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alextound 10-03-2015 08:39
Math: How to solve ranking equation
 
I no do math, can someone give me a quick math lesson on solving the ranking equation.

Thanks!

microbuns 10-03-2015 08:56
Re: Math: How to solve ranking equation
 
Do you mean in Qualifications? They just take your average score from each game you played in quals, then rank the teams from highest to lowest.

The_ShamWOW88 10-03-2015 09:03
Re: Math: How to solve ranking equation
 
They average your alliance's score as your Qualification Average and they go in the following order:

Qual Avg
Cooperative pts
Auto pts
RC pts
Tote pts
sum of Noodle pts
Random FMS sorting

See 5.3.4 of the Game Manual.

Alan Anderson 10-03-2015 09:03
Re: Math: How to solve ranking equation
 
What ranking equation do you mean? Ranking is simple: more points is better. To a first approximation, a team ranks above other teams with fewer points, and below other teams with more points.

alextound 10-03-2015 09:37
Re: Math: How to solve ranking equation
 
i mean this:

http://www.usfirst.org/sites/default/files/uploadedFiles/Robotics_Programs/FRC/Game_and_Season__Info/2015/FRC_District_Standard_Points_Ranking_System_2015%2 0Summary.pdf

ATannahill 10-03-2015 09:41
Re: Math: How to solve ranking equation
 
This was discussed in Frank's blog.

There is a document that elaborates further on the equation. You can scroll to the bottom to see what values would come out for a 32, 40, 55, 60 and 64 team event.

Alan Anderson 10-03-2015 10:16
Re: Math: How to solve ranking equation
 
That formula is only relevant for district events. It converts ranking to "District Qualification Points". A comprehensive explanation of the Inverse Error Function belongs in an advanced statistics class. All you need to know is that it is built in to tools like Matlab.

ArtemusMaximus 10-03-2015 11:15
Re: Math: How to solve ranking equation
 
Quote:
Originally Posted by Alan Anderson (Post 1455950)
That formula is only relevant for district events. It converts ranking to "District Qualification Points". A comprehensive explanation of the Inverse Error Function belongs in an advanced statistics class. All you need to know is that it is built in to tools like Matlab.
I was curious about the function, did a little digging found someone already made one for Excel VBA. I hope this helps.
http://www.mrexcel.com/forum/excel-q...ml#post1146833
Code:
Function invERF(y As Double) As Double
Dim pi As Double, x As Double, d As Double
pi = 3.14159265358979
If y < 0 Then
    invERF = 0 'interval includes the mean only
    Exit Function
ElseIf y >= 1 Then
    invERF = 10 'makes the interval include everything
    Exit Function
'for my purposes, I only want the function to process input from 0 to 1
ElseIf y < 0.596 Then
    x = sqr(pi) / 2 * y * (1 + (pi / 12) * y * y)
Else
    x = sqr(-Log((1 - y) * sqr(pi)))
End If
d = (y - ERF(x)) / (2 * Exp(-x * x) / sqr(pi))
x = x + d
Do While Abs(d) >= 0.00000001
    d = (y - ERF(x)) / (2 * Exp(-x * x) / sqr(pi))
    x = x + d
Loop
invERF = x
End Function

Function ERF(x As Double) As Double

Dim f As Double, c As Double, pi As Double
Dim j As Integer
c = 0
pi = 3.14159265358979
If 1.5 < x Then
    c = 2 - c
    j = 3 + Int(32 / x)
    f = 0
    Do While j <> 0
        f = 1 / (f * j + x * sqr(2))
        j = j - 1
    Loop
    f = f * c * (3 - c * c) * Exp(-x * x) / sqr(2 * pi) + (c - 1) * (3 * c * c + c - 8) / 6
Else
    j = 3 + Int(9 * x)
    f = 1
    Do While j <> 0
        f = 1 + f * x * x * (0.5 - j) / j / (0.5 + j)
        j = j - 1
    Loop
    f = c + f * x * (2 - 4 * c) / sqr(pi)
End If
    ERF = f
End Function

MasterMentor 10-03-2015 14:21
Re: Math: How to solve ranking equation
 
Quote:
Originally Posted by ArtemusMaximus (Post 1455979)
I was curious about the function, did a little digging found someone already made one for Excel VBA. I hope this helps.
http://www.mrexcel.com/forum/excel-q...ml#post1146833
You just have to be careful about this, the input into InvERF with the District Qual Points Formula will be negative on one side of the [-1, 1] range, and this function can only handle positive input values. Also at the midpoint it's possible to get a divide-by-zero error with this function too. Both issues are easily worked around with a little formula/programming magic, but it's important to know this isn't a perfect drop-in solution.

-MM

who716 10-03-2015 15:42
Re: Math: How to solve ranking equation
 
Basically the formula is given you just have to plug and chug, some calculators will have an inverse error function ability, if your does you find it use it and plug in the necessary values for the variables, N= number of teams at event, R=your final ranking position and alpha is a constant set by the committee based on averages of event size at 1.07. The lines on each end tell you just to round up to the nearest whole number give it a shot for our first event it would look like this:

invERF[( 33-2x13+2)/(1.07*33)]X(10/(invERF 1/1.07)+12) 13. ....... rounded up to nearest whole integer =14

remember inverse is NOT the same as going to the power of -1 if you don't have a calculator with the function already...

if you don't have this function at all on your calculator then it gets much more complicated solving for invERF as its a function itself requiring integrals and such

Ether 10-03-2015 17:56
Re: Math: How to solve ranking equation
 
Quote:
Originally Posted by who716 (Post 1456101)
invERF[( 33-2x13+2)/(1.07*33)]X(10/(invERF 1/1.07)+12) 13. ....... rounded up to nearest whole integer =14

remember inverse is the same as going to the power of -1 if you don't have a calculator with the function already...
The inverse of a function f(x) is not 1/f(x).

The inverse of f(x) is g(x), such that g(f(x))=x

For example, the inverse of f(x)=x2 is g(x)=sqrt(x), not 1/x2

Code:
octave-3.6.4.exe:10> erfinv(0.33)
ans =  0.301332146133706
octave-3.6.4.exe:11> 1/erf(0.33)
ans =  2.78335488667249

MooreteP 10-03-2015 18:09
Re: Math: How to solve ranking equation
 
Plus, for Qualifications, if the number of teams is not divisible by six, there are surrogate matches, which are the third match for teams that fill the surrogate role.

More Math!

ArtemusMaximus 10-03-2015 18:10
Re: Math: How to solve ranking equation
 
Quote:
Originally Posted by Ether (Post 1456163)
The inverse of a function f(x) is not 1/f(x).

The inverse of f(x) is g(x), such that g(f(x))=x

For example, the inverse of f(x)=x2 is g(x)=sqrt(x), not 1/x2

Code:
octave-3.6.4.exe:10> erfinv(0.33)
ans =  0.301332146133706
octave-3.6.4.exe:11> 1/erf(0.33)
ans =  2.78335488667249
I knew Ether would show up and clear all this up :D

Richard Wallace 10-03-2015 18:15
Re: Math: How to solve ranking equation
 
Quote:
Originally Posted by ArtemusMaximus (Post 1456175)
I knew Ether would show up and clear all this up :D
When the student is ready, the master appears.

Rachel Lim 10-03-2015 19:00
Re: Math: How to solve ranking equation
 
If you're looking for a more visual explanation (or a simpler one), I wrote up this summary for my team: http://goo.gl/lx2I2l

I tried to explain the math behind it without calculus or too much statistics, which makes it easier to read but not nearly as in depth as the official explanation (in my opinion). It's mostly a graphical / algebra based analysis to get at the basics of what district ranking is and how your ranking at an event factors into it.

Note: I haven't taken any statistics classes and we're not yet in districts, so I'm not sure if everything I wrote is completely accurate. Please let me know if anything is wrong and I'll try to correct it.

Ether 10-03-2015 19:07
Re: Math: How to solve ranking equation
 
Quote:
Originally Posted by Rachel Lim (Post 1456192)
Please let me know if anything is wrong and I'll correct try to correct it.
There's an extra word in that sentence.

Rachel Lim 10-03-2015 19:11
Re: Math: How to solve ranking equation
 
Quote:
Originally Posted by Ether (Post 1456198)
There's an extra word in that sentence.
Thanks for catching that. :) Did you find any errors in my analysis?

Ether 10-03-2015 19:19
Re: Math: How to solve ranking equation
 
Quote:
Originally Posted by Rachel Lim (Post 1456199)
Thanks for catching that. :) Did you find any errors in my analysis?
Based on the paper you wrote for Math Quiz 6, I wouldn't expect to find any :-)

ATannahill 11-03-2015 06:48
Re: Math: How to solve ranking equation
 
Quote:
Originally Posted by MooreteP (Post 1456174)
Plus, for Qualifications, if the number of teams is not divisible by six, there are surrogate matches, which are the third match for teams that fill the surrogate role.

More Math!
Not quite correct.

If the number of teams * the number of matches per team is not a multiple of six, then you will have surrogates.

Michigan (and I believe most other district systems) gives each team 12 matches. A benefit to this is that there will never be a surrogate.

Danny Diaz 11-03-2015 09:42
Re: Math: How to solve ranking equation
 
Quote:
Originally Posted by Rachel Lim (Post 1456192)
If you're looking for a more visual explanation (or a simpler one), I wrote up this summary for my team: http://goo.gl/lx2I2l
Impressive.

-Danny

who716 11-03-2015 12:22
Re: Math: How to solve ranking equation
 
Quote:
Originally Posted by Rachel Lim (Post 1456192)
If you're looking for a more visual explanation (or a simpler one), I wrote up this summary for my team: http://goo.gl/lx2I2l

I tried to explain the math behind it without calculus or too much statistics, which makes it easier to read but not nearly as in depth as the official explanation (in my opinion). It's mostly a graphical / algebra based analysis to get at the basics of what district ranking is and how your ranking at an event factors into it.

Note: I haven't taken any statistics classes and we're not yet in districts, so I'm not sure if everything I wrote is completely accurate. Please let me know if anything is wrong and I'll try to correct it.
this was actually helpful and understandable, helped me grab the actual meaning behind the inverse error function instead of just plugging it into a calculator too solve.

Danny Diaz 12-03-2015 14:59
Re: Math: How to solve ranking equation
 
In case you're looking for something in Excel, here's something I whipped up.

http://www.chiefdelphi.com/media/papers/3117

-Danny


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