El vínculo social articulado a partir del 19 de septiembre

In Section 2.4 we have formulated three performance score criteria. The influence of technological innovations is eliminated by taking differences within tournaments (see Section 2.6.2). The influence of the maturity level is eliminated by estimating this effect on the GPL (see Section 2.6.4) and correcting all AV-values for this global effect (see Section 2.6.4).

Finally, by relating the number (α) of best skaters to the number of participants and by using only the first 24 positions per tournament to estimate the effect of the maturity level, the influence of the changing number of skaters is taken in account.

In Section 2.4 we have formulated a pre-condition concerning performance scores for equal positions on different distance races. This pre-condition is tested in the fol-lowing way. Take, for example, all skaters finished on the ninth place of the 500m of any Olympics. Both the AV5-values and CAV5-values of these skaters are plot-ted in Figure 2.16. The figure shows that the AV-values correlate (correlation of 0.81) strongly with the seasons, and that the CAV5-values are more or less season indepen-dent (correlation 0.01). The same conclusion can be drawn by analyzing the result of a simple linear regression through the points. The AV5-values have a significant negative slope (β), and the slope of the CAV5-values is zero. From this example, we may conclude that the CAV5-values, calculated for all Olympic ninth positions, are not season depended. So since these values do not depend on the season a skater

was active in and thereby satisfy PS 2, we can use them for measuring the relative quality of a skater.

19200 1930 1940 1950 1960 1970 1980 1990 2000 2010

0.2

Figure 2.16.(C)AV5-values of skaters finished ninth on any Olympic 500m

Correlation value and slope as in example in Figure 2.16, are calculated for all tournaments and distances. In Table 2.19 a selection of the male results is presented, namely the 500m 1500m and 5000m of the Olympic Games, the 1000m of the WSCh, and the 1500m and 5000m of the WACh. The results for the WACh are based on the period 1945-2011, since before 1945 not all WACh for men have at least 24 partici-pants.

Table 2.19.Correlations (C)AV-values and years for men

500m OG 1000m WSCh

Position 5 10 15 20 25 5 10 15 20 25

Corr. AV -0.52 -0.63 -0.86 -0.90 -0.84 -0.47 -0.58 -0.64 -0.67 -0.74 βAV -0.01 -0.01 -0.02 -0.02 -0.03 -0.01 -0.01 -0.02 -0.03 -0.03 t-prob AV 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Corr. CAV 0.01 0.16 0.10 0.06 -0.04 -0.03 0.17 0.15 0.22 0.30

βCAV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01

t-prob CAV 0.98 0.52 0.68 0.82 0.88 0.82 0.15 0.20 0.06 0.01

1500m OG 1500m WACh

Position 5 10 15 20 25 5 10 15 20 24

Corr. AV -0.59 -0.63 -0.82 -0.81 -0.73 -0.48 -0.65 -0.72 -0.66 -0.71 βAV -0.01 -0.01 -0.01 -0.02 -0.02 0.00 -0.01 -0.02 -0.03 -0.04 t-prob AV 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Corr. CAV 0.04 0.30 0.12 -0.02 0.00 0.16 0.22 0.09 -0.06 -0.06

βCAV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

t-prob CAV 0.87 0.24 0.64 0.95 0.99 0.18 0.06 0.48 0.61 0.65

5000m OG 5000m WACh

Position 5 10 15 20 25 5 10 15 20 24

Corr. AV -0.55 -0.68 -0.65 -0.58 -0.57 -0.50 -0.58 -0.66 -0.69 -0.74 βAV -0.01 -0.01 -0.02 -0.02 -0.03 -0.01 -0.01 -0.02 -0.03 -0.06 t-prob AV 0.02 0.00 0.01 0.01 0.02 0.00 0.00 0.00 0.00 0.00 Corr. CAV -0.04 0.01 0.05 0.14 0.09 -0.13 0.06 -0.02 -0.17 -0.35 βCAV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01 t-prob CAV 0.89 0.96 0.85 0.58 0.74 0.28 0.65 0.86 0.16 0.01 Corr. (C)AV= correlation between the years and the (C)AV-values. β = regression coefficient between

years and (C)AV-value. t-prob=t-probability of regression coefficient β.

The first three rows of each block in Figure 2.16 show the values of the correla-tions (Corr), the regression coefficient (β), and the t-probability (t-prob) of the

AV5-values. The other three rows show the statistics of the CAV5-AV5-values. The column refers to the position of the distance race that is compared. For example, the first row and first column shows that all AV-values of skaters finished fifth on the Olympics have a correlation of -0.52 with the years, and the regression coefficient has a signifi-cant value of -0.01.

The AV-values in each block of Table 2.19 have a high correlation with the sea-sons and a significant negative regression coefficient. Note that these facts support Gould’s hypothesis. After the maturity correction, all correlations are lower than 0.40 and almost no regression coefficient is significant anymore, i.e., the CAV-values are time independent and all within the same range.

However, for the 25th position of the 1000m WSCh and the 24th position of the WACh there still is a small correlation and a significant negative slope. This is caused by the fact that a participation levels where not constant. In 1999 the WACh was restricted to 24 participators and due to the country and continent restrictions not always the best 24 where present.

For the 10000m, the AV5- and CAV5-values of equal race positions are some-what harder to compare and not included in the table. This is because the number of skaters who are allowed to skate this distance has changed over the years. The CAV5-value of the number twelve in a field of 24 skaters is likely to be lower than the CAV5-value of the number twelve in a field of only 12 skaters, mainly because the country restriction causes the effect that if the number is reduced from twenty-four to twelve not always the worst twelve skaters are left out. If a country has more top 12 skaters than allowed, some of these top skaters have to stay home.

A second reason for not always having the best skaters of the world within the top 12 of the 10000m is that during an allround tournament good stayers may not qualify for 10000m. If their position in the ranking after three distances is not within the best twelve, or within the best eight of the 5000m, the are not allowed to start at the final 10000m.

In Section 2.6.2, it is explained how the AV5-values eliminate the influence of technological innovations and therefore satisfy criterion PS 1. In Section 2.6.3, we have eliminated the influence of the maturity level on the AV5-values by estimating the GPL in each season and correct for the differences. In this section, it is shown that the resulting CAV5-values are time independent and therefore satisfy criterion PS 2.

In both corrections the changing participation numbers is also taken into account, so criterion PS 3 is also satisfied. Finally, in this section it is shown that equal distance race positions receive more or less the same CAV5-value, showing that pre-condition 1 made in Section 2.4 is satisfied. The conclusion is that CAV5-values can be used as performance scores. In Section 2.7.1 it is explained how these performance scores are used for our USS-ranking system.