La desigualdad del sufrimiento psíquico en situación de desastre

In our USS-ranking model, we use CAV5-values as inputs for the performances of the skaters. The CAV5-values are derived from actual skating times. The influence on the final ranking score is determined by the value of the tournament weights. In this section we will show how the ranking scores are influenced by the tournament weight values. We only present and discuss the changes for the men’s 1500m, 5000m, 10000m, and Overall disciplines.

For eight (ten) scenarios, the weight values of three tournaments, namely Olympic Games, World Allround Championships, and World Cup Competition, are changed; see Table 2.27

Table 2.27.Changing tournament weights

Scenario L ∈ {1500m, 5000m, 10000m} Scenario L = OVM

1 - 1 wWACh,L= 10

2 wOG,L= 30 2 wWACh,L= 15

3 wOG,L= 50 3

-4 wOG,L= 60 4 wWACh,L= 25

5 wOG,L= 100 5 wWACh,L= 30

6 w_WACh,L= 15 6 w_OG,L= 20

7 w_WACh,L= 20 7 w_OG,L= 30

8 wWC,L= 3 8

-9 wOG,L= 50

10 wOG,L= 60

changes in comparison to the weights given in Table 2.20

In order to understand how the weight changes will affect the various rankings, we have, for each scenario, calculated the share of a tournament weight in the total weight. In Table 2.28 the shares of each tournament in the total tournament weight is calculated for a skater who participated in one OG, three WACh and fifteen WCC races during his best three seasons. Note that we omit the weights of the ECh’s and the WSDCh’s. Table 2.28 shows that in Scenario 1, the original situation, the OG has

about the largest impact on the score, namely 47%. In case of Scenario 2, the OG has the same influence as the average of the three results of the WACh in the three best seasons. For Scenario 6 and Scenario 7, the OG result has a lower share in the total weight than the three WACh results. For Scenario 8, the WC has the highest share.

For the discipline Overall such a table is much harder to make, since the number of participations in the OG and the WACh varies much more between skaters on this discipline.

Table 2.28.The weight distribution

Scenario Tournament weight Share in total weight (%)

OG WACh WCC Total OG WACh WCC

1 40 10 1 85 47 35 18

2 30 10 1 75 40 40 20

3 50 10 1 95 53 32 16

4 60 10 1 105 57 29 14

5 100 10 1 145 69 21 10

6 40 15 1 100 40 45 15

7 40 20 1 115 35 52 13

8 40 10 3 115 35 26 39

Total= sum of tournaments weights of a skater skating one OG, three WACh and fifteen WCC races

The influence of the weights is analyzed by comparing, for all scenarios, the po-sitions of the skaters in the original USS-ranking with the new popo-sitions as a result of the changed weights. In order to carry out this comparison, we will discuss the following situations: (1) The stability of the top 3, (2) the number of new names in the top 10, (3) the average number of position changes in the top 50, and (4) the distribution of the absolute position changes in the top 50.

For the stability of the top 3, we investigate whether or not the top 3 remains the same (-), change within (cw), or new names enter (ne). The average changes in the top 50 is measured by taking the mean over the absolute number of changes in positions. This mean varies between 0 (all skaters stay in the same position) and x/2, where x is the number of skaters taken into account. So for the top 50, the mean can vary between 0 and 25. The distribution is depicted by spitting the top 50 into three groups, namely, skaters changing less than three positions (Position < 3), skaters changing between three to six positions (Position 3-6), and skaters changing at least six positions or more. The results for the 1500m, 5000m, and 10000m are summarized in Table 2.29, and will be discussed below.

Changes in the top 3 and top 10 ⁷ Only when the weight of the WCC is changed a new skater enters the top 3 of both the 1500m and 5000m. For all other scenarios, the top 3 of these two distances remains the same. In case of the 10000m, Hjalmar Andersen takes over the first position of Johan Olav Koss when either the weight of the OG is decreased (Sc. 2), or the weight of the WACh is increased (Sc. 6 and Sc. 7).

7Our scenario analysis applies to the rankings of 2009, so that specific skater positions may slightly differ from the results in the appendix.

Table 2.29.Ranking position variability of 1500m, 5000m, and 10000m Stability top 3

Sc. 2 Sc. 3 Sc. 4 Sc. 5 Sc. 6 Sc. 7 Sc. 8

1500m - - - ne

5000m - - - ne

10000m cw - - - cw cw

-- = no change, cw = position change within the top 3, ne = new name entering top 3.

Number of new names in top 10

Sc. 2 Sc. 3 Sc. 4 Sc. 5 Sc. 6 Sc. 7 Sc. 8

1500m 0 1 1 2 0 1 2

5000m 0 1 1 2 1 2 0

10000m 0 1 1 2 0 0 0

Average position change in top 50

Sc. 2 Sc. 3 Sc. 4 Sc. 5 Sc. 6 Sc. 7 Sc. 8

1500m 1.6 1.2 1.9 4.1 2.8 (2.7) 4.3 (3.9) 2

5000m 1.3 1.1 2 3.7 2.2 (1.6) 4.3 (2.7) 1.7

10000m 1.8 1.2 2.3 4.3 2.5 (1.8) 3.9 (2.9) 0.4

(.) number of average changes when skaters with penalties are not taken into account.

Distribution position change top 50

Sc. 2 Sc. 3 Sc. 4 Sc. 5 Sc. 6 Sc. 7 Sc. 8

Position <3, 1500m 45 45 34 25 38 27 42

Position 3-5, 1500m 5 4 10 15 8 15 3

Position >5, 1500m 0 1 6 10 4 8 5

Position <3, 5000m 43 44 35 24 40 28 42

Position 3-5, 5000m 5 6 11 12 6 16 4

Position >5, 5000m 0 0 4 14 4 6 4

Position <3, 10000m 38 42 36 26 32 25 49

Position 3-5, 10000m 10 7 8 9 15 16 1

Position >5, 10000m 5 4 10 15 8 15 3

Koss has his best score on the OG, whereas Andersen scored better on the WACh.

Table 2.29 shows that in all scenarios only at most two new names enter the top 10.

The highest entry is made by Jochem Uytdehaage on the 10000m, when the OG-weight is increased to 100 (Sc. 5). He climbs from position 12 to position 6.

Changes in the top 50 First we look at the average number of position changes. In case the weight of the OG is varied between 30 and 60 (Sc. 1, 2, 3, 4), the average change in position fluctuates between 1.1 and 2.3 for all three distances. However, when the weight is set to 100, the average position change increases to around four for all three disciplines. Table 2.28 shows that in case of Scenario 5, the OG weight represents almost 70% of the total weight, and therefore the total scores highly de-pend on the OG scores.

In case of Scenario 6, we also see an average of four position changes. Here the WACh is weighted twice as much as in the original model, so that the WACh weight has a higher impact on the final scores than the OG. In Scenario 6 and Scenario 7,

we also observe the influence of the penalty score. Penalty scores partly depend on the WACh weight, and if the WACh weight increases so does the penalty score. This means that skaters with a penalty may drop too many places if the parameters of the penalty are not adjusted. For example, Julius Seyler drops 74 positions on the 5000m list in case of Scenario 7. Therefore, we also calculated the averages over the first 50 skaters without a penalty (values between brackets in Table 2.28).

The average values show that in case of Scenario 5 and Scenario 7, namely the sce-nario’s in which the weight ratio between OG and WACh is changed the most, the rankings deviate the most from the original USS-rankings. This is also clear from the distribution of number of position changes of the top 50. Only for Scenario 5 and Sce-nario 7 more than ten skaters change more than five positions. In all other sceSce-nario’s at least 34 of the 50 skaters remain within three positions of their original positions.

Hence, if the hierarchical order of tournament weights remains unchanged, i.e., the OG is the most important tournament and is weighted slightly more than the three WACh’s, no large position changes appear. However, when we make either the OG too important, or the WACh the most important, then the top 50 changes a lot. The top 3 and top 10 are quite robust to such large changes.

Overall ranking For the Overall ranking only changes in the OG and WACh weights are applied as these have the highest weights and most impact. In the first five scenarios, the WACh weight is increased from 10 to 30 with steps of 5 and in Scenario 6 through Scenario 10 the OG weight is increased from 20 to 60 with steps of 10. Recall that Scenario 3 and Scenario 8 are equal to the original situation. In Table 2.30 the results of the changes are presented.

For all scenario’s the top 10 is represented by the same ten skaters as in the original ranking. Only in Scenario 5, one of the top 10 skaters (Gianni Romme) changes more than two positions, namely three. Heiden never leaves the first place. Ard Schenk only loses his second place to Johann Olav Koss (ranked third) if the WACh weight is deceased to 10 (Sc. 1), Koss loses is third place to the number four, Oscar Mathisen, if the OG weight is decreased to 20 (Sc. 5).

The top 50 is, as expected, more sensitive to changes in the WACh-weight than to changes in the OG weight. The WACh results have, in contrast with the single dis-tance rankings, the largest share in the total weight, meaning that the ranking scores are more sensitive to changes in this weight. However, in case of both Scenario 1 and Scenario 5, still 72% and 82%, respectively, of the top 50 are ranked within five positions of their original position. For the top 100, we observe that this percentage decreases to 57% and 74%, repsectively.

The top 100 changes the most when the WACh weigth is set to 10 (Sc. 1). In this case, only 57 of the 100 skaters deviate at most five positions from their original position. This fact is, for a large part, caused by skaters with a penalty. For Scenario 1, skaters with a penalty replace original top 100 skaters, since their penalty is related to the WACh weight, which is now low. In the other situations skaters with penalty leave the top 100 due to an increasing penalty.

If either the WACh or the OG weight is increased, the impact on the ranking list

Table 2.30.Ranking position variability of Overall

Sc. 2 Sc. 3 Sc. 4 Sc. 5 Sc. 6 Sc. 7 Sc. 9 Sc. 10 Stability top 3

Top 3, OV men cw - - - cw - -

-- = no change, cw = position change within the top 3, ne = new name entering top 3.

New skaters in top 10

Top 10, OV men - - -

-Average change

OV men, Top 20 2.4 0.95 0.25 1.1 1.4 0.4 0.6 1.1

OV men, Top 50 3.7 2.3 1.5 3.6 3.1 1.7 1.1 2

Top 50

Position <3, OV men 20 33 41 28 29 39 46 34

Position 3-5, OV men 16 13 6 13 11 7 3 14

Position >5, OV men 14 4 3 9 10 4 1 2

Top 100

Position <3, OV men 31 57 68 45 44 66 78 45

Position 3-5, OV men 26 28 21 29 21 25 17 39

Position >5, OV men 43 15 11 26 35 9 5 16

OV = Overall, Sc. = Scenario

is less than when these weights are lowered with the same amount. Decreasing the WACh weight results in the fact that the other tournaments obtain more impact on the season scores, and therefore the set of best four seasons may changes in Scenario 1 for some skaters. For example, Yevgeni Grishin performed well at the ECh in 1961, but his lesser results on the WACh of the same season made the season 1961 his fifth best season. By lowering the WACh weight, his ECh score gains more impact on the season score, and makes it to one of his best seasons in Scenario 1.

We may conclude that if we decrease either the weight of WACh or OG by 50%, these tournaments loose their influence on the final ranking scores, and the Over-all ranking list become significantly different from the original rankings. However, increasing the weights of these tournaments results in less changes.

To summarize, we may observe that in all four disciplines (1500m, 5000m, 10000m, and Overall), the top 3 and the top 10 remain more or less the same in all scenario’s. The rankings are quite robust with respect to weight changes when the relative weight structure of the tournaments is kept the same. Scenario’s that heavily change the relative tournament weight structure, show more volatile results, how-ever still the majority of the names in the top 50 change less than three positions.

The largest changes come from skaters with a penalty, because also their penalty value changes when the weight of the WACh is adjusted. The impact of the penalty function on the USS-rankings is explained in the following section.