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The restriction that skaters have to participate in at least one OG, can be ’overruled’

by using the penalty function. The penalty function is used to rank skaters without an OG participation at the cost of a penalty that is added to their final score. In this section we justify how the parameter values of the penalty function (see Table 2.23) are chosen, we analyse how many skaters receive a penalty, and how the penalty has influenced the ranking positions.

Justification of penalty parameter values The penalty function is used for skaters without an OG and increases the final ranking score of this skaters such that they will be ranked lower. The penalty itself depends on the values of the parameters γcL

and βcL, and on the total tournament weight value (wkL) of the tournaments they have participated in in their best three (four) seasons; see Section 2.7.3. In Table 2.23, the values of parameters γcL and βcLare given for each category c and discipline L. Based the average difference in CAV5-values of two consecutive positions of the three important tournaments, we will discuss the impact of the penalty score.

Now, consider the results of all distance races of distance d. For each of these re-sults the difference of any two consecutive (in the distance race result) CAV5-values is determined. The average of all these consecutive time differences are denoted by ACDd. In Table 2.31 the ACDdvalues per tournament are presented.

Table 2.31.Average difference between consecutive positions (ACD) Distance OG WACh WSCh

500m 0.03 0.13 0.04

1000m 0.11 - 0.05

1500m 0.11 0.13

-5000m 0.13 0.17

-10000m 0.21 0.18

-Table 2.31 shows that, for example, during all 500m’s of all OG’s the ACD is 0.03 seconds. Furthermore, it shows that the differences are the smallest on the 500m, and the largest on the 10000m. The ACD500mvalue of the Olympics is almost equal to the ACD500m values of the WSCh. TheACD500m value of the WACh is higher, because in this tournament also non-sprinters participate. The WACh 500m results, however, are not taken into account in the 500m rankings.

The ACD values indicate how much a race-time has to be increased on average in order to lower a skater one position on average in that race ranking. Since the USS-ranking scores are averages of tournament scores the following happens.

Consider, for example, two 1500m skaters with exactly the same CAV5-values on their best three WACh’s. Assume that skater A has skated an OG 1500m and that his CAV5-value on this OG is the same as the average CAV5-value of his three WACh’s. So without a penalty both skaters would be ranked on the same position.

If we would increasing the final average CAV5 score of the non-Olympic skater B with 0.11 (the ACD1500mof the OG), this would mean that his ranking position now

drops, on average, 21 (namely the number of OG’s) positions, because there are, on average 21 skaters with about the same score of skater A (see pre-condition 1, Section 2.6.5)).

In Table 2.23, it can be seen that the γcL-values are chosen about equal to the val-ues of Table 2.31. This means that if a skater has missed an OG, but has participated in all other important tournaments, he will only receive the fixed penalty value, γcL, and increases his score such that he finishes, on average, one place lower on any distance race, so in total he drops about 21 positions.

In case a skater misses, besides an OG, other important tournaments, he receives one more time the value of γcLper ten missing tournament weight points with re-spect to the required weight value, i.e., βcL=(0.1)γcL. So for each ten missing tourna-ment weight points, he drops one position extra on all his distance races. This means that if a skater misses, besides the OG, also one WACh result (WACh has a weight of 10), he receives twice the value of γcLas penalty. Based on the values from Table 2.31, we see that his ranking score is set equal to a skater finishing, on average, two positions below him.

Consequences of the penalty Table 2.32 shows, for all disciplines, the total number of ranked skaters (row 1), and the total number of skaters with a penalty (row 2).

Table 2.32.Number of skaters with penalty

500m 1000m 1500m 5000m 10000m OV SP

# ranked 356 266 550 506 287 377 238

# with penalty 116 88 223 204 126 128 97

Percentage 33% 33% 41% 40% 44% 34% 41%

# with penalty in:

Top 50 3 5 4 3 4 0 2

Top 100 7 10 11 15 24 3 6

Top 200 22 40 49 57 71 23 61

Percentage

Top 50 3% 6% 2% 1% 3% 0% 2%

Top 100 6% 11% 5% 7% 19% 2% 6%

Top 200 19% 45% 22% 28% 56% 18% 63%

#=total number of skaters

The table shows that quite a large number of skaters receive a penalty. The lower part of Table 2.32 shows that the majority of the penalized skaters are ranked outside the top 100, and for the larger ranking lists even outside the top 200. For the 1500m ranking, only four of the 88 (2%) penalized skaters are ranked within the top 50 skaters. In case of the Overall ranking all skaters with a penalty are outside the top 50.

The percentage of penalized skaters is slightly lower for the individual sprint dis-tances compared to the 1500m, 5000m, and 10000m. The first reason for this fact is that the maximum number of participants on the OG 5000m and the OG 10000m is

lower. For the 1500m the situation is somewhat special. This distance is during OG’s accessible for all skaters, so also for skaters who normally only participate in 500m and 1000m races. These skaters have no other 1500m results and are not ranked, other ’real’ allround skaters may loose their position to these skaters due to partici-pation restrictions.

The other reason is that a lot of WACh skaters either choose to skate the 1500m or the 5000m/10000m. Although WACh skaters have results for all these three dis-tances, they only have OG results for their most favorite disdis-tances, resulting in a penalty for the other OG distances.

Finally, we observe that a lot of penalized skaters, that are ranked below the 200th position, are skaters from the last two decades; they have participated mostly in the WCC and WSDCh. Especially for the 1500m and 5000m, we observe that, from the last 100 skaters, 75% receive a penalty.

Rankings ’with’ and ’without’ the penalty The first part of this section deals with the, above described, ACD-values. Based on these differences and pre-condition 1, we have indicated that the average decrease in positions for skaters, who only receive the fixed penalty value, is equal to the number of OG’s, namely 21. Since most penalized skaters will also receive a variable penalty, based on the other tour-naments they missed, the average decrease will be higher. In Table 2.32, the number of penalized skaters is listed. It can be observed that most of them are in the second part of the ranking lists. Below we will analyze how the penalty affects the ranking position, and show how many positions they actually drop.

The penalty influence is analyzed by comparing the positions of the penalized skaters in the USS-rankings with their positions in case they receive a penalty value equal to 0, i.e., γcL= 0and βcL= 0. In Table 2.33 the results are given. The first two rows show the average decrease in position of the first 100 penalized skaters and of all penalized skaters, respectively. The figures show that, for most disciplines, the average drop of the first 100 penalized skaters is higher than the average of all penalized skaters. Note that the 1000m and Sprint have no more than 100 penalized skaters. Many of the low ranked penalized skaters are already in the lower part of the USS-rankings, and thereby cannot drop much further. The values confirm more or less what is to be expected, namely a decrease of at least 21 positions. As said, since most penalized skaters receive besides the fixed penalty also the variable penalty, the average drop is more than 21 positions.

Only the 10000m shows a slightly lower value, but this can be explained by the fact that αI,100000m= 0.1, so only half the value of the ACD of the 10000m; see Table 2.31.

The second part of Table 2.33 shows the number of penalized skaters in the top 30 and the top 100 in case the penalty value is set to zero. The table shows that most of the penalized skaters leave the top 30, because the expected drop is at least 21 positions. For the top 100, we see that approximately 50% of the skaters with a penalty stay in the top 100.

Table 2.33.Comparing positions of penalized skaters with and without the penalty value 500m 1000m 1500m 5000m 10000m OV SP

# skat. pen 116 88 223 204 126 128 97

Average drop first 100 pen. skat. 28 23 34 25 17 30

-Average drop all pen. skat. 30 23 26 15 14 25

-# pen. skat. in top-30 (no pen) 3 5 5 3 2 3 2

# pen. skat. in top-30 (with penalty) 1 1 1 3 0 0 1

# pen. skat. in top-100 (no pen) 17 11 28 31 31 12 11

# pen. skat. in top-100 (with penalty) 7 10 11 15 24 3 6 (#= total number of, pen. skat. =penalized skaters)