Friday, July 22, 2011

Tie-Breaker




Two sailors had the following scores in a seven race series with one throwout allowed.


Sailor A    4   4   3   4   2   2   2
Sailor B    2   2   2   2   8  16   1


After the throwout each sailor had 17 points.

Which sailor had the most consistent series? Which sailor had the worst individual races? Which sailor won the tiebreaker under the current Racing Rules of Sailing?

This is not some theoretical exercise. These are real results from a regatta sailed this week.

15 comments:

World Tour Stories said...

So is this how it has to be.. I have to remind your schizophrenic twin brother to add us back up in your blog roll every time we get removed?

Litoralis said...

Which sailor had the most consistent series?

Either sailor could arguably be considered the most consistent. None of Sailor A's finishes were outside the top 4. Sailor B had four races with second place finishes and 5 out of 7 races in the top 2. Sailor B also beat Sailor A in 5 out of the 7 races.

Which sailor had the worst individual races?

Sailor B

Which sailor won the tiebreaker under the current Racing Rules of Sailing?

Sailor B. The rules say that "[i]f there is a series-score tie between two or more boats, each boat’s race scores shall be listed in order of best to worst, and at the first point(s) where there is a difference the tie shall be broken in favour of the boat(s) with the best score(s)."

Tillerman said...

Why do people care so much whether their blogs are on my blogroll? There are over 100,000,000 blogs out there. Of these I put about 40, the ones I happen to enjoy the most, on my blogroll. Do I really have to explain to the other 99,999,960 why they are not on my blogroll?

There are about 3.4 billion women in the world. I chose to marry one of them. I don't have to explain to the other 3,399,999,999 why I didn't marry them. Most of them have got over it by now.

Tillerman said...

Litoralis is correct of course. See Rule A8.1 If there is a series-score tie between two or more boats, each boat’s race scores shall be listed in order of best to worst, and at the first point(s) where there is a difference the tie shall be broken in favour of the boat(s) with the best score(s).

Sailor B wins because he has more first places (one in fact) than Sailor B.

At the weekend we were sitting around, over a couple of beers, discussing the regatta results. They hadn't been posted yet but the two leaders had worked out that they were probably tied on points (depending in fact on whether or not I had beaten one of them in a particularly close race.)

So were discussing tie-breakers and someone pointed out that the current system means that the person with the worst race would win the tie-breaker. This seemed odd to me.

I noticed that it's true in this case too. Is it mathematically inevitable that the sailor with the worst race (or the worst race to count if there is a throwout) will always win the tie-breaker?

The results quoted are actually for 2nd and 3rd places in the Sunfish Junior North Americans sailed this week in Barrington RI. A youngster whom I used to sail with in NJ was the kid who lost this particular tiebreaker and came third. He was one of the sailors in this story.

Tillerman said...

To answer my own question, no it is not always true that the person with the worst race wins a tiebreaker.

For example....

A 1,4,4,5
B 2,3,3,6

A wins, but B had the worst race.

David said...

Mathematically speaking, A is significantly more consistent than B with a standard deviation of 1.0 vs 5.5 (or .98 vs 2.56 with the throwout.)

Who "deserves" the win (I know, you didn't ask that)? B, them's the rules. Besides, as Litoralis points out, B beat A "on a more consistent basis."

Tillerman said...

Exactly David. There are so may ways to write tiebreaker rules that it's always possible to find a way to argue that the other guy should have won it.

Pat said...

Last December at the race mgmt. seminar, I was given a problem to explain to the class, in which a series tie between two boats was still tied after using the first (A8.1 rank and stack) tie-breaker and the second (A8.2, recency) tie-breaker method had to be used.

Of course, scoring rules can be changed, though clubs that do so without careful thought might get bitten by unintended consequences.

Tillerman said...

Quite right Pat. A8.2 gives the tie to the same boat in this case (for beating the other boat in the last race.)

Those two tiebreaker rules can award the win to the boat who actually finished behind the other boat in more races. Some folk think that's unfair and that the boat that beat the other the most should win the tie.

But then you have to consider three way ties and it really starts to get complicated...

Baydog said...

On a totally unrelated topic (how unusual), how did you make your little blog thingy a laser insignia? I want to do that.

Baydog said...

And did anyone ever point out a million times before that you can't spell Litoralis without s-a-i-l-o-r?

tillerman said...

What little blog thingy? Where

Baydog said...

On my blogroll, in front of Proper Course, where the 'Blogger' B usually is.

Tillerman said...

Oh yes, there it is. And my2fish has a Sunfish logo too. Aren't they cute? You should have a dog, Baydog!

Arvin tells me it's called a "favicon" and you can load up a customized on by going to the Blogger Dashboard, clicking on Design and then Edit Favicon. Clever these androids, eh?

Unknown said...

A. 2 3 18 6 14
B. 9 2 7 7 9
C. 6 10 5 8 6
From a race in New Jersey yesterday. A three-way tie for fifth place in Opti. Before you calculate however, under this regatta, you must drop the highest score for each sailor. My son was "B"

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