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Ailowynn

Evade token 2.0 math?

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Has anyone else looked at these numbers? I gave it a shot just out of curiosity, but I’m not any kind of mathematical person, haven’t done much more than calculate a tip since high school. So check my thinking:

 

If you have 1 defense die, your chances of the evade being useful are 1-P(evade), which gets you 5/8 or 63%.

For a 2 die ship, the evade is only NOT useful if you roll two natties, so 3/8 * 3/8. That means the evade is useful 86% of the time (or, in other words, it’ll block .86 of a hit). 

For 3 dice, that goes up to 95%; for 4 dice, you’re at 98%; and past that, you’re pretty well guaranteed to block one hit out of the evade.

 

Now compare that to a defensive focus. 

For 1 die, you have a 2/8 chance to roll a focus. So 25% of a block from it. 

For 2 dice, your chances of getting at least one evade out of the focus would be 1-P(evade or blank & evade or blank), right? That gets you a 44% chance of at least one block, but you also might get two evades out of the one focus (which would be...what, 1/16? 6.25%). So you’ve got (.44-.0625)*1 + .0625*2 evades from the focus, which works out to .5025.

For 3 dice, it’s .578 to roll 1+ foci. Getting 2+ foci would mean 1/4 & (1/4 or 1/4). So... .25*.5625 = .141, and then the probability of rolling three foci is .25*.25*.25 = .0156. 

So P(1 focus) = .578 - (.141+.0156) = .421

P(2 foci) = .141 - .0156 = .1254

P(3 foci) = .0156

So you expect to get .876 evades from that focus token. 

And then four dice is just way too complicated for me. 

 

 

TL;DR my hack-and-slash math gets me the following numbers:

EVADE TOKEN

1 agi: 0.63 of a block

2 agi: 0.86 of a block

3 agi: .95 of a block

FOCUS TOKEN

1 agi: 0.25 of a block

2 agi: 0.5025 of a block

3 agi: 0.876 of a block

 

The real trick is that that’s per shot. If you’re a 3-die ship getting shot two or three times, I imagine a focus is just better, since it can get you multiple evades, but I don’t know how to do those numbers. Anyone else able to corroborate or deny those numbers? 

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So I think there's two ways of looking at it, I did the maths for our Slack channel the other day but killed the excel so don't have it to hand.

The first part is what the value of an Evade token is now, next to it's 1.0 value.  So in 1.0 an Evade token is worth 1 hull, while in 2.0 its value is dependent on the number of dice you're rolling (more dice mean more chance that you'll have a blank to mod), and on whether you also have a Focus token to spend so you need it to be a blank, or a focus result will convert the Evade as well. 


The second part is the raw defensive efficiency of Evade vs Focus.  So in 1.0 an Evade is better until you get to 4 green dice, while in 2.0 the tipping point to Focus being better is at 3 green dice.

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2 minutes ago, Boba Rick said:

Things are going to die so much faster in 2.0

It's going to be a lot harder to be completely bulletproof.  When somebody shoots at you you can expect to take a bit of damage.

The best defence will be avoiding arcs.

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3 minutes ago, Boba Rick said:

Things are going to die so much faster in 2.0

This makes me and my B-wing loving heart so happy.  Costing on B-wings is going to be tricky.  Lots of hit points and very shooty might be terrifying again.  I hope they get a fancy new sculpt because I sold 2 of mine when they became crap.

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The focus math isn't right. Since the effect of the token is global ("spend it or don't") then each green die can be considered in isolation: each gives a 0.25 chance of being an eyeball, so you can just multiply the number of green dice by 0.25 to get the expected value of spending the token.

At three green dice, the evade is worth 0.95, while the focus is worth 0.75.

That said, the evade is only worthless when the ship is taking more damage than it has in green dice, and all the dice are already evade results. Evade's still good.

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34 minutes ago, Boba Rick said:

Things are going to die so much faster in 2.0

Maybe, but i do not think so.

-Its harder to get mods (predator is only in arc, no PTL to name a few)
-Offensive dice are tonned down (tie phantom is now only 3red)

-some of the big damage stuff is removed (TLT, Harppons)

-Evade is still really good on ships that should have it, and is worse on ships that really shouldn't be evading anything anyways.

 

 

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I haven't checked the math, @Ailowynn, but I think your assumptions are in the right place, generally speaking. There is another, odd factor to consider; in one sense, each type of token becomes more valuable as the number of dice increase, but also it becomes less valuable. This is because as your quantity of defense dice increases, so do your odds of avoiding damage altogether without need of modification.

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19 minutes ago, SOTL said:

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Thanks for the work. Might I suggest having the same y-axis/scale on the "Single Token"<->"Both Tokens" comparisons.

Just to clarify, "New Evade (if Focus)" how am I to understand that one? 
 

Finally, this basically tells me just how stupidly broken 1st edition reinforce was... 

Edited by Sciencius
spelling

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8 minutes ago, Sciencius said:

Thanks for the work. Might I suggest having the same y-axis/scale on the "Single Token"<->"Both Tokens" comparisons.

Just to clarify, "New Evade (if Focus)" how am I to understand that one? 
 

Finally, this basically tells me just how stupidly broken 1st edition reinforce was... 

"New Evade (if Focus)" = if you've already got a Focus token then the Evade is only usefully adding to your defense if you roll a blank, where if you don't have a Focus then an eyeball or a blank will do for you.

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56 minutes ago, SOTL said:

"New Evade (if Focus)" = if you've already got a Focus token then the Evade is only usefully adding to your defense if you roll a blank, where if you don't have a Focus then an eyeball or a blank will do for you.

Well now I am not really sure I understand...I thought that was what "Both Tokens" were supposed to give me?  

Suggestion:

I think, it would have been much more clear and usefull to everybody, if you had made graphs like:

Left panel: 1st edition with 4 curves:  no tokens, evade, focus, focus+evade 

Middel panel: 2nd edition with 4 curves: no tokens,  evade,  focus, focus+evade

Right pane: 2nd edition +one force-charge with 4 curves: no tokens,  evade,  focus, focus+evade

using the same scale on the y-axis on all 3 panels. 

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14 minutes ago, Sciencius said:

Well now I am not really sure I understand...I thought that was what "Both Tokens" were supposed to give me?  

Suggestion:

I think, it would have been much more clear and usefull to everybody, if you had made graphs like:

Left panel: 1st edition with 4 curves:  no tokens, evade, focus, focus+evade 

Middel panel: 2nd edition with 4 curves: no tokens,  evade,  focus, focus+evade

Right pane: 2nd edition +one force-charge with 4 curves: no tokens,  evade,  focus, focus+evade

using the same scale on the y-axis on all 3 panels. 

Feel free to do it yourself.

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1 hour ago, SOTL said:

Feel free to do it yourself.

Oh thanks I guess...I was only trying to help you become better at presenting data such that it becomes more usefull to others than yourself and because I was genuinely interested. And surely, it would require much less work for you since you already did all the calculations (except the force-charge part) and did the graphs - than if I should start from scratch ;) 

But since yours are not easy to understand and you are unwilling to help, I might actually find the time. It would make a very nice 1st->2nd edition post and others might find it so interesting it could find its way into the "Index of usefull links" post ;) 



 

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5 minutes ago, Sciencius said:

Oh thanks I guess...I was only trying to help you become better at presenting data such that it becomes more usefull to others than yourself and because I was genuinely interested. And surely, it would require much less work for you since you already did all the calculations (except the force-charge part) and did the graphs - than if I should start from scratch ;) 

But since yours are not easy to understand and you are unwilling to help, I might actually find the time. It would make a very nice 1st->2nd edition post and others might find it so interesting it could find its way into the "Index of usefull links" post ;) 



 

Please do this! also the force-charge is interesting, as this will help determine how usefull version 2 Palpatine is going to be. 

Edited by RedHotDice

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1 minute ago, BDrafty said:

Evade still seems like a strong action if your ship has access to force tokens. Other than that, you just have to treat it as 1 garanteed evade when you roll.

Well it's a good thing they removed it from the Advanced then. /s

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23 hours ago, SOTL said:

The second part is the raw defensive efficiency of Evade vs Focus.  So in 1.0 an Evade is better until you get to 4 green dice, while in 2.0 the tipping point to Focus being better is at 3 green dice.

This is only true when the ship is only attacked once.  

When considering focus vs evade (in 1.0 or 2.0) you also need to account for how many times the defender is attacked that round (or expects to be attacked).   Even in 1.0 if you are attacked two or more times focus is more likely to prevent more damage than evade at 3 green dice (at 2 green dice you have to be attacked 4 times for focus to come out ahead).


See https://teamcovenant.com/general/when-is-focus-better-than-evade

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On 5/10/2018 at 1:24 PM, SOTL said:

Actually it's not 'even in 1.0' it's 'only in 1.0'.

The new Evade now has the same multi-attack benefit mechanic as focus did/does.

I don't think that's accurate, it looks like it's 'even in 1.0' not 'only in 1.0'.  "Even in 1.0 if you are attacked two or more times focus is more likely to prevent more damage than evade at 3 green dice", this is true in 2.0 as well.  (It is worth mentioning that the numbers given are averages without including the standard deviation, for example there could be times in 1.0 when a guaranteed evade to keep the ship alive at one hull might be a wiser choice than risking a focus with a chance to stop two damage).   While the evade token average does now increase on multiple attacks, the limit is 1 and it does not increase at an equivalent rate as focus does, (logarithmic vs linear so it quickly over takes and then is quickly overtaken).

In 1.0 and 2.0 if a 3 green dice ship is attacked once then evade will on average block more damage than focus. This can be seen in the chart above.

3 green dice ship attacked once
Version 1.0
evade = 1.0 avg
focus = 0.75 avg
Version 2.0
evade = 0.95 avg
focus = 0.75 avg



In 1.0 and 2.0 if the 3 green dice ship is attacked two or more times then focus will on average block more damage than focus. This data is not included in the charts above.
 

3 green dice ship attacked twice
Version 1.0
evade = 1.0 avg
focus = 1.06 avg
Version 2.0
evade = 0.99 avg
focus = 1.06 avg


At 0 green dice it doesn't matter which you take now for damage mitigation so go ahead and focus.  At 1 green die take the evade if looking for max damage mitigation.  At 2 green dice you also almost certainly want the evade if looking for max damage mitigation (unless you're facing a swarm and that single ship is getting attacked 4+ times).  At three green dice you'll want to focus if likely to be attacked at least twice but may want to evade if only attacked once.

At four green dice you probably want to take focus even when only attacked once (higher avg damaged blocked).  But again there will be some situations where you may want to consider the standard deviation.  If you really need to ensure that at least one damage is blocked because it will leave you at 1 hull and you can get an important shot off then you may want to take the new evade at four green dice with only one incoming attack (in that case even though the average is slightly higher with focus the chance of having 0 total evades is also higher).

One more note, here we've been looking at maximizing blocking damage but of course you need to consider the utility of focus being usable on attack as well.  At times the best option may be to take focus even if the defensive average is a bit lower since that results in increased damage output and is less likely to result in a wasted action, going unused.

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You're overthinking it.  The maths now work for green dice rolled, so the graph lines I presented are true if that's one attack with 3 green defence dice (for example) or three attacks with 1 green dice each time.

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To expand on that here's a comparison of being attacked one, two or three times in a single round.  I used http://xwing.gateofstorms.net/advanced/ for some of the calculations.  Please point out any errors you find.

Token Value - Additional Evades

Attack x1     Green dice    
  0 1 2 3 4
           
Focus 0.0000 0.2500 0.5000 0.7500 1.0000
Old Evade 1.0000 1.0000 1.0000 1.0000 1.0000
New Evade 0.0000 0.6250 0.8594 0.9473 0.9802
           
           
Attack x2     Green dice    
  0 1 2 3 4
           
Focus 0.0000 0.4375 0.7810 1.0660 1.3160
Old Evade 1.0000 1.0000 1.0000 1.0000 1.0000
New Evade 0.0000 0.8594 0.9802 0.9972 0.9996
           
           
Attack x3     Green dice    
  0 1 2 3 4
           
Focus 0.0000 0.5790 0.9400 1.2000 1.4140
Old Evade 1.0000 1.0000 1.0000 1.0000 1.0000
New Evade 0.0000 0.9473 0.9972 0.9999 1.0000

Note that there are two factors that can complicate the exact values a bit when looking at multiple attacks with focus. The first is whether you assume each attack does enough damage for the token to be useful (you could save a focus token only to have the second attack do no damage).  The second is whether you assume greedy use of tokens (use focus the first attack that any eyes are rolled) or perfect knowledge (don't use focus on the first attack for 1 eye because the second attack you'll roll two eyes) or something in between (like making the choice per attack that would result in the optimal avg).  But I think these numbers are indicative enough, for example the variance between greedy and perfect knowledge for three green dice and two attacks is only about 2%.

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1 minute ago, SOTL said:

You're overthinking it.  The maths now work for green dice rolled, so the graph lines I presented are true if that's one attack with 3 green defence dice (for example) or three attacks with 1 green dice each time.

That's true for the new evade.  But not for focus.  Focus will start to overtake evade where it did not before with extra attacks.

It make senses when you think about it.  Whether you roll them all together or separate the chances of having at least one die that isn't a natural evade is the same (and that's all you need to maximize on the evade token).  But rolling multiple times increases the chances you'll have 2 or 3 eyes in one roll, which increases the focus value.  If you only roll one die at a time you'll never get the focus average over 1.0 if you roll 5 dice you get it over 1.0 avg in one roll.  If you roll 3 dice you'll be well over that average in three rolls.

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Which I think is exactly what my chart shows - the focus line rises to infinity while the evade line flattens out.

We're both right, you're just wrong in that we ever disagreed ?

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