El arte en el espacio público: apropiación colectiva del lugar

Restriction (2.9) with k = OG of Section 2.7.2 requires that at least one of the best seasons is a season in which the skater has participated at the Olympics. However, not all skaters have participated in an Olympic tournament, because either there were no Games organized (period 1892-1924), or they simply did not participate.

These skaters will never satisfy restriction (2.9) for k = OG, and therefore the model will not find a solution and score for these skaters.

In order to overcome this problem (2.9) with k = OG is neglected for these skaters and replaced by a penalty. The penalty consists of two parts, namely a fixed part and a variable part. The fixed part is only added to the value of BPiLif there was an opportunity to participate in Olympic Games. This means that skaters from before 1924 will receive no fixed penalty.

The variable part depends on the number and weight of the other tournaments the skater took part in. For instance, skaters who took part in all the major tour-naments except for the Olympics will receive a lower penalty than the ones who only skated World Cup races. We will use the weights wkLof the tournaments in which the skater has participated in to determine the value of the variable part of the penalty. The lower this sum of the weights is the higher the penalty.

Specification of the penalty function

The fixed and variable part of the penalty depend on the period in which the skater was active:

• Category I: Skaters only active before 1924, the year of the first Olympic Winter Games;

• Category II: Skaters, still active after 1924.

Since skaters from Category I never have had the opportunity to participate in Olympic Winter Games, the fixed part of the penalty will be zero for this category.

The total penalty value p that is given to a skater who never participated in the Olympics is calculated as follow:

For each skater i and discipline L, let Ψ^B∗_iL be the set of best seasons without the Olympic Games restriction (2.9) and let c be the label of the categories, i.e., c ∈ {I, II}. For each c and L, we define

γcL = penalty value of the fixed part of the penalty;

βcL = penalty value of the variable part of the penalty given per ’missed’ weight point;

η_iL = the number of ’missed’ weight points;

Z_L = the required value of tournament weight points,

The penalty function p(Ψ^B∗iL)is defined and calculated as p(Ψ^B∗_iL) = γ_cL+ η_iLβ_cL with

ηiL = max{0, ZL− X

t∈Ψ^B∗_iL

X

d∈L

X

k∈K_itd

wkL}.

In the penalty function both γcLand βcLare values measured in seconds; the value of p(Ψ^B∗_iL)will be added to the optimal value BPiL of the skater. For each discipline Land category c, the values of γcLand βcLcan be found in Table 2.23. The function shows that ηiLand so the variable part depends on the total sum of the tournament weights (wkL) of the tournaments in which the skater participated in his best sea-sons. For each weight point this total weight differs from value of ZL, the skater will receive a penalty equal to the value of βcL. However, in case the total sum of tournament weights in the set of best seasons is at least equal to ZL, the skater has participated in sufficient many other important tournaments and only receives the fixed penalty value. In the following section we explain how the values for ZLare chosen. In Section 2.9.2 we discuss how the values of Table 2.23 are chosen and how the implementation of the penalty function has influenced the rankings.

Table 2.23.Penalty parameters Penalty parameter

Discipline γ_cL β_cL

I II I II

500m - 0.05 - 0.005

1000m - 0.05 - 0.005

1500m 0 0.1 0.015 0.01

5000m 0 0.1 0.015 0.01

10000m 0 0.1 0.015 0.01

Sprint - 0 - 0.005

Overall 0 0.1 0.005 0.005

The required tournament weights

A skater will only receive a fixed penalty in case his total tournament weight is at least equal to the required tournament weight ZL, i.e., ZLis the minimum total tour-nament weight that is needed to make the variable part equal to zero. In Table 2.24 the values of ZLare given. We take the value of ZL equal to the sum of the weights of the most important tournament of L besides the Olympics.

For L ∈ {500m, 1000m, SPM}, the World Sprint Championships are the most important tournaments besides the Olympics and if a skater participates sLtimes in this tournament, ηiLwill have the value 0. Because both distances are skated twice during this tournament, the value of ZLis twice (four times for SPM) the value of the weight.

For L = 1500m, 5000m, 10000m, Table 2.24 shows that ZL is chosen to be equal three times (sL=3) the sum of the weights of the two allround tournaments (WACh and ECh). As from 1996 on, these distances are also skated at the World Single Dis-tances Championships, these skaters have the advantage that they can reduce the penalty with races from the World Champions Single Distances, since this tourna-ment also has a weight of 10.

Also the overall list L = OV uses the weights of both allround tournaments, but these weights are multiplied by 3, because at least three distances are skated during allround tournaments. The penalty is not increased if skaters miss the 10000m.

Table 2.24.Penalty parameters, ZLvalues

Dis. L Z_L

500m s500m(2wWSCh,L)

1000m s1000m(2wWSCh,L) 1500m s_1500m(w_WACh,L+ w_ECh,L) 5000m s_5000m(w_WACh,L+ w_kECh,L) 10000m s10000m(wWACh,L+ wkECh,L) Sprint sSP(4wWSCh,L) Overall sOV(3wWACh,L+ 3wkECh,L)

Example

In order to illustrate the calculation of the penalty function, we consider a male skater from around 1995, who will be ranked on the 1500m. We assume that this skater has never participated in the Olympics, and in his best three years he com-peted only once in World Allround Championships and three times in the European Champoinships. Furthermore, he skated the 1500m eleven times at the World Cup Competition.

From Table 2.20, we know that wWACh,1500m = 10, wECh,1500m= 5and wWCC,1500m = 1. Hence, Z1500m= s1500m(wWACh,1500m+ wECh,1500m) = 3((10) + (5)) = 45. The total sum of the weights of his tournaments is equal to wWACh,1500m+ 3wECh,1500m+ 11wWCC,1500m= (1)(10) + (3)(5) + (11)(1) = 36, so that ηi1500m= 45 − 39 = 9. The values α and β are equal to 0.1 and 0.01, respectively (see Table 2.23) and the penalty is therefore equal to 0.1 + (9)(0.01) = 0.19 (seconds). This value will be added to his BPi1500m.