Welcome to the ZOID Stat Central

Where

A Happy Member is a Numerate Member


Table of Contents
Why is Scoring so Complex? Percentile-Range Scoring Mean-Standard Deviation Scoring The Measure of Fairness
Handicapping Back to ZOID Documentation Back to the Main ZOID Page. Back to the Fighting and Voting FAQ.


Why is Scoring so Complex????

As previously mentioned, a happy member is a numerate member, and if you aren't happy yet, we aim to make you that way by helping you understand a complex but fair method for scoring fighters in competition. First, you deserve an explanation about why scoring at ZOID CITY Community Competition is so complex. Scoring at ZOID CITY Community Competition is so complex because a complex system is the only way to ensure a fair fight. A fair fight happens when evenly matched competitors win due to effort in recruiting votes. A fair fight happens when more than one or two fighters does well. A fair fight does not occur among competitors who are grossly mismatched, when one fighter's raw vote totals are so high that others can not possibly catch up, or when victory results from factors such as choice of house or team or the good luck of being placed in a weak field.

ZOID CITY Community Competition uses uses perccentile-range scoring to compute scores. This allows us to give the same numerical scores at all levels of turnout, give you as a fighter a precise measure of your performance, and to handicap based on the performance of the entire field. Percentile range scoring, let's you know in percent or hundreths how close your score is to that of the top fighter. Should ZOID grow very large, we may also adopt mean-standard deviation scoring. This is a formula that compares all fighters' scores to the average score for the field rather than the top one. Both methods score fighters based on the performance of the total field of competitors as a whole, rather than on the scores of the first three finishers. Both methods are also well suited to large groups of fighters and larger numbers of ballots. This means that all competition at ZOID CITY is at-large and that there is a single field of fighters.

Neither scoring method requires algebra to learn,though you do need all the arithmetic you were ever taught and a feeling of comfort with mathematics in general If you are unsure of your mathematics, print off this page, and have someone who is good at math help you understand sccoring.



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Percentile-Range Scoring

There is nothing unspirited or wrong with saying or caring about the question "how well did I do?" It is a question to which you deserve to know the answer in exhaustive and loving detail. Numbers are your friend. A poor performance should be motivation to work harder or a signal to take a time out from fighting. A good performance is a reward even when you don't win.

To understand percentile range fighting, think of the fighters' scores strung out on a rope or scale. At the right or top of the scale is the best scoring fighter. She has a score of 100. At the bottom of the scale or rope is the worst scoring fighter. She has a 0. The scale or rope is called a range. It is divided into hundreths or percentiles and your score is how high or close you came to getting that hundred. A second place fighter with a 95 waged a much better fight than a second place fighter with a 20. The same is true for fighters in third, fourth, fifth place etc... A competition where half the fighters had percentile range scores above fifty would indicate that we are a community of active and competitive fighters, and we can all give ourselves pats on the back.

OK, now how do we figure percentile range scores? First the rope or scale is called a range. The first place fighter's score is a maximum, and the last place fighter's score is called a minimum. Let's say that in a group of fighters the mimimum score is two and the maximum is ten. The range is the maximum minus the minimum.

10-2= the range or 8.

To compute a percentile range score for each fighter subtract the minimum from that fighter's raw vot total. ZOID CITY always makes raw vote totals available in real time so you can get your percentile range score (unofficially) whenever you want it. Let's say a fighter has a score of 9.

First she subtracts the minimum from her score.
9-8=7

Next the fighter divides this number (her raw vote total-minimum or 7) by the range (8). She should get a fraction or decimal and unless she has a first place score, the figure will always be less than one (1). Let's see it in action:

7 (score-minimum)/8 (range)= .875

Since fractions and decimals make a lot of people uncomfortable, the figher than can multiply this figure (.875) by 100 to get a whole number.
br> .875 ((sore-minimum/range) x 100= 87.5 or 88 since we usually round up. The fighter has an 88 which is a fairly respectable score.

Of course you do not have to score the entire field of fighters or even yourself by hand, though it is really not that difficult. ZOID CITY always makes its scorinng spreadsheet template available at paralink The user name is zc2zc3 the account is zc2zc3 and the password is "public" without the quotes. The spreadsheet is called minrange.xls and it is in an old version of Excel. With it, you can score along at home. Yes, because numbers are your friend any one can score.

Finally, under percentile range scoring, any fighter with a percentile range score above ninty (90) at the end of the week receives the coveted pencil, the mark of a winner, at ZOID. This is true regardless of whether we handicap.

The advanatages of percentile-range scoring are that it scores fighters based on the performance of the whole field rather than simply first, second, and third place. There can be multiple winners and the elegant system allows for performance based handicapping.



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Mean Standard Deviation Scoring

Mean-standaard deviation scoring has never been used at ZOID, though it could supplement the system we currently have. It would work extremely well in some ways with very large groups of fighters. The theoretical cut off for switching to mean-standard deviation scoring is thirty-six or more fighters in a heat, though in practice it will be somewhat higher, depend upon the score ranges, numbers of ballots we obtain, and group consensus. Mean-standard deviation scoring is an excruciatingly fair system because it scores your site's against performance by comparing it against the field average or mean rather than that of the top fighter.

Mean-standard deviation scoring is also called "curving from the middle," and it is used in real life for students' exams in large university courses in the United States. It is considered the most humane approach when there must be winners and losers. Also mean-standard deviation scoring works exceptionally well with large groups. The larger the group of fighters becomes (even into the hundreds or thousands) the more accurate mean-standard deviation scoring becomes.

Here is how it works. Let us start with a field of five fighters (In real life the field would be much larger).

Fighter A -- 2votes
Fighter B -- 4votes
Fighter C -- 6votes
Fighter D -- 8votes
Fighter E -- 10votes

First let's figure the mean. The mean is the weighted average. It is the total of all scores added up divided by the number of fighters.

2+4+6+8+10= 30 this is the total.

30/5 = 6 This is the mean or average.

Next the scorer figures the standard deviation. The standard deviation is the variation or spread of scores about the mean. It is the average distance from the mean for fighters' scores. Some fields have very large standard deviations if the scores vary very much and some fields where fighters have very similar scores have very small standard deviations. If scores are spread out, the standard deviation is large. If scores are clustered tightly together, the standard deviation is small.

To figure standard deviation. The scorer figures out how much each site's score differs from the mean. Note some of these numbers are going to be negative.

Fighter A -4
Fighter B -2
Fighter C 0
Fighter D +2
Fighter E +4

Notice that some of these numbers are less than zero or negative. In order to make these numbers positive (the standard deviation is always a positive number), the scorer needs to square these values. That means she multiplies each number times iteslf.

Fighter A +16
Fighter B - +4
Fighter C - 0
Fighter D +4
Fighter E - +16pnts

Now she adds these all together. Remember she is taking an average of the spread.

16+4+0+16+4 = 40.

Of course this is a high number because it is a sum of numbers that have been squared, and clearly no score approaches 40 so the scorer has to take the square root of this total to get the standard deviation. Calculators can give ou square roots (There is one built right inside most computers.), so can tables, and you can even estimate them.

The square root of 40 is 6.32

Now in mean-standard deviation scoring a fighter's score is based on the number of standard deviations above or below the mean number of votes for the field. To figure this score, the scorer subtracts the mean from the fighter's score and divides by the standard deviation. Let's take a look at how this works.

Fighter raw vote difference from mean score
Fighter A 2 votes -4 -4/6.32 or -.66
Fighter B 4 votes -2 -2/6.32 or -.33
Fighter C 6 votes 0 0/6.32 or 0
Fighter D 8 votes +2 +2/6.32 or +.33
Fighter E 10 votes +4 +4/6.32 or +.66







Notice that Notice that scores obtained undner mean-standard deviation scoring tend to be low. Scores over +2 and below 2 are extremely rare. Also half of all fighters walk away with negative scores, meaning scores below zero. This means a change to mean-standard deviation scoring would be jarring. For this reason, there will be no change to mean-standard deviation scoring without the consensus of the active membership. That will mean you.

Under mean-standard deviation scoring, the winner has the highest mean-standard deviation score. This score will rarely be above a three. There is no rounding off, as decimal point differences count. Remember a fighter with a +3 mean standard-deviation score is doing quite well though such a high score sometimes indicates that the competition is not fair.



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The Measure of Fairness

One of the big advantages of statistical scoring is that it provides a wealth of data that lets any one gague and let's the scorer reamedy the fairness of our competition. Numbers do not lie. With percentile range scoring, common sense should tell anyone that a competition that is fair is one in which several fighters out of a field of ten to fifteen do reasonably well, and only a few fighter have percentile-range scores near zero. A competition where most scores huddle in a ball at the bottom of the range is unfair. Put another way, at leat two fighters should have percentile-range scores of fifty or better. If this is NOT happening, it is time to handicap the competition.

If ZOID used any form of mean-standard deviation scoring, the mean and standard deviation would act as the measure of fariness. A fair competition is one where many fighters campaign and get results from their work. The mean should therefore be high and since scores of these hard working evenly matched fighters will cluster together, the standard deviation will be low.



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Handicapping

Occasionally a gross mismatch among sites occurs. Some fighters have been exchanging votes for months. Some fighters have a base of outside support they can draw upon that is just much larger than that of others. They may be running a large mailing list from their site or a popular interactive game or web board. By contrast other fighters share a computer with their parents, hold down full and part time jobs, have family responsibilities or are on mailing lists where consistent daily begging is not allowed. Handicapping prevents a fighter with stupendous scores from knocking others to the bottom of the range. Here is how it works:

Under percentile-range scoring, a fighter with a score fifty votes more than, or double the next closest competitor's (whichever is more) still keeps her triple digit (100) score, but the scorer recalculates the remaining fighters' scores WITHOUT the high scoring fighter's vote total. This means that there is a new spread sheet that allows for this double calculation. Those other fighters scores are based on the adjusted figure. All fighters' scores are marked as handicapped. And handicapped scores are considered abbsolutely as valid as nonhandicapped scores. And yes, two or more fighters receive 100's and pencils. It is often said that " there is a race for the second pencil." Handicapping prevents fighters from being knocked out on day one.

Under mean-standard deviation, a fighter with a score of +3 or greater wins, but once again the scorer recalculates, the mean, standard deviation, and scores without the high-scoring fighter's vote total. Fighters adjusted scores are the ones used.

Possibility of a two tiered distribution....

A binodal or two tiered score distribution happens when one group of fighters does much better than another. If you graph this you see two humps like the back of a cammel. Each hump represents a group of fighters whose scores cluster about two different numbers. If this occurs with some frequency, the House Managers, and Trustees, with consensus of the community, will split the upper levels of competition into two tiers like major and minor leagues or A and B swim teams, in order to give everyone a shot at winning. Again scores in either division will be considered equally valid, and all scores will be noted as split.




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