Math: How to solve ranking equation

[alextound]

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]

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]

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]

Originally Posted by Alan Anderson

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

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]

Originally Posted by ArtemusMaximus

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]

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]

Originally Posted by who716

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

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]

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!

[ATannahill]

Originally Posted by MooreteP

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.

[ArtemusMaximus]

Originally Posted by Ether

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

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

[Richard Wallace]

Originally Posted by ArtemusMaximus

I knew Ether would show up and clear all this up

When the student is ready, the master appears.

[Rachel Lim]

Originally Posted by alextound

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

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]

Originally Posted by Rachel Lim

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]

Originally Posted by Ether

There's an extra word in that sentence.

Thanks for catching that. Did you find any errors in my analysis?

[Ether]

Originally Posted by Rachel Lim

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 :-)