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