%
20. → 4%
25. → 6.25%
30. → 9%
35. → 12.25%
40. → 16%
45. → 20.25%
50. → 25%
55. → 30.25%
60. → 36%
65. → 42.25%
70. → 49%
75. → 56.25%
80. → 64%
85. → 72.25%
90. → 81%
95. → 90.25%
100. → 100%

Stun Grenade:
(hyperbolic scaling see clover guide for more info)
4.76. → 0.23%
9.09. → 0.83%
13.04. → 1.7%
16.67. → 2.78%
20.00. → 4%
23.08. → 5.33%
25.93. → 6.72%
28.57. → 8.16%
31.03. → 9.63%
33.33. → 11.11%
35.48. → 12.59%
37.50. → 14.06%
39.39. → 15.52%
41.18. → 16.96%
42.86. → 18.37%
44.44. → 19.75%
45.95. → 21.11%
47.37. → 22.44%
48.72. → 23.74%
50.00. → 25%

Bandolier:
(special scaling see clover guide for more info)
20.45. → 4.18%
30.41. → 9.25%
36.71. → 13.48%
41.21. → 16.98%
44.64. → 19.93%
47.38. → 22.45%
49.65. → 24.65%
51.57. → 26.59%
53.23. → 28.33%
54.67. → 29.89%
55.96. → 31.32%
57.11. → 32.62%
58.14. → 33.80%
59.08. → 34.90%
59.95. → 35.94%
60.74. → 36.89%
61.47. → 37.79%
62.15. → 38.63%
62.79. → 39.43%
63.38. → 40.17%

Old War Stealthkit:
(scales with damage taken)
1. → 0.0001%
5. → 0.25%
10. → 1%
15. → 2.25%
20. → 4%
25. → 6.25%
30. → 9%
35. → 12.25%
40. → 16%
45. → 20.25%
50. → 25%
55. → 30.25%
60. → 36%
65. → 42.25%
70. → 49%
75. → 56.25%
80. → 64%
85. → 72.25%
90. → 81%
95. → 90.25%
100. → 100%

Ghor’s Tome:
4. → 0.16%
8. → 0.64%
12. → 1.44%
16. → 2.56%
20. → 4%
24. → 5.76%
28. → 7.84%
32. → 10.24%
36. → 12.96%
40. → 16%
44. → 19.36%
48. → 23.04%
52. → 27.04%
56. → 31.36%
60. → 36%
64. → 40.96%
68. → 46.24%
72. → 51.84%
76. → 57.76%
80. → 64%
84. → 70.56%
88. → 77.44%
92. → 84.64%
96. → 92.16%
100. → 100%

Sentient Meat Hook:
(hyperbolic scaling see clover guide for more info)
16.67. → 2.78%
28.57. → 8.16%
37.50. → 14.06%
44.44. → 19.75%
50.00. → 25%
54.55. → 29.76%
58.33. → 34.02%
61.54. → 37.87%
64.29. → 41.33%
66.67. → 44.45%
68.75. → 47.27%
70.59. → 49.83%
72.22. → 52.16%
73.68. → 54.29%
75.00. → 56.25%
76.19. → 58.05%
77.27. → 59.71%
78.26. → 61.25%
79.17. → 62.68%
80.00. → 64%

Spinel Tonic:
(unfavorable effect so chance increases)
20. → 36%

Critical Strike chance:
(base 1% chance + items)
1. → 0.0001%
6. → 0.36%
11. → 1.21%
16. → 2.56%
21. → 4.41%
26. → 6.76%
31. → 9.61%
36. → 12.96%
41. → 16.81%
46. → 21.16%
51. → 26.01%
56. → 31.36%
61. → 37.21%
66. → 43.56%
71. → 50.41%
76. → 57.76%
81. → 65.61%
86. → 73.96%
91. → 82.81%
96. → 92.16%
100. → 100%

Flamethrower:
50. → 25%

When can you use it?

Let’s say you’re going for Mithrix.

You’re on the final stage now and you weren’t lucky enough to get any AtG Missiles but you have a couple of Ukuleles and 7 Tri-Tip Daggers. You also got a Happiest Mask.

You went and opened the Lunar Pods and a Purity popped out.
Well… you should probably take it.

The Ukuleles and Happiest Mask probably won’t do much during the Mithrix fight.
You have 7 Tri-Tip Daggers which add up to a 100% chance to bleed enemies.
So why not reduce your skill cooldowns by 2 seconds?

Generally, if you’re planning on ending a run and don’t have very important items you want to activate or have a high activation chance on items that stack then taking a Purity probably won’t hurt.

Even if you’re not going to Mithrix but are planning on obliterating soon, missing out on something like Ghor’s Tome isn’t going to ruin your run.

If you want to use Purity or not really just depends on the loot you have and on the loot you’re planning to get. If you’re close to ending your run and you don’t have AtG Missiles then you probably won’t get any more AtG Missiles. Then sure, go take the Purity.
But if you see a Purity at the Bazar after stage 2 and don’t have items to activate, it doesn’t mean that you’re not going to gain those items later and regret picking up Purity.

Just look at your items, look at how far into the run you are and decide if the Purity is a good idea

Thanks again!

Thank you for checking out this guide.

Again, if you see any mistakes in any of my calculations or anything else please let me know so I can correct them.

I hope you now know how bad Purity exactly is and when it might be not as bad and I wish you lots of Lunar Coins in your runs. (unless you edit them in then i wish you lots of lunar altars idk)

Hope you enjoy the Guide about Risk of Rain 2 – How bad is Purity?: the Actual Numbers, if you think we should add extra information or forget something, please let us know via comment below, and we will do our best to fix or update as soon as possible!