Competition standing system - cite?

Factual Questions
1

I’m trying to find a reference/name/origin of a competition standing system.

Maybe, just maybe someone can help.

The basic problem is in finding a perfectly fair way of ranking the results of a series of races. Just about every sport I know of uses either one of ladder, bracket system, or a sum of numerical scores (ie Formula 1). Many years ago I remember hearing of what was claimed to be provably the only fair ranking system. This would have been sometime in the '80s.

In simple terms, you rank all competitors so that ranking becomes a partial ordering based upon who has beaten who more often. Where beaten means “finished ahead of” in the final results for a race. (Such a system can yield ties, and needs a separate tie breaker).

But I can’t find any sport that uses the system, nor can I find any reference to the system. I’m sure I’m just not looking in the right place. Minimally the system should have a name. If I could find the reference I remember, it would be brilliant.

Most sports are a series of many one-on-one tournaments and such a system would translate into a ladder. But for a regatta style competition, where a series of races is run with all competitors competing, all the usual tournament don’t apply.

(I’m trying to promote this as a viable regatta system. I have written a program that calculates rankings, and would really like to provide appropriate credit.)

2

It sounds like it might be related to the Condorcet criterion for elections.

3

Awesome. Utterly Awesome. :smiley:

That gets it. I am wondering if I didn’t misremember its application to sport (or just invented that bit myself.)

4

Why stop there … spin up yourself a mighty tall tale … Roman legions … beautiful sirens … intervention of the gods … be creative …

5

Sirens will suffice :smiley:

It is odd however. I felt sure that there was some existing application in sporting contests, and I spent ages looking for one - and came up a blank. Surely somewhere it has been so used. It seems so, well, obvious.

6

It would be interesting to see a comparison of a series of races using standard ranking and the system you propose. It seems that each race may have differing conditions that affect the results. We ran through this a few months ago comparing Olympic medals to world records. An Olympic win shows you could beat someone under those specific conditions, that day, that time, in this place, and it did not matter that elsewhere the loser ran a better time.

Dennis

7

The problem with Condorcet methods is that they do not take into account the margin of difference between two competitors. In some contests, there is an ability to extract meaningful data beyond the order that the competitors finished. When that’s the case, purely using Condorcet strategies throws away information and thus can turn out to be biased against someone who just barely finishes behind another most of the time, but when he does get ahead, wins by a lot. From what I can imagine, this applies quite reasonably in sailing so long as the competitors understand that their individual times matter more than their relative placement and so do not take excessive risks in order to try to just barely beat one other boat. I don’t know whether this flies in the face of competitive racing in terms of tactics that might be used to stay ahead of other ships but slow yourself down overall compared to leaving a potential gap but having a faster individual time, but I imagine with enough competitors in each race the likelihood of this mattering drops to zero.

That’s not to say that “least aggregate time” is the best measure for sailing, as it would more heavily penalize those who have bad days when the overall speed of the race is slow. I would suggest that you instead normalize the individual races’ times, giving a 1 to the fastest ship, a 0 to the slowest, and linearly interpolate the rest of the scores. If there same ships do not compete in every race, this isn’t quite fair, giving an advantage to those who race against weaker teams. In such a case you might give a 0 to the, say, 4th slowest and all slower ships, and thereby start the linear interpolation from a faster ship than the absolutely slowest.

8

Curiously sailing regattas is exactly the target I want to apply this in.
The standard sailing regatta is run on a points system. Minimum points wins. One point is allocated for first and so on down the fleet. So in a fleet of 20, if you come 20th, you get 20 points. DNC (Did Not Compete) DNF (Did Not Finish) RET (Retired), DSQ (Disqualified) and so on score one plus the number of competitors. So 21.

If enough races are sailed in a regatta it is usual that each competitor is allowed to drop their worst score. Except for a DSQ, which cannot be dropped.

In mixed fleets the times are corrected to account for different speed boats. There are a whole range of rating and yardstick systems that provide corrections. Once the corrections are done the finishing order is determined and points allocated.

There have been regattas where total time is used. Round the world racing was one. But the problem is that you can get a situation where one competitor gets a magic ride in one race and becomes unassailable, which drives the interest out of the regatta.

The problem with these scoring systems is that they discourage risk taking and reward playing the averages. This is because the penalty for messing up is almost impossible to retrieve. The front runners in a regatta may have a series of podium finishes, so they are collecting 1,2 or 3 points per race. After say 10 races they would be averaging about 15 points each. But say the fleet is 20 strong. A single bad risk taking call might send a boat half way down the fleet, to finish with 10 points. Suddenly they are out of contention. 25 points to 15. Say there were 15 races in the regatta. That competitor would need to win every single race from then on to win, just to cancel out a single mid-field finish. This is why there is a drop one rule. But even with a drop one rule risk taking is discouraged. All sailors know that a single bit of gear failure can result in a DNF. Everyone keeps the drop in their back pocket in case of bad luck.

The point is that races can become boring if there is not so much incentive in risk taking. The goal is to spice things up.

Sailing is a very tactical race. Even ocean racing. Right now the Vendee Globe round the world solo non-stop race is on. The competitors are entering the Southern Ocean, and even now they still watch one another, and if needed will change course to ensure that they maintain a covering position. Round the cans racing gets much more tactical, and match racing is totally tactical. Everyone works towards the finish position and doesn’t care about the actual elapsed time.

You will see highly tactical racing based upon the points. Because of the way the points works you will get situations late in a regatta where sailors that will deliberately mark one another. A boat that is in a winning position will deliberately sit on top of a boat that could potentially beat them in the points if it got a high finish. Using the rules of sailing it is possible to prevent a boat from being able to sail on their desired course, and it is possible to ensure they finish in a dreadful position, ensuring your own win in the regatta. One notes that in Formula One this is explicitly not allowed. In the recent Olympics the Croatian Laser sailor tried this tactic on the Australian who was challenging him for gold. It backfired, the Aussie got out from under him and managed to get away to a score that actually allowed him to win the regatta. Had the Croatian guy sailed his own race and not tried, he would almost certainly have won the gold, but he tried too hard to ensure the win. So it doesn’t always work.

OK, the point being - sailing doesn’t care about time, it cares about finishing position. And the way it is currently done is a problem IMHO. It could be fixed with a Condorcet scoring.

9

It may be the case that the Arrow Impossibility Theorem (or a slight variant of it) applies to the things you’re talking about, which means that it’s impossible to rank all competitors fairly:

10

It seems they standardized on just about the worst possible scoring system. Rather game-theory clueless of them. :slight_smile:

You touched on a meta-challenge facing any cumulative scoring system: Is the real competition for this race or for the season standings?

IMO ideally each team should be motivated by the system to work flat-out to win today and every day. There should never be a time when a competitor would rationally think: “The ideal for my season standings is to do X right now, whereas the ideal for today’s race is to do Y right now.” This applies double-ugly in sports where teams field multiple competitors in the race. As is common in some flavors of auto racing.

To be sure the announcers can try to spin these season- or team-level tactics as another dimension in the chess game. ISTM that’s repainting the bug as a feature.
As to the international regatta industry I doubt you (even backed by the awesome power of the worldwide SDMBers) will be able to change much. But ISTM glowacks just above has the germs of the right approach.

To incentivize aggressive exciting racing incentivize finishing times, not order of finish. And to incentivize proper race-level vs. season-level thinking, reduce the penalty for aggressive tactics that don’t pan out. Which may mean reducing the penalty for some reasonable percentage of especially crappy finishes. In sailing this might also mean taking “go for broke” literally and providing a free DNF to any / all significant equipment failures.

11

It is interesting to contrast the various sports.

The three I look to are sailing (because that is my interest) and as exemplars of regatta style race sports, Formula 1 and cycling tours.

All three are on the surface the same deal. A series of races, and a cumulative winner over the series. All three use quite different ways of finding the winner. But more importantly, under the surface the nature of the race is very different. All are tactical, but in each the nature of the sport makes for very different tactics.

Cycling and motor racing run along a track/road. There is no choice about route. Sailing defines markers, and you are free to get between them using as much ocean as you like.

Motor racing, overtaking is a dangerous and difficult task. Being faster than the car in front is not enough. You need to get past. Many races have been won by avoiding being overtaken. Cycle racing, overtaking is trivial. You just need the legs. Tactically this is much more complex. The only time you really want to overtake is in the last sprint to the line. Leading saps energy your competitors are not using. Sailing, you can sail a totally different course and reach the next mark ahead if you judge the wind, tide and currents correctly. This leads to the tactic of “covering.” If you are ahead of a major competitor and they change course - you change as well - with the intent of staying in between your competitor and the mark. This is on the basis that if they do find better wind, you will be there ahead of the to enjoy it as well, and if you both run into poor wind, you both suffer, but you are still ahead. The risk in not covering is that you lose position, even if by covering you both end up slower. In the closing races of regattas it is not uncommon to see the top competitors engaged in a mini race oblivious to the position of the rest of the fleet.

The fact that sailing is a race in 2D instead of one is what makes it different to other racing. It isn’t just a matter of sailing faster, there is a huge element of skill in reading the conditions and using them. Winds shift all the time, picking the shifts is a key skill. There is a saying, “if you are behind you won’t get ahead by following the leading boat”. However the nature of the regatta scoring system is that it discourages taking that risk. The rules of sailing allow for tactical plays as well. The right of way rule (port tack must give way to starboard tack) is used mercilessly to gain position. Similarly, the rule on maintaining proper course can be used to force another boat’s course unfavourably. Car racing and cycle racing have no equivalent (except that car racing essentially makes such tactics illegal.)

So the nuances make things different, and difficult to relate.

I do plan on running the last decade or so of F1 results though the system, and may also look to the Tour de France similarly. Mostly however you don’t see much change from the results as they stood. (Which is a good thing.) However I suspect that any of these sports could usefully try a Condorcet system to advantage.

12

As I understand it, Arrow’s Theorem only applies when all you have is ranked choice. Indeed, that is all that is considered right now, and that’s why there are issues. The logical underpinning fails when you consider that there is more to the finishes than a ranked list. Once you can give arbitrary scores to each of the competitors based on their performance, you are able to state precisely what matters the most and how the competitors are supposed to weight the various tactics that are available. That’s not to say that it’s 100% fair, but once you get off from a ranked list Arrow’s Theorem’s hypotheses become a non-issue, to the point of not being necessary in a system that is considered “fair”, due to the ability to the system to be more precise about how to rank each competitor.

13

Is the first statement one of fact, or one of law? That is, must the only thing that is considered be finishing order, or is it just that the finishing order happens to be the only thing that matters right now? As I have indicated, using a large range of numbers in the form of their time on a segment, possibly normalized, introduces more information.

Another competition that has a similar problem is duplicate bridge. You play a large number of hands against the same set of people (that is, all the other people who play your cards), and the question becomes how to weight the scoring. There are 3 possible approaches: One, you get a point for each competitor you score better on for each hand, half point if you made the same score. Two, your scores on each hand are aggregated. Three, you do something in between that makes the impact of large score swings smaller than the second approach, but larger than the first approach which considers any difference in score to be of equal size. The second approach is effectively never used from what I understand because of the heavy influence of high-scoring hands, but the third exists in the form of IMPs. See link for details of how point differences correspond to match-points. I’m not saying that something like IMPs are the right model, but it was clearly designed due to the inability of simple match-points (the first system) to make a distinction between different amounts of scoring differentials on single hands.

14

Its the idea of repecharge.

The one unfair thing in ordinary ranking systems is that a team that is sure to be in the finals and can afford to throw a round. If they notice that if they lose to team X, team X will then have more points than the notionally stronger team Y then they lose on purpose to X… and then X is in the finals and Y is kept out.
repecharge aims to fix that by giving team Y a chance to get the finals anyway. Notionally if it is truely stronger and worthy then it gets its place. (not true, they may be demoralised by being forces to fight yet again or facing external practical issues… injuries, costs, tiredness, homesick ,etc )
However repecharge is an extra event… not just a points adjustment system.

You could have a points system do the same…
A bonus point for the teams which have beat the lowest scoring finalist more often than not. By that way, team Y may get the bonus point it needs to keep the spot in the final despite the game throwing toward team X.

15

No, it is just a matter of how things are done now. But this question does lead to a finer set of distinctions in different competitions that make the question more interesting.

In a lot of sailing (and say much motorsport) it isn’t just a matter of catching up with someone - you need to pass them, and passing is itself a skill. This is perhaps not obvious in sailing as it would appear that you have a wide open sea to pass in, but the nature of the physics of sailing mean that courses intersect and there is a whole rulebook on how this is managed and it can become highly tactical.

The other thing is the nature of competitions. Many sports (most team sports) martial arts, and many games, are two competitor - winner loser. The problems of coping with capturing additional ranking information is going to be significantly harder. Repecharge
is the best known way of handling some of the problems in competitions. We used to use it Judo back when I tried to compete.

But for a competition where there are many simultaneous competitors the problems seems to come from a different direction. Especially when creating a series/regatta. One problem being that aggregate times can disproportionately be affected by a lucky break of a single stroke of bad luck. The cycle tours seems to be the most highly developed tactical sport that uses aggregate time. There you see how a team will field a set of riders whose only job is to protect their leader, and ensure to set him up for best performance in a leg, often to the detriment of their own standings. A big part of their job is to make sure he never drops off the back of the pack as doing this only once will drive him out of contention. It would be interesting to apply a Condorcet ranking for the green jersey, but the nature of history is that most people only care about the yellow one.

So my concern with a Condorcet scheme is limited to multi-competitor races that comprise a series. And the particular concern is to try to remove barriers to more aggressive risk taking tactics.