68 1. Streaks
distribution for match results:
{4459.56, 1742.79, 1235.17, 1241.94, 1746.56, 2181.98} .
The graph in Figure 32 compares these two simulated distributions
with the actual distribution of the matches in our data:
{5453, 1157, 993, 813, 1338, 2854} .
The simulation from the odds model gives a good fit to the actual
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
0.5
Match Outcome
Proportion
of
Matches
independent simulation
data
odds simulation
Figure 32. Simulated and actual distribution of match outcomes
data and is clearly superior to the independent sets model. We see
that, consistent with the findings of the article [22], the independent
set model underestimates the proportion of “heavy defeats”; these
correspond to the set outcomes (1, 1) and (0, 0).
Before turning to the best-of-five set data, we digress slightly to
suggest another way to estimate α and k, which involves minimizing
the chi-squared goodness-of-fit statistic for the model. Recall that
if we let Obsi denote the i’th count in the observed distribution of
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