I\'m about to start exam corrections which will soak up a lot of my time over the next few weeks so this is going to be my last post on this topic (Yay!).

I understand this point of view expressed in Ruairi\'s example completely. Surely we should be taking into account the relative times? This works perfectly across a series of events where the field doesn\'t change, such as a 3-Day or 6-Day, where people run the same set of courses, and therefore the pool of points availble to everyone in a class is the same.

The problem is how to quantity the \'required\' effect in a meaningful, consistent way for a league, across a whole year, with huge variations in field. In the example given, using our points system, Runner B would probably win the league on the basis of a 20% better time at one race. For me the key qeuestion is, how much worse does Runner A have to do in one race, to cancel his wins in 4 other races? I don\'t know of any fair, consistent, meaningful way to do this. The current system tries to do this and I hope I have illustrated the flaws inherent in that.

When the system was originally being discussed the idea was being mooted that it somehow captured the difference in inherent difficulty of one one event compared with another. Personally I think that\'s a pipe dream. There are too many factors involved, many of them subjective and almost imossible to quantify. Maybe in race 5 runner B ran a far superior race, better route choice, fine navigation and running speed and maybe in that case he deserves a higher league place. Or maybe there was a control which for some reason was problematic from one direction but not another, and runner A happened to choose to come from that unfortunate direction. Or maybe runner A twisted his ankle and that reduced his running speed. I would argue that we should not be using subjective, unquantifiable factors in determining the final league positions.

Runner A\'s results shows him to be the most consistent across the range of league events. In three of the races where he ran against runner B, he won, admittedly by a very small margin. Maybe he was just lucky, but he was consistently lucky!

Most of the problems with the current system can be addressed by:

1. Scaling the points to the same maximum for every event.
2. Remove ineligible runners before calculating points.
3. Remove runners with times more than double the winners before calculating points.
4. Score male and female runners separately.
5. Score adults and juniors separately.

I have not analysed the effects of scaling on runners further down the field but as it will produce more consistent results at the top of the field I not overly concerned.

Although these changes address the issues, I also feel that they make an already opaque system, even more complicated and opaque.

Rory said:

- The \"Formula 1\" system with 1000 points for the Winner decreasing by 10 points per place (the purest rank-based system there is)

No problem with testing alternatives but why make it more complicated than it needs to be? Awarding one point per place, is simpler, easier to understand and interpret, and unless I\'m missing something, will produce the exact same ranking.

I notice no mention of excluding ineligible runners from the scoring. Let me go back to the orange course results I mentioned previously. The results I gave were based on the current system where everyone who runs on a course affects the scoring. If instead we only score the female juniors then Niamh\'s 1 win, 4 seconds and 1 third becomes 4 wins and 2 seconds. This would give both girls 6 place points resulting in a tie. I firmly believe that runners who do not qualify for prizes in a particular category should not be included in the scoring for that category.

It would be great if this was the exam question! It\'s far harder than anything I came across in college.

The current system does take into account the relative times (albeit in an obscure way). If we based the league table on time alone, then an abnormally difficult event will unfairly benefit or penalise runners who show up.

Scaling points to have the same maximum per event has the same result. It assumes all events of equal standard which we know they are not.

Runners may indeed be \'lucky\' when finding a control. This is why it\'s better to base the points on the average runner rather than an individual.

So that leaves us with the original question...do we remove outliers or not?! If outliers are shown to be unfairly influencing the scores then we should. In my earlier post with the histograms there is some evidence of this due to the numbers involved but I didn\'t think it was significant.

I agree we could certainly split the scoring by gender and adult\\junior status but that would just amplify the effect of small sample sizes. As separate prizes are given to these categories anyway, does it really make much difference?

To sum up, Ruairí\'s example highlights perfectly the differences between the two scoring systems. Both produce very different types of results (a bit like proportional representation -v- first past the post - which system produces a better government?!). I think Paul and I both have very valid arguments in favour of each alternative. It\'s up to the community to decide which system they prefer!

Stuart

Hi Paul
Yes I get your point, you want the results to be based on % of winning time, I can throw that in as well (someone who takes twice the time of the winner gets 500, three times 333, etc)
I just want to do a really quick comparison of the main types ofmethod with the least work possible. 
If we see that there are significant differences over a full league then it can be fine tuned by excluding ineligible runners etc.
Yes one point per place will work the same as 10 points per place but it will make the graphs look nicer.
Enjoy the exam corrections I have some work to do myself for the night o season.
Rory

I\'m neutral on the position based versus the time based system.
The advantage of the position based system proposed by Paul is that a win is a win, regardless of time difference. Runners out of category can be excluded. It is also easy to understand, and easier to allocate OPC points.
If we want a time based system no system is going to be perfect. The current system is fairly good. It is less impacted by who turns up on the day. I think it\'s better at rewarding consistency and participation. I suspect Eoghan Whelan would have won the blue if he had done more than 6 events. Also it keeps more uncertainty of who will win up to the last day. There\'s unlikely to be a tie, which is more likely in position based (separate based on head to head?). The main flaw is because of the low numbers very slow runners can pull down the overall points on the course.

On the OPC points, since I\'ve been doing league prizes I only started allocating them in the last 3 or 4 years. They rarely make a difference except when someone needs it to make up the 6 events, as with Colm and Eileen this year. When we had a position based system years ago, with 50 points for a win, the OPCs also got 50 points (correct me if I\'m wrong, Marcus)

I think this discussion about the calculation system is fantastic and I am in awe of those who have the mathematical skills to make sense of it. I feel that a little bit of historical context is worth putting on the record:

In the noughties (up to 2006) I produced the two Leinster League tables (Autumn Series and Spring Cup), and an inter-club league, using a spreadsheet. Points were awarded as 50 for first place, 46 for 2nd, then 43,40,38,36,35,34,33,32,31,30... etc. OPC points were awarded as the highest points you scored in the other events in that league. Only one set of OPC points per competitor per league was allowed. The points system pre-dated me, I presume it was put in place in the ‘90s. The inter-club league spanned both Autumn and Spring individual leagues.

Producing the spreadsheet was extremely laborious and eventually I managed to persuade Stuart Scott to use his legendary programming skills to automate the process. He asked me for an algorithm, I did some googling and found the Scottish six-day .PDF file that we use now. So if anyone wants to blame someone for the system currently in use, please blame me.

While running the spreadsheet system I received very little feedback, but what I do remember is:

1. The points-based system does not reward exceptional performance
2. If there are only five or six events in a league then the OPC points can skew the results
3. Mushing the women and men together makes women’s league placing depend to some degree on the men who tend to run the same course.
4. Runners running-down a course or two mess up the league for everyone else (e.g. the normally Brown runner who takes it easy for the day and wins the Green).

They are the only comments I remember receiving and they have all been thoroughly analysed in this discussion.

Moving to the Scottish 6-day system was an attempt to fix #1. I think #2 is probably (?) fixed by the recent reversion to a single ten or eleven event league. #3 and #4 remain problems.

While inadequacies in the scoring system do need to be addressed, I would like to see us also address other issues with the league (with apologies to David Masterson for polluting his thread with items that are nothing to do with how the results are calculated; I love the way the discussion started with the words “Maths Warning”).

-          Fixing items #3 and #4 above

-          Finding a way to better highlight juniors’ performance

-          Re-vitalising the inter-club league (are we the only sport in Ireland that does not have an inter-club competition?)

-          Building on Val’s work to promote the league winners. It should be a very prestigious title to hold and something that you fight to retain.

I know none of the above contributes to the discussion about the scoring system, but I thought maybe the historical context would be of interest.

Trivial point: one of the reasons I did the spreadsheet in the noughties was because I wanted to become familiar with Excel’s VLookup and HLookup functions. I still hate them.

Marcus Geoghegan
Ajax