Chief Delphi - Math: How to solve ranking equation

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- - Math: How to solve ranking equation (http://www.chiefdelphi.com/forums/showthread.php?t=135638)

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)

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

Quote:

Originally Posted by alextound (Post 1455935)

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.

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