"Scoring The Overall" Part 2: Proportional, Progressive and Regressive scoring - which is best for boomerangs?


 

Click here to read: Part 1: Tracking records - the necessity of standardize scoring in multi-event sports

Part 2: Proportional, Progressive and Regressive scoring - which is best for boomerangs?

     These three systems differ from each other though on their impact on low-level and high-level scores. To understand which option would be best for the sport of boomerangs we can make a simple case study using one event with four different scores. Let’s use the Accuracy event with scores of 10, 30, 70, and 90. The low-end scores of 10 and 30 will represent novice-level scores and the high-end scores of 70 and 90 will represent more advanced-level scores (Fig. 2).

 

Note: all event-scores are translated into a 1000-point scale.
This is done to give each event-score a unique point-value without the use of decimal points. 

 

     From Fig. 3 below we can see that with Proportional scoring an increase in score from 10 to 30 results in a change in overall points from 100 to 300. A 200-point difference. Likewise, we see that an increase in score from 70 to 90 also results in a 200-point difference from 700 to 900 overall points.

Proportional scoring

(linear)

low scores

value

high scores

value

 

L10

100

L70

700

 

L30

300

L90

900

difference

 

200

 

200

Fig. 3

     This seems fair enough and definitely easy to understand and implement. In fact, this is the type of system that was used from 1912 to 1934 in the decathlon. But in 1934 the IAAC required that a new progressive scoring system based on exponential functions replaced the proportional scoring system. The main reasons for this change was to give increasing value to increasing levels of performance. This seems sensible for elite-level performances like those achieved by Olympic decathletes. However, it has some draw backs in the way it affects event specialist and generalist.

     To understand this effect, imagine that a world class sprinter like Usain Bolt decides to compete in the decathlon. He might not be as good as the other Olympic decathletes in some of the field events or the longer runs, but he will have a huge advantage in the shorter sprinting events. With progressive scoring he would receive a huge bonus in those events and gain an advantage in the overall compared to the event generalists. This can clearly be scene in our example with respect to P70 and P90 (fig.2). The difference in overall points jumps 375 from 125 to 500 (fig. 4)

Progressive scoring

(exponential)

low scores

value

high scores

value

 

P10

2

P70

125

 

P30

8

P90

500

difference

 

6

 

375

Fig. 4 

     For this reason, the IAAC updated the decathlon scoring system in 1962 then again in 1984 to make the scoring less progressive. The 1984 system is still used today. It is a great improvement over previous proportional and progressive systems especially for comparing elite-level athletes. But, in a sport like boomerangs in which beginners, novices, and advanced-level athletes compete side by side, there is another problem with progressive scoring. There is very little overall point-value at the low end of the scores. As you can see in the graph of P10 and P30 (fig. 2) the overall point-values are only 2 and 8 respectively (fig. 4). This means there is very minimal reward for beginners to increase from 10 to 30 points in Accuracy – only 6 points overall compared to 375 points overall for an increase from 70 to 90 on the high-end. This makes a progressive scoring terrible for beginners and for adverse wind conditions when even the best throwers are scoring very low. We need a standardize systems that corrects the problems inherent in a progressive scoring system. This system would need to meet certain criteria to be useful for boomerangs:

  1. Event specialist (high-end scorers) should not receive excessive overall points in one event giving them an advantage over generalists in the overall
  2. Beginners and novices should receive a substantial gain in overall points as they improve their scores in the low-end of the scoring range. This is also true for high wind conditions.
  3. The events should be scored on the same scale if at all possible so that some events are not weighted over others. For example, each event is converted into a 1000-point scale.

     The only system that can do this is a regressive one – one based on logarithmic functions. Referencing fig. 2 above and fig. 5 below, we can see here that on the low-end of the scores when a thrower improves their score from 10 to 30 points, they gain 225 points in the overall moving from 519 to 744. This is a great encouragement for beginners to always do their best. On the high-end of the scores we can see that the event specialist who scored 90 will still gain overall points over the other thrower with 70 but only a gain of 54 in the overall. This means that there is still extra reward at the top but not so much that the specialist gains a huge advantage in the overall.

Regressive scoring

(logarithmic)

low scores

value

high scores

value

 

R10

519

R70

923

 

R30

744

R90

977

difference

 

225

 

54

Fig. 5

     For these reasons a regressive scoring system based on logarithms would be much better for boomerangs. The Relative Scoring System that we have been testing the past several years is based on logarithms and accomplishes all the criteria state above. It has worked so well that it has been officially adopted by four nations already: France, Brazil, Spain and Switzerland. Those nations will now be able to track overall records while those nations who are still using rank-based scoring cannot. It’s time to change that. We don’t have to repeat the mistakes of the proportional and progressive decathlon scoring system from 1912, 1934, 1962, and 1984. We can just skip those mistakes and adopt a regressive scoring system.


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