## The Boomerang Sport Scoring

In a multi-event sport like boomerangs, events are scored in several different ways: high times, low times, total points, total catches, etc. To determine the overall ranking from these disparate event scores, it’s necessary to have a scoring system that transforms the event scores into an overall score. Both the Relative Scoring System (RSS) and the Rank-Based Scoring System (RBS) serve that purpose but there is a fundamental difference in the way they carry out that transformation. The RBS transforms the **rankings **of each event into overall points and the RSS transforms the **scores** from each event into overall points. Fundamentally, that means that the RBS emphasizes the quantity of your rank while the RSS emphasizes the quality of your score.

This is a seemingly subtle difference but, if we look more closely at how these two systems function, we will see they have very different impacts on the overall rankings.

Before we take a closer look at these two systems let’s be clear about the role of a scoring system versus the role of the rules in a sport. This will help prevent any misunderstandings and false arguments about the function and purpose of a scoring system.

- Although scoring systems transform event scores into an overall score, the event score will always be your actual score for the event. If you have a 34s flight in MTA, your score in MTA is 34s no matter how the overall points are determined. Event scores will always be used for awards and records. The point-values produced by scoring systems only count towards the overall.
- Scoring systems cannot and should not account for changes in wind conditions. This is the role of the rules of the sport such as wind-speed limits, wind delays, make-up days, and alternate wind events like TC 100 to make the sport as fair as possible. Scoring systems’ only function is to transform one set of numbers into another set.
- Just like variable wind conditions, other variables are controlled for by the rules of the sport and not the scoring system. These include differences in equipment, skill level, height, age, etc.

## with those possible misunderstandings out of the way let’s take a closer look at these 2 types of scoring systems

The RBS assigns overall points to the rankings in each event: 1 point for 1^{st} place, 2 points for 2^{nd} place, etc. The overall points of each event are then added together to determine the overall ranking. On the other hand, the RSS transforms event scores into overall points of 0-1000 using logarithms. These are then added together for your overall ranking. Although the math in the RBS is simpler than in the RSS, it is not necessary to understand the math to understand the difference between the results of the two systems. The easiest way to see this is to look at examples of how a thrower’s overall score is affected by a change in his event performance. Let’s consider three examples.

- First, let’s look at a low score in the Australian Round from a tournament of 12 throwers in Kiel 2015. The low scores were as follows: 14, 30, 37, 44, 46, 47. There were 3 NP so 14 was 9
^{th}In the RBS, If the thrower with 14 were to improve by double up to 28, he will still be in 9^{th}place and receive the same 9 points towards his overall. However; in the RSS, since the overall points are relative to the score, that thrower will gain overall points for his score improvement regardless of his rank. The benefit here is that the RSS always encourages you to make the better performance even if you are at a very low score. - A second example looks at the effect of an exceptionally high score in the two systems. Thrower B is up in endurance and the top 5 scores currently are 42, 43, 46, 48, and 51. In the RBS Thrower B only needs to get the top rank to maximize his score. To get 1
^{st}place he only needs to get 52 catches. So even if he is capable of 68 he will gain no benefit from doing better than 52. However, in the RSS he will increase his overall points as he continues to improve beyond 52. In both of these first two examples throwers benefit from improved performance at the high and low ends of the scores regardless of rank. - A third example looks at the effect of the two scoring systems in the middle scores. Thrower C scored 54 in Accuracy and took 10
^{th}place out of 20. The rest of the scores are as follows: 31, 35, 38, 40, 44, 46, 47, 49, 52, 53,**54**, 55, 56, 57, 58, 61, 63, 66, 70, and 74. Scores in the middle tend to be more densely packed with fewer scores at the high and low ends. Let’s consider that Thrower C improves his score by just 5 points. In the RBS we can see that just 5 points improvement in score can result in 4 improvements in rank all the way up to 6^{th}A huge improvement in his overall for only 5 points! In the RSS the overall score will also improve, as we have already seen in the other examples. However, since the difference in event scores is relatively small from 54 to 60 the difference in overall points will also be relatively small.

## To summarize the 3 examples above:

Within the RBS, very small changes in middle event scores result in disproportionally large changes in the overall score. Likewise, in the RBS, very large changes in high and low event scores result in disproportionally small changes in the overall score. However, in the RSS all changes in event-score result in proportional changes in the overall score. The point here is that event scores are of little importance in the RBS; only how many people you beat. Whereas in the RSS the overall score is relative to the event scores. This is a fairer way to score overall and, additionally, encourages all throwers at all levels to always be their best regardless of their rank.

This unfair distribution of overall points in the RBS causes another serious problem concerning scoring the overall. In general, some events like Accuracy, Australian Round, and Fast Catch have more tightly packed scores than the other events which means the ranking in those events will have a greater impact on your overall score. Likewise, MTA, Endurance, and Trick Catch generally have less tightly packed scores which will have a smaller impact on the overall score. To make this easier to understand let’s consider 2 scenarios in which we compare 1^{st} and 2^{nd} place scores in ACC and TC. These scores are easy to imagine. In ACC 1^{st} and 2^{nd} are 72 and 70 and in TC they are 72 and 58.

A difference of 2 points in a tightly packed event like ACC receives the same overall points as a difference of 14 points in a less tightly packed event like TC. Not fair! The RSS fixes this problem. In the same way that scores are relative to each other in the event, they are relative to each other between the events.

Consider 2 throwers in 2 events. Thrower D scores 40 in ACC and Thrower E scores 80 doubling D’s score. However, in AR thrower D scores 60 while E scores 30 (half of D’s score). In this case, they would be in a tie after those 2 events despite how many other throwers were involved or how they ranked because they both doubled the other’s score.

There is yet another way that the RBS can unfairly and disproportionally reward overall points in the middle scores. In MTA we use 3 timers and a backup to make sure that we can be as accurate as possible for the thrower’s time. However, mistakes still occur. So let’s imagine a scenario in which only 2 timers have valid times. In this case, we use the worse of the 2 times.

As mentioned before, the RSS transforms event scores into overall points using logarithms. Those points basically range from 0-1000 and are distributed among all possible scores in each event. However, the overall points are on a continuous scale which means it IS possible to score more than 1000.

Having said that, the current proposal affixes the 1000p to a score of 100 in; Accuracy, Australian Round, and Trick Catch; 80 in Endurance; 15s in Fast Catch; and 50s in MTA. Again, the nature of the math used to transform event scores does not change the relative nature of the overall scores regardless of where the 1000p mark is set. If a competitor scores better than the 1000p mark they will receive more than 1000 points towards the overall.

These points can then be put into tables and included in rulebooks, posted at tourneys, and kept in throwers kits. Since the tables will be standardized we will quickly become accustomed to using them at competitions and during practice. These standardized tables also have an additional benefit: they can be used for international, national, personal, and historic rankings.

We have used the RBS for many years and it has served us well. It is familiar and comfortable. It is easy to use even without computer software. However, it is flawed! A summary of a few of these flaws includes 1. In the RBS if a competitor doubles another competitor’s score he doesn’t receive double overall points. In fact, he may only receive 1 placing point advantage if no other competitor scores between them, and 3.

We need to test it out to see if it is fairer in practice. If we do not have a consensus, then we will still have the RBS to fall back on. There is nothing to lose by trying. But if we don’t try, we may miss the opportunity to make our sport fairer for all involved.