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I am trying to figure out the effect of FNP types of rolls on my Tyranids.
I think I found an enlightening conclusion in the numbers.
Please correct me if I'm wrong.

Tyranids
Catalyst psychic power grants a 5+ FNP. Leviathan Hive Fleet grants a 6+ FNP.
Genestealers have a 5++ save. 33% of rolls will save and 66% will fail. Of the 66% that fail, Catalyst will save 33% and Leviathan will save 16.5%.
To find the total percent of saving throws that will succeed, we add the 5++ percent and the FNP%.
The save calculation for Genestealers with Catalyst is: 33% + (66% x 33%) = 54.78%, the 5+ FNP improved the save by 64%
For Leviathan: 33% + (66% x 16.5%) = 43.99%, the 6+ FNP improved the save by 32%

Space Marines
(Not sure what it's called) psychic power grants a 5+ FNP. (I'm sure some other ability) grants a 6+ FNP.
Space Marines have a 3+ save. 66% of rolls will save and 33% will fail. Of the 33% that fail, a 5+ FNP will save 33% and a 6+ FNP will save 16.5%.
To find the total percent of saving throws that will succeed, we add the 3+save percent and the FNP%.
The save calculation for Space Marines with 5+ FNP is: 66% + (33% x 33%) = 77.55%, the 5+ FNP improved the save by 16%
The save calculation with 6+ FNP is: 66% + (33% x 16.5%) = 72.11%, the 6+ FNP improved the save by 8%

Finally
FNP has 4 times the effect on a unit with a 5+ armor save as a 3+ armor save.

Further
For a 2+ armor save: 5+ FNP improves the total save by 6.6%, 6+ FNP by 3.3%
For a 4+ armor save: 5+ FNP improves the total save by 33%, 6+ FNP by 16.5%
For a 6+ armor save: 5+ FNP improves the total save by 166%, 6+ FNP by 83%

Yes, if you assume no AP. Units with weak armour will get more utility from an FNP type save than units with strong armour simply because they'll be using it more often.

Against AP -2 you'll see them get the same utility (since a 3+ becomes equivalent to a 5++ in that scenario).

If you had a 2++ save then you'd get almost no value from FNP because you'd save the vast majority of wounds with your invulnerable.

I always knew that a FNP helped a weak armor save more, but I never quantified it. I think it helps you decide when to take Catalyst or Fortune and when you don't need them.

It also helps with quick calculations of how many models you can expect to survive if you cast a certain power here or there.

 ArmyC wrote:
I am trying to figure out the effect of FNP types of rolls on my Tyranids.
I think I found an enlightening conclusion in the numbers.
Please correct me if I'm wrong.

Tyranids
Catalyst psychic power grants a 5+ FNP. Leviathan Hive Fleet grants a 6+ FNP.
Genestealers have a 5++ save. 33% of rolls will save and 66% will fail. Of the 66% that fail, Catalyst will save 33% and Leviathan will save 16.5%.
To find the total percent of saving throws that will succeed, we add the 5++ percent and the FNP%.
The save calculation for Genestealers with Catalyst is: 33% + (66% x 33%) = 54.78%, the 5+ FNP improved the save by 64%
For Leviathan: 33% + (66% x 16.5%) = 43.99%, the 6+ FNP improved the save by 32%

Space Marines
(Not sure what it's called) psychic power grants a 5+ FNP. (I'm sure some other ability) grants a 6+ FNP.
Space Marines have a 3+ save. 66% of rolls will save and 33% will fail. Of the 33% that fail, a 5+ FNP will save 33% and a 6+ FNP will save 16.5%.
To find the total percent of saving throws that will succeed, we add the 3+save percent and the FNP%.
The save calculation for Space Marines with 5+ FNP is: 66% + (33% x 33%) = 77.55%, the 5+ FNP improved the save by 16%
The save calculation with 6+ FNP is: 66% + (33% x 16.5%) = 72.11%, the 6+ FNP improved the save by 8%

Finally
FNP has 4 times the effect on a unit with a 5+ armor save as a 3+ armor save.

Further
For a 2+ armor save: 5+ FNP improves the total save by 6.6%, 6+ FNP by 3.3%
For a 4+ armor save: 5+ FNP improves the total save by 33%, 6+ FNP by 16.5%
For a 6+ armor save: 5+ FNP improves the total save by 166%, 6+ FNP by 83%

FNP has the same effect on all armor values, in effect it is wrong to think about it in terms of save, it is best to just consider the model with 50% more wounds for 5+++ and 20% more wounds for 6+++.

You can get to this conclusion using your numbers, but looking at a different parameter. You compared the percentage of saves which got saved. I suggest you to compare the amount of wounds that were NOT saved without the FNP divided by the amount of wounds NOT saved with the FNP. You will notice that this parameter is equal no matter the armor save,


Automatically Appended Next Post:
In general, when mathammering a damage, you do it like you just did. Instead, when mathammering a save, you consider the inverted results. This is the reason why incrementing a wound roll from 3+ to 2+ increases damage by 25%, but increasing a save from 3+ to 2+ reduces the damage taken by 50%.

Spoletta, I see your point.
However, don't you think my calculations are useful in determining which unit should receive the support or which spell or ability to take in the first place?

 ArmyC wrote:
Spoletta, I see your point.
However, don't you think my calculations are useful in determining which unit should receive the support or which spell or ability to take in the first place?

That's a question that i often pose to myself, actually i do it every time i manifest catalyst.
Those powers are not targeted to the unit that will receive the best benefit out of it, but to the unit that is most likely to be prioritized by your opponent.
Usually, the higher cost per wound of a model, the more likely it is that he will be focused. So, If you added to your calculations the cost per wound of the receiving model, you would have a good idea of who to prioritize in a vacuum (matchups have a lot to say though, if i have only infantry i'm not going to bother with your quadlas pred).

FNP confers exactly the same benefit on a unit with a 2+ armour save as on a unit with a 6+ armour save.

 ArmyC wrote:
Spoletta, I see your point.
However, don't you think my calculations are useful in determining which unit should receive the support or which spell or ability to take in the first place?

Not really. If your choice is between giving 50 points of Gaunts an extra couple of wounds or a 200 point warlord hive tyrant an extra couple of wounds, which do you think is more worth while?

If you put catalyst on a unit of gaunts, it's probably not a huge deal to still take them out since anti infantry firepower isn't hard to come by, while on a flyrant, there's usually a relatively limited amount of things that can effectively engage it.

What about if you've got 2 units of identical gaunts? What's to stop your opponent from simply pouring bolterfire into the non-catalyst squad?

If you've got a bunch of gaunts sitting on an objective on turn 7 that will win you the game as opposed to a non-warlord flyrant who is off being a distraction, it's a bit of a no-brainer.

If you've got a small handful of gaunts away from anything that matters while you've only got a single flyrant remaining holding all your synapse and decent firepower, it's also a bit of a no-brainer.

What if you desperately need your carnifex/hive guard/zoanthropes/exocrine/whatever to deal with a certain key unit of theirs that you're going to have a bunch of problems with if you just have gaunts/warriors/ravenors/etc?

If you've got a unit about to charge and will get benefit out of it in overwatch, your fight, enemy shooting (if they disengage) and enemy fight (if they don't disengage) phases, is that not better than just a unit that might get shot at in the enemies shooting phase?

At the end of the day, no matter what you put it on, you're still saving 1/3 of the wounds that would normally go through after armour/invul regardless of target, so it's more about handing out layered saves to the things that need it rather than things that get a proportionally higher use out of it. The things that need it will vary from turn to turn, dependant on the situation.

6+ FnP is a flat 1/6 increase in durability.

If the unit has a 2+, fewer wounds will roll that 6+ FnP, but you have fewer models in that unit (because 2+ costs points one way or another).

Nearly* all units gain the same ratio of survivability. For mathhammer in this regard, they are equal. Termies will survive 17% more fire.

*There are a couple exceptions:
-Models with some FnP rules - such as Uthwe - get less from an added FnP because the rules for some of them state they do not stack.
-Multi-wound models can get complicated:
--A 3-W model taking hits from a 3W weapon gains a huge amount - nearly 50% more durability from just a 6++, in this case
--A 1-W model taking hits from a 3W weapon gains almost nothing - less than half a percent increased durability

That said, even a flat 17% increase in durability might sound flat, but isn't really. That unit of Gaunts are going to be 17%+ more effective. Because their role is to tie up the opponent, if the opponent can't wipe them out fast enough. And even a 17% increase has a good chance of tipping the scales, if they were close at all. But putting it on something like a Farseer or Blaster-Born is going to do basically nothing - because if they're taking hits, they're going to be dead regardless. You use them in ways that doesn't let them take hits.

You're looking at it from the wrong angle.

Do you think that going from 10% chance to save to 20% (a +100% increase) is better than going from 80% to 90% (a +12,5% increase)?

In reality, going from 80% to 90% doubles your durability. You take half as many wounds. And going back to the fnp problem. Unless a model has some kind of modifier to its fnp, it always gives the same level of protection.

macexor wrote:
You're looking at it from the wrong angle.

Do you think that going from 10% chance to save to 20% (a +100% increase) is better than going from 80% to 90% (a +12,5% increase)?

In reality, going from 80% to 90% doubles your durability. You take half as many wounds. And going back to the fnp problem. Unless a model has some kind of modifier to its fnp, it always gives the same level of protection.

This. You don't care how many saves you make. You care how many saves you fail. A 6+ FNP is a 20% increase in durability, regardless of save -- if it took on average X lasgun shots to kill each model without the FNP, now it takes on average 1.2 times X.

Dionysodorus wrote:

macexor wrote:
You're looking at it from the wrong angle.

Do you think that going from 10% chance to save to 20% (a +100% increase) is better than going from 80% to 90% (a +12,5% increase)?

In reality, going from 80% to 90% doubles your durability. You take half as many wounds. And going back to the fnp problem. Unless a model has some kind of modifier to its fnp, it always gives the same level of protection.

This. You don't care how many saves you make. You care how many saves you fail. A 6+ FNP is a 20% increase in durability, regardless of save -- if it took on average X lasgun shots to kill each model without the FNP, now it takes on average 1.2 times X.

You mean ~17%. Also since FNP can't be removed but is applied unit wide, it gains more value the more models in a unit. Something that Tyranids have a easier time getting large numbers of. So yes I would say Tyranids benefit more IF they focus on large units of gribblies.

Well, number and quality of the wound

20 no-save wounds get the same value from FnP as 10 4++ wounds.

20 no-save wounds and 10 4++ wounds both get increased by 17%. But 3.4 no-save wounds are going to be worth just as much as 1.7 4++ wounds, as they'll both take just as much additional firepower to remove.

Also, there are tactical considerations that are hard to mathhammer. If the opponent has a 50/50 shot at removing the Gaunts without FnP before they tie up the shooters, FnP is huge. But if a squad of Fire Dragons are more likely than not going to be shot with twice the firepower needed to kill them, FnP isn't going to do much.

 Quickjager wrote:

Dionysodorus wrote:

macexor wrote:
You're looking at it from the wrong angle.

Do you think that going from 10% chance to save to 20% (a +100% increase) is better than going from 80% to 90% (a +12,5% increase)?

In reality, going from 80% to 90% doubles your durability. You take half as many wounds. And going back to the fnp problem. Unless a model has some kind of modifier to its fnp, it always gives the same level of protection.

This. You don't care how many saves you make. You care how many saves you fail. A 6+ FNP is a 20% increase in durability, regardless of save -- if it took on average X lasgun shots to kill each model without the FNP, now it takes on average 1.2 times X.

You mean ~17%. Also since FNP can't be removed but is applied unit wide, it gains more value the more models in a unit. Something that Tyranids have a easier time getting large numbers of. So yes I would say Tyranids benefit more IF they focus on large units of gribblies.

6+ FnP is a 20% increase in durability. Let's start with an easier example.
Imagine you have a 4+ FnP save. You save half of your wounds. You have 10 hp. Your enemy needs to deal 20 damage to you in order to kill you, because you'll save half of it. You're twice as durable.
With 5+ FnP you save 1/3. In this case he needs to deal you 15 wounds, because 1/3 will be saved. Your are 50% more durable.
With a 6+ FnP save, he'll need to deal you 12 wounds, cause you'll save 1/6, that is 2 in this case. 20% durability.

If 5+ FnP is 1/3, than your increase in durability equals 1/(1-FnP).
6+ gives 20%, you're 1.2 times more durable
5+ gives 50%, you're 1.5 times more durable
4+ gives 100%, you're 2 times more durable
3+ gives 200%, you're 3 times more durable (only 1/3 of wounds dealt go through)
2+ gives 500%, you're 6 times more durable (only 1/6 of wounds dealt go through)

At least that's the way I count it.

Leviathan doesn't stack with Catalyst. It explicitly says so.

Also, FNP will have a bigger effect on multi-wound models, too.

Dealing 3 damage to a 3 wound model, FNP gives it a solid chance to survive.

And yes giving something a save, when it had no save, is a huge increase in survivability.

FNP is one of our worst hive fleet traits. Tyranids aren't strong because they have defense.

This is like one of those logic puzzles that really trips you up until you realize there was a faulty premise. In this case it's forgetting the commutative property of multiplication, A visual example:


A 6+ FNP is always a 16.7% reduction in damage, if you take 100 wounds it will save you 17ish wounds, if you take 6 it will save you 1. The percent increase in toughness is the same throughout, so it's as valuable to terminators as it is to pox walkers. If you have 200 points of pox walkers and 200 points of deathshroud terminators, their 5+ DR will save the same number of points from death assumign no multi-wound weapons. It will be a different number of models and a different number of wounds, but that all comes out in the wash.

*EDIT* Removing my bad math. It's quoted below if you really want to see it. *EDIT*

Medicinal Carrots wrote:
FNPs statistically work like a straight wound multiplier. The more wounds you start off with, the greater the total benefit you will get from a FNP. Since multipliers compound (like interest), the more FNPs you stack on a single unit, the more effective each one will be. To calculate the effect of a FNP, it's W * (1 + chance of FNP success). If you have multiples, you multiply all FNPs together with your wounds.

E.G.: A 1 wound model with a 5+ FNP has 1*(4/3) or 1.33... wounds. If it just has a 6+ FNP, it's 1*(7/6) or 1.166... wounds. If it has both, that's 1*(4/3)*(7/6) wounds. That works out to 28/18 or 1.55... wounds.

Saves statistically work as conditional wound multipliers, since they don't work against everything. To figure out what effect they have, you use the same formula, just adjust the chance of success based on AP and whether or not it's a mortal wound (where you skip the armor and just use the FNP multiplier).

E.G: A 1 wound model with a 5+ invuln and no normal save doesn't care about AP, so it has an effective 1*(4/3) = 1.33... wounds. If that model also has a 5+ and a 6+ FNP, it has 1*(4/3)*(4/3)*(7/6) = 112/54 = 2.074074...wounds.

A 1 wound model with a 3+ save and no invuln cares about the AP. Against AP 0, it's got 1*(5/3) = 1.66... wounds. Against AP-1, it's 1*(3/2) = 1.5, AP-2 is the same as a 5+ invuln, and AP-3 is 1*(7/6) = 1.166.. Against AP-4, it gets no save, so it's 1*(3/3) = 1.

If a 1 wound 3+ normal save model gets a 5+ and 6+ FNP, vs AP 0 it now has 1*(5/3)*(4/3)*(7/6) = 140/54 = 2.592592... wounds. About half a wound better than the 5++.

If we go to a Terminator with the same 5+ and 6+ FNP, vs AP 0 it now has 2*(11/6)*(4/3)*(7/6) = 5.703703... wounds. A bit over a 3.5 wound increase compared to a little over 1.5 for a model with a 3+ and only 1 wound.

A FNP gives you the most benefit on unit with the most wounds remaining, the best save, or other FNPs already in effect. Roughly in that order. 20 Genestealers will get more benefit from Catalyst than an unwounded Hive Tyrant will. The break even point against AP 0 is 12.5 Genestealers. Against AP-1, the break even is 11.75.

This isn't quite right. See macexor's post three up from yours. A 6+ FNP is a 20% increase in effective wounds, not 16.7% -- you need to use 1 over its fail chance, not 1 plus its success chance. What you're doing implies that a model with a 1+ FNP only effectively doubles its wounds, when it's actually invincible. But the numbers start looking pretty silly even at 3+. Does it really seem to you like a Marine's save is only worth an extra 2/3 of a wound vs AP0? He only suffers 1 wound for every 3 he otherwise would; he's three times as durable.

Dionysodorus wrote:

Spoiler:

Medicinal Carrots wrote:
FNPs statistically work like a straight wound multiplier. The more wounds you start off with, the greater the total benefit you will get from a FNP. Since multipliers compound (like interest), the more FNPs you stack on a single unit, the more effective each one will be. To calculate the effect of a FNP, it's W * (1 + chance of FNP success). If you have multiples, you multiply all FNPs together with your wounds.

E.G.: A 1 wound model with a 5+ FNP has 1*(4/3) or 1.33... wounds. If it just has a 6+ FNP, it's 1*(7/6) or 1.166... wounds. If it has both, that's 1*(4/3)*(7/6) wounds. That works out to 28/18 or 1.55... wounds.

Saves statistically work as conditional wound multipliers, since they don't work against everything. To figure out what effect they have, you use the same formula, just adjust the chance of success based on AP and whether or not it's a mortal wound (where you skip the armor and just use the FNP multiplier).

E.G: A 1 wound model with a 5+ invuln and no normal save doesn't care about AP, so it has an effective 1*(4/3) = 1.33... wounds. If that model also has a 5+ and a 6+ FNP, it has 1*(4/3)*(4/3)*(7/6) = 112/54 = 2.074074...wounds.

A 1 wound model with a 3+ save and no invuln cares about the AP. Against AP 0, it's got 1*(5/3) = 1.66... wounds. Against AP-1, it's 1*(3/2) = 1.5, AP-2 is the same as a 5+ invuln, and AP-3 is 1*(7/6) = 1.166.. Against AP-4, it gets no save, so it's 1*(3/3) = 1.

If a 1 wound 3+ normal save model gets a 5+ and 6+ FNP, vs AP 0 it now has 1*(5/3)*(4/3)*(7/6) = 140/54 = 2.592592... wounds. About half a wound better than the 5++.

If we go to a Terminator with the same 5+ and 6+ FNP, vs AP 0 it now has 2*(11/6)*(4/3)*(7/6) = 5.703703... wounds. A bit over a 3.5 wound increase compared to a little over 1.5 for a model with a 3+ and only 1 wound.

A FNP gives you the most benefit on unit with the most wounds remaining, the best save, or other FNPs already in effect. Roughly in that order. 20 Genestealers will get more benefit from Catalyst than an unwounded Hive Tyrant will. The break even point against AP 0 is 12.5 Genestealers. Against AP-1, the break even is 11.75.

This isn't quite right. See macexor's post three up from yours. A 6+ FNP is a 20% increase in effective wounds, not 16.7% -- you need to use 1 over its fail chance, not 1 plus its success chance. What you're doing implies that a model with a 1+ FNP only effectively doubles its wounds, when it's actually invincible. But the numbers start looking pretty silly even at 3+. Does it really seem to you like a Marine's save is only worth an extra 2/3 of a wound vs AP0? He only suffers 1 wound for every 3 he otherwise would; he's three times as durable.

You're right. I screwed up the formula. That's what I get for doing this instead of sleep. The basic ideas still stand, that FNP is a wound multiplier and saves are a conditional multiplier and they compound, but the math is wrong.

Correct formula should be W * (Inverse of chance to fail the FNP or save). Like 1*(3/2) for a 5+ FNP on a 1 wound model. Re-doing my examples:

1. A 1 wound model with a 5+ FNP has 1*(3/2) or 1.5 wounds. If it just has a 6+ FNP, it's 1*(6/5) or 1.2 wounds. If it has both, that's 1*(3/2)*(6/5) wounds. That works out to 18/10 or 1.8 wounds.

2. A 1 wound model with a 5+ invuln and no normal save doesn't care about AP, so it has an effective 1*(3/2) = 1.5 wounds. If that model also has a 5+ and a 6+ FNP, it has 1*(3/2)*(3/2)*(6/5) = 54/20 = 2.7 wounds.

3. A 1 wound model with a 3+ save and no invuln cares about the AP. Against AP 0, it's got 1*(3/1) = 3 wounds. Against AP-1, it's 1*(2/1) = 2, AP-2 is the same as a 5+ invuln, and AP-3 is 1*(6/5) = 1.2 Against AP-4, it gets no save, so it's 1*(3/3) = 1.

4. If a 1 wound 3+ normal save model gets a 5+ and 6+ FNP, vs AP 0 it now has 1*(3/1)*(3/2)*(6/5) = 54/10 = 5.4 wounds. Twice as much as the 5++.

5. If we go to a Terminator with the same 5+ and 6+ FNP, vs AP 0 it now has 2*(6/1)*(3/2)*(6/5) = 21.6 effective wounds. Almost 4 times as much as for a model with a 3+ and only 1 wound.

A FNP gives you the most benefit on unit with the most wounds remaining, the best save, or other FNPs already in effect. The effect basically depends on the effective wounds before you add the new FNP. A save that's twice as good means roughly double the effective wounds (so going from a 6+ to a 5+ or 5+ to a 3+ means each wound is twice as effective). Going from a 5+ to a 4+ is 1.5 times as effective, so it equates to 1.5 as many wounds. 20 Genestealers will get the same benefit from Catalyst that an unwounded Hive Tyrant will against AP 0. Against AP-1, it only takes 15 Genestealers to get the same benefit as a Hive Tyrant, and AP-2 or more means 10 Genestealers get the same benefit as the Tyrant.

macexor wrote:

 Quickjager wrote:

Dionysodorus wrote:

macexor wrote:
You're looking at it from the wrong angle.

Do you think that going from 10% chance to save to 20% (a +100% increase) is better than going from 80% to 90% (a +12,5% increase)?

In reality, going from 80% to 90% doubles your durability. You take half as many wounds. And going back to the fnp problem. Unless a model has some kind of modifier to its fnp, it always gives the same level of protection.

This. You don't care how many saves you make. You care how many saves you fail. A 6+ FNP is a 20% increase in durability, regardless of save -- if it took on average X lasgun shots to kill each model without the FNP, now it takes on average 1.2 times X.

You mean ~17%. Also since FNP can't be removed but is applied unit wide, it gains more value the more models in a unit. Something that Tyranids have a easier time getting large numbers of. So yes I would say Tyranids benefit more IF they focus on large units of gribblies.

6+ FnP is a 20% increase in durability. Let's start with an easier example.
Imagine you have a 4+ FnP save. You save half of your wounds. You have 10 hp. Your enemy needs to deal 20 damage to you in order to kill you, because you'll save half of it. You're twice as durable.
With 5+ FnP you save 1/3. In this case he needs to deal you 15 wounds, because 1/3 will be saved. Your are 50% more durable.
With a 6+ FnP save, he'll need to deal you 12 wounds, cause you'll save 1/6, that is 2 in this case. 20% durability.

If 5+ FnP is 1/3, than your increase in durability equals 1/(1-FnP).
6+ gives 20%, you're 1.2 times more durable
5+ gives 50%, you're 1.5 times more durable
4+ gives 100%, you're 2 times more durable
3+ gives 200%, you're 3 times more durable (only 1/3 of wounds dealt go through)
2+ gives 500%, you're 6 times more durable (only 1/6 of wounds dealt go through)

At least that's the way I count it.

Yes in terms of durability, and yes I already know how to do math thank you. But a FNP will only save 1/6th of the time regardless of model cost is what I am trying to say. Going from a 3+ to a 2+ is doubling your durability (assuming AP0) but your math is flawed in the first place because you rounded up. You assumed the 1/6 SAVE somehow over 12 wounds, that is assuming the 2nd save is in first 4 rolls of the 2nd range of 6. When there is a chance that the roll to save 1/6 of the will occur on the 5th or 6th roll. Which leads to a 17% chance (rounded). WHICH makes sense because you only have 17% chance (rounded) of making that save on a D6

@Quickjager

While I was writing my previous post, I was thinking I was answering OP's post. That's the reason why I've described it the way I did. Sorry if it felt like an attack.

But you're misunderstanding the subject. Yes, there is a 16.6% chance to make that FnP roll. But it doesn't translate into 16.6% increase in durability. Thinking, that when you've got only 10 hp, the second FnP save doesn't happen (first save in the first 6 wounds, then there are only 4 wounds left as you've said, so no FnP roll guaranteed on the second) is a naive way of thinking. I use averages to make the counting easier, but that doesn't make them wrong.

To approach your "there are only 4 wounds left, so no guarantee to make that 12th FnP roll" I can use several tools.

The saves you've already made, can actually be saved once again. So in your scenario, after the first 6 points of damage, you still have 5 and not 4 wounds left. This whole thing resembles a lot geometric series. The sum of it is a*(1-r^n)/(1-r), where a in this case is the number of our wounds, are - the ratio is our FnP save chance 1/6 (16.6%) and n the number of times we repeat this process. Since we can actually repeat "feel no paining" the same wound over and over again, n approaches infinity and our previous sum becomes a*(1-0)/(1-r) => a/(1-r). In our case 10/(1-1/6) = 12. That's actually the formula I've used before.

You can also look more into how each and every roll can be a 6 and count the probability of saving n wounds.

Somehow it turns out, that in case of taking 12 wounds, on average, exactly 10 of them will go through. Here I'm not really rounding up anything, am I?

The easier way to demonstrate this would be to ask yourself "How much damage can I take before I die?" You've got 10 wounds and a 6+ FnP. X damage must be done to kill you. Chance to fail a FnP roll is 5/6, so X * 5/6 = 10. This gives us exactly X = 12.

I have a feeling we are talking past each other still. I am trying to show that the your example of 10 wound model having 20% durability is incorrect.

I agree you roll 12 times, you get 6 twice statistically leading to 10 wounds taken.

I am saying however that the statistical chance of the distribution of the two 6+ saves both being in the first 10 wounds is what makes it incorrect that it is a 20% increase in durability. Which I found led to a 17% increase rather. If possible could you tell why this is not the case? Rather if you would also explain how grimgold isn't correct in his explanation either.

The explanation is easy. I've written it above. The wounds you have saved can be saved over and over again.

 Quickjager wrote:
I have a feeling we are talking past each other still. I am trying to show that the your example of 10 wound model having 20% durability is incorrect.

I agree you roll 12 times, you get 6 twice statistically leading to 10 wounds taken.

I am saying however that the statistical chance of the distribution of the two 6+ saves both being in the first 10 wounds is what makes it incorrect that it is a 20% increase in durability. Which I found led to a 17% increase rather. If possible could you tell why this is not the case? Rather if you would also explain how grimgold isn't correct in his explanation either.

Grimgold's right that a 6+ FNP is a 17% reduction in damage. A 17% reduction in damage is equivalent to a 20% increase in durability.

I mean, just ask: how many BS4+ lasgun shots does it take, on average, to kill a Marines? You'd just do 1 / (1/2*1/3*1/3), right? You find the expected wounds per shot and then flip the numerator and denominator to get expected shots per wound. So you get 18 shots. Now what if the Marine has a 6+ FNP? We apply the same procedure: 1 / (1/2*1/3*1/3*5/6) = 21.6. And 21.6 / 18 is 1.2; the Marine got 20% more durable.

Again, you can easily see that you're thinking about this the wrong way by looking at better FNPs. If a model has a 1+ FNP, that's a 100% reduction in damage, yeah? But obviously it's much better than a 100% increase in durability. A 1+ FNP doesn't just make you twice as durable; it makes you infinitely more durable. In the specific case you're talking about, you're just not considering that sometimes you do make 2 of those FNPs in the first 10 wounds. And each wound you save gives you another opportunity to roll. If you work out the distribution of results you'll find that it takes on average 12 unsaved wounds to kill a 10 wound model with a 6+ FNP. If you want to do something empirical, you could try this with a 2+ FNP (since the difference between 17% and 20% is going to be harder to discern). Just roll until you get a 1 and write down how many dice you had to roll to get to that point. You should find that on average you have to roll 6 dice, not ~1.83, which is what your approach predicts.

It is a 20% increase, and there are 2 additional proofs that might make that clearer.

First off, you're making a naive calculation assuming the FNP as a static 1/6 roll done one time. The problem with that approach is that each successful FNP save doesn't just save your wound then, it gives you the opportunity to make an additional FNP attempt later on. If you factor in a second attempt, that second attempt has a 1/36 chance of happening, so you need to add that to the initial 1/6 chance. But wait, a second save gives you the chance to attempt a third FNP later on, and so on indefinitely, so long as you keep making the save.

So the actual increase isn't 16.67%. If you factor in 2 attempts, it's 19.44%. If you factor in the 3rd it's 19.91%. You have to keep adding in an infinite number of potential attempts, because there's an increasingly slim chance that you will continue to make an improbable string of saves. If you infinitely sum (1/6)+(1/6*1/6)+(1/6*1/6*1/6)... the result comes to 0.2, or 20%.

This is the exact same reason that the Ultramarines warlord trait results in an affective 50% increase of Command Points instead of a 33% increase. Each successful roll gives you additional rolls.

Now let's try working from the end result backwards for the second approach. The total Durability Increase (DI) is the difference beteween Final Durability (FD) and Initial Durability (ID), or FD-ID. The percentage of durability increase is the total Durability Increase divided by the Initial Durability, or DI/ID. Put together, that's (FD-ID)/ID.

As an example, if you start with $100 and end up with $12, your total increase is $20 ($120-$100), and your percentage increase is 20% ($20/$100).

The next thing to consider is that a 1/6 FNP does represent 16.67% durability. However, it represents 16.67% of the Final Durability. To continue with the money, that $20 is only 16.67% of the final total ($20/$120), it's not the percentage increase.

Mathing that out, we get Final Durability = Initial Durability + difference from FNP. Or FD=ID+FNP. Combined with the fact that the Feel No Pain is 1/6th of the Final Durability (FNP=FD*1/6), we can substitute and get that FD=ID+(FD/6).

We need to solve for a term to figure things out from here, so let's solve from FD:
FD-(FD/6) = ID
FD*5/6 = ID
FD = ID*6/5

Now to get the Durability Increase and percentage of the increase:
DI = FD - ID
DI = ID*6/5 - ID
DI = ID/5

Percentage of increase = (ID/5)/ID
That comes to 1/5 or 20%

People I was asking HOW I was wrong ffs, not if I was wrong. You don't do that by saying well here is a proof. That does nothing.

I was looking at calculating damage reduction, not durability. Which was my mistake none of you pointed out.

 Quickjager wrote:
People I was asking HOW I was wrong ffs, not if I was wrong. You don't do that by saying well here is a proof. That does nothing.

I was looking at calculating damage reduction, not durability. Which was my mistake none of you pointed out.

I mean, I only made this distinction explicit and asserted the equivalence of a 17% damage reduction and a 20% durability increase in my first sentence, but sure.

Also a proof is literally what you're asking for when you ask someone to explain why you're wrong about math. It's not like you actually gave an argument or anything for why you thought it was only a 17% durability increase which someone could have looked at and pointed out where you went wrong. The farthest you went was criticizing other people's correct arguments with some gibberish about rounding saves up.

I dIdn't read yours because I wasn't asking you Dion. So what you got a problem now that you don't got someone pay g attention to you?


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If the worse thing you got to say is someone is gibbering when they were asking how they were wrong. Then damn I have to say that other thread is right, toxic player attitude like that is what's wrong with dakkadakka.

Well showing you the correct answer is a form of correction. And it's not like you gave any formulas, that we could correct.

You got genuine answers. People trying to explain that matter. No one was really toxic. If I were to be honest, your answers kinda were. But no offense taken by me. And I hope I didn't offend you.

And that is a perfectly fine opinion, you didn't offend macexor I was simply saying I hoped YOU could have corrected the fundamental issue which was I was doing reduction not durability. Which happens, and yes I skipped over Dion, because I wasn't concerned with Dion's answer as I was interested in YOUR answer; and you know what I am sorry if I am came across as toxic. Its simply much easier to be direct rather than curate myself on a phone.

So right now yea wow I had a misunderstanding. Realized I was doing something wrong and wanted to improve, go on hang me for it.