M57 wrote:

btilly wrote:

The way that I'd like to see it presented is that there is a combat luck percentile.  A number like 56.5% or in the case of the above game probably something like 1.6%.

It can be explained as, "How lucky were your combat rolls?  If every combat roll was redone, this estimates how likely it is you would have done worse."

What would the 56.6% mean? ..that 6.6% of your rolls were better than expected?

What might a standard deviation look like?

I feel obligated to make an argument for a "dramatic" system.  If 1.6% is "really unlucky," it doesn't sound like it.

For example, something more like Z-score * 50, expressed as a whole number.  -100 would be 2 Standard deviations, and be very unlucky..

56.6% would mean that your luck was just barely better than average.

A standard deviation is proportional to the square root of the variance.  So if there were 1000 dice rolls in your game, that might be a luck of -25.  With 40 dice rolls it might be -5.  The relationship between how lucky or unlucky your luck score is and how much playing that you did is implicitly captured by the z-score.

I am against a more "dramatic" system because I don't like seeing lots of arbitrary numbers whose meaning is confusing.  I know the math so can figure out that you get -50 or worse 15.9% of the time, -100 or worse 2.2% of the time, and -150 or worse 0.13% of the time.  But you'd have to study a lot of games to get a sense of those figures from experience.

luck score: How many more troops of yours survived dice rolls than should on average.

luck percentile: Your odds of having a worse luck score.

Those make sense to me, and capture pretty much everything that I want to know about how badly the dice screwed me.  (Or helped me in an awesome game.)

btilly wrote:

56.6% would mean that your luck was just barely better than average.

So 45% would mean worse than average. This is OK, but it would be preferable if "worse" could be a negative percentage.  I'm thinking of the  perceptions and understandings of average players, some of whom might be in high school or even middle school.

For instance, a 12% luck percentile (as you define it) could equate to a -76% "Bad Luck Percentile", where the range is -100% to +100%.  Wouldn't this mean that of all players with a negative reading, that player is among the "unluckiest" 24%. 

Or do you think 50 as a base-line is clearer for most people?

Straight percentile is probably the clearest to the average person. 0%-100% is way more embedded in our culture than a -100 through 100 scale with 0 as "average".

I got percentile scores on any standardized test I took going back to middle school. Heights of kids at a certain age are sometimes reported in terms of percentile.

Most importantly, as btilly pointed out, the interpretation is direct. "My rolling will be this bad or worse 1.6% of the time." It means what it means. (It's pretty bad for a single game, yet it should happen every 62-63 games or so!!)

Hugh wrote:

 "My rolling will be this bad or worse 1.6% of the time." It means what it means. 

Sorry, I'm confused. What's the equivalent percentile to the 1.6% number?  56.5%?

"My rolling will be this bad or worse 1.6% of the time" is how you interpret rolling that is in the 1.6 percentile. I wasn't referencing the 56.5% example.

In general, if the luck score returns "Your rolling was in the x-th percentile," it means that you will roll that badly or worse x% of the time. It means nothing else. (This is straight combat results over the course of a single game involving many types of rolling. It's not situational or placement luck, etc, etc.)

M57 wrote:

Hugh wrote:

 "My rolling will be this bad or worse 1.6% of the time." It means what it means. 

Sorry, I'm confused. What's the equivalent percentile to the 1.6% number?  56.5%?

Those numbers as they stand are percentiles - just with an extra decimal place of accuracy.  So 1.6% is somewhere between the cutoffs for the first and second percentiles.  And 56.5% is between the cutoffs for the 56th and 57th percentiles.

ooh.  Now I'm picturing a interactive luck graph where you can set the begin/end time & it displays your percentile over that time period.

Ozyman wrote:

ooh.  Now I'm picturing a interactive luck graph where you can set the begin/end time & it displays your percentile over that time period.

I am not offering to build that.

There is no reason that this would not be possible though.

Ozyman wrote:

ooh.  Now I'm picturing a interactive luck graph where you can set the begin/end time & it displays your percentile over that time period.

+1