Preserve Math

[BigT 0]

Hey guys - I saw this preserve math post on reddit and I thought i'd share it here in case anyone was curious about when it's worth using.

I should preface this guide by saying that it's *NOT* my work, it's from reddit user /threw_it_up.

Pasted:

With the buff to the preserve prayer comes the obvious question: Is preserve worth using?

The first thing to look at is how much preserve costs to use, and if it could potentially save you money.

There are two schools of though on how to use preserve. The first is that when using it you should repot at the same level as you would have without preserve, but after a longer amount of time. The second is that you should repot after the amount of time, but at a higher level.

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I'll look at the first case.

Let's say you normally repot at 6 levels below your maximum, or every 6 minutes. With the 50% slower drain of preserve, if you were to repot at the same level, it would be every 9 minutes.

So after 18 minutes of combat you would need to repot three times without preserve, and only twice with it, saving you one dose of your boosting potion.

But how much prayer did you use during that time, and how much did it cost you?

That depends on a couple of things, your prayer level (which controls how much each dose of prayer potion restores), the cost of a prayer potion, and your prayer bonus.

Let's say that you have a prayer level of 99 and are using a holy wrench, have a prayer bonus of 15, and that prayer potions cost 9245 gp (their current price).

With 15 prayer bonus the rate of drain of preserve is 1 point every 30 seconds¹ . At that rate 18 minutes of using the preserve prayer will drain 36 prayer points. One dose of prayer potion costs 2311.25 gp and would restore 33 prayer. To restore 36 prayer points would then cost 2521.36 gp.

The trade off you've made to save 1 dose of your boosting potions is to spend 2521 gp in prayer potions. Or, if you want to save an entire 4 dose boosting potion, it would cost 10085 gp in prayer potions.

Currently a super combat costs 8826 gp, so you would be spending more money using preserve than you would by simply repotting sooner.

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What about the second case though? What if you repot after the same amount of time but at a higher level?

If you repot after 6 minutes using preserve your stats will have gone down by 4 levels. This is effective the same as repotting every 4 minutes without preserve. This becomes the exact same problem as above, but with different starting numbers.

In 12 minutes you will use:

• 3 doses without preserve

• 2 doses with preserve

12 minutes of prayer drain costs:

• 1680.91 gp

So, when repotting every 4 levels, to save a single 4 dose boosting potion will cost 6724 gp in prayer potions.

It's important to note that in both of these examples you will spend the same fraction of time at each level, whether or not you use preserve, meaning that your average DPS will not be changed by using preserve.

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This shows that the amount on time you wait before repotting affects the value proposition of using preserve.

I made this formula to show how much preserve will cost in prayer potions in order to save a single 4 dose prayer potion:

 4 * R * 3 *  ( P / A  ) *  ( 60 / [20 * {1 + B /30} ]  )

Where

• R = The amount of level drain before repotting

• P = The price of 1 dose of prayer potion

• A = The amount of prayer restored by 1 dose of prayer potion

• B = The prayer bonus of the equipment being used.

Given that the level drain before repotting seems the most interesting variable, I controlled for the other variables and made a table showing different values of R.

In this table:

• P = 2311.25

• A = 33

• B = 15

Level drain between repotting	Cost to save 1 full boosting potion
1	1681 gp
2	3362 gp
3	5043 gp
4	6724 gp
5	8405 gp
6	10085 gp
7	11766 gp
8	13447 gp
9	15128 gp
10	16809 gp
11	18490 gp
12	20171 gp

Tl:dr if the cost of your boosting potions(s) is more than the cost of prayer to save 1 full potion, then it financially beneficial to use preserve.

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Looking at the table it's pretty clear that in most situations you won't be saving money by using preserve, so are there any other reasons you might want to use preserve?

The answer is yes.

Here are some reasons why you might want to use preserve even though it's not financially beneficial:

• When you have access to free prayer restoration.

When fighting some bosses you return to your POH after every kill, usually before your prayer drains to zero. In these circumstances you will get the benefits of preserve for no cost at all. Some bosses where you might restore after every kill are: Corp beast, KQ, Zulrah, and Abyssal sire.

• When using an imbued heart.

An imbued heart can only boost your magic level once every 7 minutes. There is no option to 'repot' sooner when using one. As such, using preserve will result in DPS improvements when using magic and an imbued heart.

• You are trying to save inventory space

Typically, you are going to need more doses of prayer potion to keep preserve going than you save, but in some cases you might have multiple boosting potions taking up more space. Abyssal sire and DKs are an example of places where you will have a super combat and a ranging potion, meaning that you save two doses instead of one (which is twice the inventory space).

[Origen 531]

Well, just scrolling through this math makes my head hurt.

[vSICKNESSv 30]

Oml lol

[Jonttu 78]

Ok

[modlulz 43]

dx

[Jasper 110]

14 hours ago, Or1gen said:

Well, just scrolling through this math makes my head hurt.

exactly this lmao  

[Sybren 2,255]

Thanks for sharing this, I highlighted the most important part