[eDebate] 100 Point Scale Thoughts

A Numbers Game edebate edebate
Wed Sep 23 13:40:31 CDT 2009


> -Point inflation- is it happening to the 100 point scale and if so what is
> the impact?

There is point inflation in the 100-point scale from Wake to Wake to
GSU over the past three seasons, but not statistically significantly
more point inflation than there was at Gonzaga over the past three
seasons.

To compare two point distributions that may not have the same shape,
we can find the probability that a randomly drawn point value from
distribution A exceeds a randomly drawn point value from distribution
B. GSU 09-10 point values exceeded Wake 08-09 point values 54.4% of
the time.

Using the Mann-Whitney U test, we can determine a rough(*) confidence
interval around the percentage. The 95% confidence interval for how
often point values from GSU 09-10 exceed point values from Wake 08-09
is 52.5% to 56.4%.

For comparison, the 95% confidence interval for Wake 08-09 over Wake
07-08 is 51.5% to 55.2%.

Comparing to the 30-point scale, the 95% confidence intervals for Gonzaga are

49.3% to 55.6% for 09-10 over 08-09
52.1% to 58.6% for 08-09 over 07-08

Since these overlap the confidence intervals for the 100-point
inflation, we can't be confident that either point scale is
experiencing more inflation.

The point distributions at the tournaments that have used the
100-point scale are:

http://chart.apis.google.com/chart?cht=lxy&chs=600x300&chd=t:69.000,70.000,71.000,72.000,73.000,74.000,75.000,76.000,77.000,78.000,79.000,80.000,81.000,82.000,83.000,84.000,85.000,86.000,87.000,88.000,89.000,90.000,91.000,92.000,93.000,94.000,95.000,96.000,97.000,98.000|0.0009,0.0098,0.0028,0.0084,0.0056,0.0098,0.0364,0.0173,0.0163,0.0229,0.0215,0.0518,0.0238,0.0476,0.0541,0.0588,0.0779,0.0452,0.0508,0.0536,0.0485,0.1049,0.0466,0.0588,0.0480,0.0331,0.0275,0.0112,0.0028,0.0033|68.000,70.000,71.000,72.000,73.000,74.000,75.000,76.000,77.000,78.000,79.000,80.000,81.000,82.000,83.000,84.000,85.000,86.000,87.000,88.000,89.000,90.000,91.000,92.000,93.000,94.000,95.000,96.000,97.000,98.000,99.000|0.0012,0.0068,0.0006,0.0019,0.0025,0.0056,0.0211,0.0112,0.0124,0.0180,0.0118,0.0466,0.0199,0.0311,0.0553,0.0491,0.0907,0.0534,0.0653,0.0901,0.0740,0.1131,0.0603,0.0559,0.0472,0.0155,0.0193,0.0087,0.0044,0.0031,0.0037|69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99|1,1,1,1,2,3,12,4,6,17,12,63,16,48,56,66,130,126,264,197,146,181,88,98,68,50,50,13,1,3,4&chds=68,100,0,0.2,68,100,0,0.2,68,100,0,345.6&chco=ff0000,00cc00,aa44ff&chtt=100-point|speaker%20point%20distribution%20by%20percentage&chdl=Wake%20%2707-%2708|Wake%20%2708-%2709|GSU%20%2709-%2710&chxt=x,y&chxr=0,68,100|1,0,20&chg=15.625,0,3,2,6.25

or

http://tinyurl.com/100-point-inflation

The point values were pulled from debateresults.com and the GSU results sheet.

> -Half points - Ross originally posted that he created the 100 point scale
> instead of a 50 point variant in order to eliminate half points. The 07 Wake
> 100 point instructions also say to avoid half points. I didn't compare
> against other tournaments, but GSU did have 1/2 points being awarded.

At Wake in 07-08 and 08-09, debateresults.com recorded no half points.
At GSU this year, 8 of 1728 (0.5%) point assignments were half points.

> If
> 87 is the average than half of the field should fall below and half above-
> this means there are 86 units to differentiate the bottom half of the field
> (even if most aren't used) and only only 12 units to differentiate the top
> half of the field.

The histograms for the 100 point tournaments are definitely not symmetric

The second year of Wake's 100 point scale, even though there was
inflation from the year before, point differentiation both among the
four debaters in each round and across each debater's tournament were
significantly better than under the 30-point scale. (
http://code.google.com/p/anumbersgame/wiki/SpeakerPointScale ) A
100-point scale that's only a 29-point scale has been better at
differentiating performances than a 30-point scale that's really a
7-point scale.

The clustering in the 100-point scale at 5-point intervals (and at 87
for GSU this year) may also indicate that judges are really not
comfortable differentiating as much as might be desirable. Using more
of the scale might just produce more noise and more clustering at 5-
and 10-point intervals.

(*) Confidence intervals are do not recalculate the variance
adjustment for ties when estimating U, which makes a very small
difference in these particular cases



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