Author Topic: Overall Score question....Please help!  (Read 1044 times)

maneframe150

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Overall Score question....Please help!
« on: December 14, 2014, 06:28:23 PM »
I run a league that is points based.  Top 10 points leaders proceed to the TOC or Tournament of Champions.  If 2 players tie for the 10th spot in points we use the "overall score" as the tie breaker to see who will proceed to the TOC.  We use the formula that was already in TD:

(1-exp(-average(scores))) * 100

After our last game of this season, 10th and 11th place were tied.  They guy in the 11th place row had a better "overall score."  He also had a better "total take."  Yet, he is listed in 11th place.

So, couple of questions:

1. How EXACTLY does the "overall score" work so that I could explain this to my players?

2. Is there any way to sort the stats by points and THEN by "overall score?"  Or does TD randomly print those with the same number of points?

Thanks in advance for your help....

Junior

Corey Cooper

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Re: Overall Score question....Please help!
« Reply #1 on: December 15, 2014, 04:31:54 PM »
Wish I could give you a good explanation but frankly I'm not much of a math wiz.  When paired with the Tournament Scores formula (log((n + 1) / r), it essentially becomes a logarithmic function, increasing rapidly at first but slowing that increase as the input value gets larger.  That's a pretty basic description, and it really says nothing as to why this is a good way to rate players.  But it's a common poker scoring/rating mechanism.

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2. Is there any way to sort the stats by points and THEN by "overall score?"  Or does TD randomly print those with the same number of points?

Not at this time, but it's something I would like to do.  Currently the Stats tab (any place with ordered tables, just about) orders the list by a single column (whichever column the user chooses).  The "fallback" compare function is the player's name.  That is, ties are broken using player names.  Certainly not the best, but does most of the time guarantee a deterministic sort.

maneframe150

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Re: Overall Score question....Please help!
« Reply #2 on: December 15, 2014, 06:22:09 PM »
Corey,

What does "(1-exp(-average(scores))) * 100" mean?  I'm no computer programmer... Can you tel me what this is doing?  What's exp? What does -average mean? and so forth....

Also, do you know of a better tie breaker?

My league uses number of players - rank +1 to score points in tournaments.  We also get 1 point per hit. Don't know if that helps any...

Thanks for the response.

Corey Cooper

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Re: Overall Score question....Please help!
« Reply #3 on: December 15, 2014, 09:14:44 PM »
No need to be a programmer.  Definitely some math, though.

(1-exp(-average(scores))) * 100

... is just a mathematical expression.

scores is the value of the "scores" variable, which is actually the output of the Tournament Score formula (also in the Stats Profile).  The Tournament Score formula is computed for each tournament (for each player), so scores holds a set of values.  For example, for a tournament with 25 people, if I busted out 3rd then my score would be 2.16 (from the Tournament Scores formula log((n + 1) / r)).  If I bust out 1st in a 50 player tournament, my score would be 3.93.  So this variable might hold a set of values like (2.16, 3.93, .89, 1.10).

average() is a function that returns the average of the values you provide to it.  For example, average(1,2,3) would return 2.  average(10, 30, 80) would return 40.  So average(scores) returns the average of the player's scores.

-average(scores) just means the negative of the average score.  -average(scores) is the same as average(scores) * -1

exp() is a function that raises E (Euler's constant) to the power of the number provided.  You'll have to look that one up.  For this formula, it would be E raised to the power of the negative of the average of the player's scores.

Once you get to this point, exp(-average(scores)), the result is going to be between 0 and 1, with the result actually being closer to 0 the better your average score.  So, 1 - exp(-average(scores)), or subtracting this value from 1, basically inverts it such that the better your average score, the closer to 1 you get.  Finally, multiplying by 100 changes the scale from 0 to 1, to 0 to 100.  This is just an easier scale for most people to comprehend.

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Also, do you know of a better tie breaker?

This is really personal preference I guess.  The nature of the formula should keep ties to a minimum.  When one does occur, you could say, for example, the player with the highest single score, or the player who played more tournaments (or fewer), etc.

Corey Cooper

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Re: Overall Score question....Please help!
« Reply #4 on: December 16, 2014, 10:16:40 PM »
Meant to add: in addition to the "Cheat Sheet" button on the various formula dialogs, which opens a page with information on all variables, functions, operators, etc, you can highlight any part of the formula and a tooltip should appear with information on the highlighted part.  Not exhaustive, but can be helpful.