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<DIV>George,</DIV>
<DIV> </DIV>
<DIV>I don't think that we have a problem since all calculations we are using the same number of digits for each pilot. It will be a mess if for each pilot we use different number of decimals for scores, K-Factors and totalization. In our calculations the only variables is the score and K-Factors. The normalization is just to assign 1000 point to the winner of each round (maximum of sum of scores x K-factor). In this estimates, we don't apply any statistics.</DIV>
<DIV> </DIV>
<DIV>We use two decimal points to estimate the normalized score over the 1000 points. That gives more than enough precision for this type of estimate.</DIV>
<DIV> </DIV>
<DIV>Regards,</DIV>
<DIV> </DIV>
<DIV class=signature id=signature>--<BR>Vicente "Vince" Bortone</DIV>
<DIV> </DIV>
<BLOCKQUOTE style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #1010ff 2px solid">-------------- Original message -------------- <BR>From: <glmiller3@suddenlink.net> <BR><BR>> I'm going to open a can of worms here in hopes of coming up with a better system <BR>> out of the discussion. Perhaps this has been discussed before and I'm not aware <BR>> of it. Let me preface this by saying I am not a mathematician or statistician, <BR>> but I have some familiarity with both subjects and the following question has <BR>> been growing in my mind for some time. <BR>> <BR>> It seems to me that we are judging our maneuvers with limited accuracy (within 1 <BR>> point in FAI and X.5 points in AMA classes) we are then creating the ILLUSION of <BR>> accuracy by multiplying that score by a K factor and then normalizing to a 1000 <BR>> point scale. Here is a fairly brief explanation of "Significant Digits" that <BR>> I've copied from the web which will int
roduce you to this thought if you haven't <BR>> seen it before: <BR>> <BR>> ****"SIGNIFICANT DIGITS <BR>> <BR>> The number of significant digits in an answer to a calculation will depend on <BR>> the number of significant digits in the given data, as discussed in the rules <BR>> below. Approximate calculations (order-of-magnitude estimates) always result in <BR>> answers with only one or two significant digits. <BR>> <BR>> When are Digits Significant? <BR>> <BR>> Non-zero digits are always significant. Thus, 22 has two significant digits, and <BR>> 22.3 has three significant digits. <BR>> <BR>> With zeroes, the situation is more complicated: <BR>> <BR>> Zeroes placed before other digits are not significant; 0.046 has two significant <BR>> digits. <BR>> Zeroes placed between other digits are always significant; 4009 kg has four <BR>> significant digits. <BR>> Zeroes placed after other digits but behind a decimal point ar
e significant; <BR>> 7.90 has three significant digits. <BR>> Zeroes at the end of a number are significant only if they are behind a decimal <BR>> point as in (c). Otherwise, it is impossible to tell if they are significant. <BR>> For example, in the number 8200, it is not clear if the zeroes are significant <BR>> or not. The number of significant digits in 8200 is at least two, but could be <BR>> three or four. To avoid uncertainty, use scientific notation to place <BR>> significant zeroes behind a decimal point: <BR>> 8.200 ´ has four significant digits <BR>> 8.20 ´ has three significant digits <BR>> <BR>> 8.2 ´ has two significant digits <BR>> <BR>> Significant Digits in Multiplication, Division, Trig. functions, etc. <BR>> <BR>> In a calculation involving multiplication, division, trigonometric functions, <BR>> etc., the number of significant digits in an answer should equal the least <BR>> number of significant digits in a
ny one of the numbers being multiplied, divided <BR>> etc. <BR>> <BR>> Thus in evaluating sin(kx), where k = 0.097 m-1 (two significant digits) and x = <BR>> 4.73 m (three significant digits), the answer should have two significant <BR>> digits. <BR>> <BR>> Note that whole numbers have essentially an unlimited number of significant <BR>> digits. As an example, if a hair dryer uses 1.2 kW of power, then 2 identical <BR>> hairdryers use 2.4 kW: <BR>> <BR>> 1.2 kW {2 sig. dig.} X 2 {unlimited sig. dig.} = 2.4 kW {2 sig. dig.} "****** <BR>> <BR>> My Point is this: <BR>> <BR>> I've seen many contests decided by less than 10 points on a scale of 4000 which <BR>> has been expanded from (at most) 2 significant digits. As a matter of <BR>> "statistics" I think that any separation of less than 100 points (two <BR>> significant digits, ie, 3X00 points) is "artificial accuracy". Unfortunately, <BR>> I don't have any great ideas about how
to improve upon the current system, I'm <BR>> just pointing out what I think is a scientifically valid problem with it. <BR>> <BR>> I smile when I see round scores posted to ten thousanths of a point on a scale <BR>> that has been expanded from two significant digit accuracy to a 1000 point <BR>> scale. This turns a two significant digit answer into eight significant digits! <BR>> (ie, 1234.5678) I think that scientifically, the scores would be more <BR>> accurately posted as in scientific notation at x.x * 10 to the second power. <BR>> Most of the contests that I've been to this year have been decided essentially <BR>> by random statistical "noise" rather than actual scoring decisions. <BR>> <BR>> <BR>> Has anyone ever thought/talked about this before ? <BR>> <BR>> Let me add, that despite what I think are statistically invalid methods, in most <BR>> cases the system seems to work pretty well. In general the superior pilots get <BR>>
; enough better scores to overcome the "noise" but it sure would be nice to come <BR>> up with a more mathematically valid solution, IMO. <BR>> <BR>> George <BR>> <BR>> <BR>> <BR>> <BR>> _______________________________________________ <BR>> NSRCA-discussion mailing list <BR>> NSRCA-discussion@lists.nsrca.org http://lists.nsrca.org/mailman/listinfo/nsrca-discussion </BLOCKQUOTE></body></html>