Quote:
Originally Posted by MikeE
I thought Mike Bortfeldt explained that well enough.
We're not seeing a break so much as a graph representing two populations of different sizes.
Everything to the right of the Y-axis shows the fairly expected distribution of winning margins. This represents just under 90% of all matches.
The data to the left of the Y-axis shows a similar albeit reflected pattern. It is scaled down in frequency since it comes from the ~11% of matches that would have a different winner without the penalties.
There are some other effects due to penalties being larger and more quantized than the point value of scoring objectives, but the main cause is due to sub-population size differences.
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The plot is showing frequency, not percentage. In a "normal" world, the winning margin would be normally distributed about some mean, and so would the penalties. When the penalties are applied, the winning margin would "shift" to the right - but there would not be a large, discrete jump at 0.
In our "less normal" world, we probably have a large skew to the left - the winning margin is far more likely to be small than large. But, I would expect it to still be more or less continuous (as you point out, there are quantization effects because of the scoring objectives... just as scores of say 4 or 5 in football are unlikely). I would expect the penalty point distribution to be continuous, as well, but with even larger gaps between likely values.
When the penalties are subtracted from the penalized score, I expect the resulting distribution to be continuous. The jump right at zero is not expected.
I'll withhold my tin foil hat theories as to why this is until I can take a look at Ester's raw data.