Error Mathematics

[Skidushe]

Hi all, I was doing some error analysis on match percentages, with regards to deriving @MacSquirrel_Jedi 's mouse trick Numerically. If anyone was curious it lies here:

https://tomhepz.com/post/monitor-match-math/

With some of the relevant plots here:

https://www.desmos.com/calculator/sezgpjgs9w

Was curious what people thought a suitable minimisation metric would be since in theory I should be able to form a function of optimum match given some metric by numerically integrating over some Error function in effect 'Deriving' Jedi's Trick.

Edited May 11, 2022 by Skidushe

[cremtty]

I ve done it before. It was around 60% mdh for me ( in my memory. maybe 65%) . It depends on what norm you use. (eg. L^1 L^2 norm etc)

However It's scientific meaning might not be that strong. It assumes flicking with closing eye situation so someone might like this theory, the other will not like.

Edited May 12, 2022 by cremtty

[MacSquirrel_Jedi]

It looks interesting. I still didn't had the mood to express the formula. Mainly because I will have to completely rework my utility again. I also found out that I have a problem expressing functions... too long from school. Actually i think i never learned it  Also i have covid now  

18 hours ago, Skidushe said:

in effect 'Deriving' Jedi's Trick.

It should not be too much hard. You are looking for this:

The formula should contains the range (2x matching points on screen). So you will be able to define where you want to find the minimum error. For example 0-100% (Jedi's Trick) or 0-70% or wierd match like 20-70%. If the two match points will be the same like 50-50% it will turns to a standard monitor distance match to one point => Error = 0 

[fortunate reee]

29 minutes ago, MacSquirrel_Jedi said:

have covid now

good luck

[Skidushe]

18 hours ago, cremtty said:

I ve done it before. It was around 60% mdh for me ( in my memory. maybe 65%) . It depends on what norm you use. (eg. L^1 L^2 norm etc)

However It's scientific meaning might not be that strong. It assumes flicking with closing eye situation so someone might like this theory, the other will not like.

Fits with what little analysis I have done, you're right that it completely depends on what Norm you use. I was acting everything on vertical and it always comes out around 60% (vertical) to minimise %error or (%error)^2  and about 70% (vertical) if you want to minimise (error) or (error)^2.

That being said, I don't think it's reasonable to bother minimising over the screen for any functional application, since you're (closed eye) flicks are way more likely to be distributed towards the centre of the screen than the edge. I think multiplying by a normal probability distribution would be more useful.

In that case multiplying by a normal distribution PDF with a std. deviation of 0.3 the best mm %age comes to around 30% (vertical)

[cremtty]

3 hours ago, Skidushe said:

Fits with what little analysis I have done, you're right that it completely depends on what Norm you use. I was acting everything on vertical and it always comes out around 60% (vertical) to minimise %error or (%error)^2  and about 70% (vertical) if you want to minimise (error) or (error)^2.

That being said, I don't think it's reasonable to bother minimising over the screen for any functional application, since you're (closed eye) flicks are way more likely to be distributed towards the centre of the screen than the edge. I think multiplying by a normal probability distribution would be more useful.

In that case multiplying by a normal distribution PDF with a std. deviation of 0.3 the best mm %age comes to around 30% (vertical)

Oh I never thought about normal distribution. Could you be more specific? Ah maybe  you multiply distribution (mean = 50% md , std something) to error?
Then it means ignoring errors on the edge and near the crosshair. Might be good idea.

[Skidushe]

2 hours ago, cremtty said:

Oh I never thought about normal distribution. Could you be more specific? Ah maybe  you multiply distribution (mean = 50% md , std something) to error?
Then it means ignoring errors on the edge and near the crosshair. Might be good idea.

If you take the mean position of flick to be the centre of your screen and the std deviation to be ~0.3 (implies ~98% of all flicks on screen) and multiply the % error over this Probability Density Function to form a new metric which better represents where you care about flicking to (although now doesn't really represent mathematical error in any sense). You could do what you said and set the mean to be different from 0, but I think 0 better represents the fact tracking is equivelent to a 0 distance flick which we care about.

[cremtty]

12 hours ago, Skidushe said:

If you take the mean position of flick to be the centre of your screen and the std deviation to be ~0.3 (implies ~98% of all flicks on screen) and multiply the % error over this Probability Density Function to form a new metric which better represents where you care about flicking to (although now doesn't really represent mathematical error in any sense). You could do what you said and set the mean to be different from 0, but I think 0 better represents the fact tracking is equivelent to a 0 distance flick which we care about.

Ah I always think the half of the monitor. That's why i never thought about normal distribution. I get the meaning of mean=0 now.