I want to calculate % of luck number / expected attacking hits, and luck number / expected defense losses.  I am not sure how to separate those different kinds of luck from the one luck number.  And I would need that info to find out the expected attacking hits and expected defense losses.

 I know the numbers can be extracted from the existing table somehow, but I am not sure what data is in each field.  Can someone recommend how to do this using the existing data from the luck tables?

thanks

I don't understand what you want when you say..

"% of luck number/expected attacking hits."

A luck number of 0 means that you are getting the expected number of wins.

Hey M,

I have to ask a question, before I can answer.  From the luck number provided, how can I separate out luck for attack and luck for defense?  I am pretty sure it combines both into that one number.

After I have that answer I want to calculate (luck# for attack / expected hits on attack).  So, for example if I have a -3 luck number for attack only, it means I had 3 less hits on attack than expected.  If it was expected that I have 30 hits, then I would calculate 3/30 = 10%.  So I got 10% less hits than expected.  to me this is more valuable than a luck number or percentage based on rolls.

Wow! An interesting way to interpret luck stats. I don't think anyone had thought of this before.

So in your game:

http://www.wargear.net/games/view/102696

You had the following luck stats:

    Player     Kills      Deaths    Luck

You had 0.81 more kills than expected over 17 kills, or 4.76% more kills than expected overall.

• Now this is where I'm not sure the numbers are accurate because attack dice have different probabilities, but breaking this up you made 10, or 59% of these kills as an attacker for 2.8% more kills than expected as an attacker.

You had 2.21 less deaths than expected over 10 deaths, or 22.1% less deaths than expected overall.

• Breaking this up you incurred 6, or 60% of these deaths as attacker for 13% less deaths than expected as an attacker.

I suppose we could weight these two percentages by dealing with their absolute values.

[(.221 x 10) + (6 x .13)] / 16 for 18% more luck than expected when attacking.

Is this what you had in mind?  I'm not even sure that my math is right, but you get the idea.

One thing I forgot to mention.  While I don't think anyone has suggested figuring out the percentages for attack dice and defense dice, the idea of finding a ratio of expected to number of dice thrown for the data as presented has been discussed.  The problem is that these numbers will approach zero as the number of dice thrown gets higher and higher.

My suggestion for a quick fix was to divide by the square root of the number of total dice thrown, in effect simulating a standard deviation type number. The number won't be a percentage anymore, but once you're looking at samples of 50+ or so, it will start to"settle in".  

Hey M,

Thanks for the comments.  Yes, that is what I had in mind, you are on the right track.  I am short on time now, I will will review in detail later and give a more considered reply.

M,

I think the problem is trying to break down the .18 luck for kill to the portion that occured when attacking and the portion that occured when defending.  As you note, since we don't know what was rolled when attacking, I dont think we cant break down the number from the data that is available.

SquintGnome wrote:

M,

I think the problem is trying to break down the .18 luck for kill to the portion that occured when attacking and the portion that occured when defending.  As you note, since we don't know what was rolled when attacking, I dont think we cant break down the number from the data that is available.

I agree; it's probably not too far off the mark but the only way to really know would to get the breakdown of the numbers.  I don't know if you've check out previous threads on the subject, but while that percentage number is a critical component of analyzing the Luck Stat, the number is all but meaningless without having the context of how many rolls there have been.

M,

I can see your point, but I am not sure I agree.  First, I think number of rolls is not as important as expected results.  For example, if I roll d6, 3 v 1, 100 times I should get aboout 66 kills.  Let's say I only get 55 kills.  It is illuminating I think to view the -11 luck againt the 66 expected rather than the 300 rolls.  In addition, if the same 300 rolls are 3 v 2, then it can mean something completely different.  So the 300 rolls should not be used in any ratio, instead we should use the expected results.  Still thinkin about it though, let me know your opinion.

Also, I agree with your point in one of your posts above about the percentage going to zero the more we roll.  This should be a result of your luck eventually evening out (Luck=0).  This is fine I think, because I would like to see whose luck doesnt't go to zero, etc and how far off they are.  And lastly, I think the luck % roll would be used mostly for small stretches of games (i.e. last 10 games) since it will go to zero over time - but an interesting way to see if you recently losing streak was impacted by poor luck.

SquintGnome wrote:

I think number of rolls is not as important as expected results.  For example, if I roll d6, 3 v 1, 100 times I should get aboout 66 kills.  Let's say I only get 55 kills.  It is illuminating I think to view the -11 luck againt the 66 expected rather than the 300 rolls.

 Is that -11 over 300 rolls more ..or less unlucky than  -25 over 1000 rolls?  The number of total events plays a critical part in putting the LS in perspective.

In addition, if the same 300 rolls are 3 v 2, then it can mean something completely different.

The Luck Stat takes those probabilities into account.  -11 means -11 given the dice mods and number of dice rolled for both attacker and defender.  Also, in your example of 3v1, I'm pretty sure it would count as 100 rolls/events (even though you rolled 300 dice) because only 1 was defending and you could only lose 1 with each attack.

And lastly, I think the luck % roll would be used mostly for small stretches of games (i.e. last 10 games) since it will go to zero over time - but an interesting way to see if you recently losing streak was impacted by poor luck.

The probability that luck will go to exactly zero actually decreases over time.  Given 1000 players rolling 1 million events each, the mean LS will get closer and closer to zero, but it's very unlikely that any one of them would have a LS of 0 and extremely unlikely that any two of these players would have LSs of exactly 0.

As long as there is no calculation of the deviation from the statistical norm given the number of rolls, the LS has little meaning from game to game.

M57 wrote:

..The probability that luck will go to exactly zero actually decreases over time.  Given 1000 players rolling 1 million events each, the mean LS will get closer and closer to zero..

Sorry, I was not clear.  I did not mean to say that the LuckStat will get closer to zero.  I meant to say that the percentage score that we have been deriving will get closer to zero.  Of course, the max LS scores will get higher and higher as the sample size increases.

Good explanation M57.

Let me give an example for what I am looking to get from luck stats.

Below are listed 3 scenarios, each with the same number of dice rolls and hits.

Scenario                     100 rolls, 3 v1          100 rolls, 3 v2         50 rolls, 3 v1 & 50 rolls 3 v 2

Dice Rolled                        300                           300                               300

Iterations                         100                           100                               100

Actual hits                         83                             83                                 83

Expected hits                    66                            108                                87

Luck                                 -17                             +25                               +4

Luck% vs expected        -25.8%                        +23.15%                        +4.60%

Luck% vs dice rolled       -5.67%                         +8.33%                        +1.33% 

Luck % vs iterations       -17%                             +25%                            +4%

To me, the most (and only) meaningful ratio is Luck% vs expected which is (luck / expected kill) or you can say [ (expected kills - actual kills) / expected kills].  I would like to see this in the luck stats for attacking and defending.  The other ratios demonstrate their shortcomings.

Luck / Put-at-Risk              + 17%            - 16.7%          - 2.7%

But as I stated before, these are not good comparisons because in each case there are a different amount of total units killed (put at risk)

Using my oversimplified attempt to normalize the denominator by taking it's square root, I get:

Luck / Sqrt (Put-at-Risk)       + 1.7            - 1.8               -0.32

..I reversed the positive/negative signs

Hi M,

Yes, you are right, I reversed the signs.  It is from the attacker's perspective.

I agree the last column is not helpful, I put it there to show its weakness as well as the line above it.  And, yes my preferred ratio does not account for units at risk, but I think it is more important to focus on expected results regardless of units at rish.  Adding that info is a good perspective though. 

 I agree also with your formula, but I prefer to leave it as a percentage because it may be more meaningful to some.

SquintGnome wrote:

 I agree also with your formula, but I prefer to leave it as a percentage because it may be more meaningful to some.

My formula is certainly flawed, but the percentage # you are computing is significantly less "meaningful" because the distribution represented by that number becomes dramatically skewed as the sample size increases.

I agree that more people understand what a percentage is, but that doesn't change the fact the the straight percentage number is all but irrelevant if you don't consider how many units were at risk. At least my proposed computation balances things a little and and lets users crudely compare disparate sample sizes.

If I recall correctly, I suggested using 33 as a multiplier, which would basically put all but the extremely unlikely outcomes on a scale from 0-100.   Create a subjective legend and done:

0-25 = marginally lucky

25-50 = lucky

50-75 = very lucky

75-100 = extremely lucky

100+ suggests divine intervention

Consideration of units at risk is intrinsically part of the expected results so the percentage I noted above works great for me. 

Well, I guess we will agree to disagree on this one.

SquintGnome wrote:

Consideration of units at risk is intrinsically part of the expected results so the percentage I noted above works great for me. 

Well, I guess we will agree to disagree on this one.

When you say intrinsically do you mean to say that after a 5000 units at risk attack, a luck/expected number of +10% is just as lucky as getting a luck/expected number of +10% after a 100 units at risk attack because the number at risk is built in?  If so then yes, we can agree to disagree.

Yes, that is what I am saying. I feel that +10% would be the same level of luckiness regardless of the units at risk.  I say that realizing there are subleties since it should be less likely to be +10% after more rolls, but I still feel it is the same 'luckiness' - just more surprising that you can maintain that level after many rolls.  So you would have to look at number of rolls / units at risk to get the whole story.