A math question

[Olorin]

Guess I shouldn't even make a joke about par!! :doh::doh:

Never, ever make a joke about par!

 

[Olorin]

assuming that you're playing all 18 from either the short or long tee

This statement of condition also needs to be taken into account. Since all 18 holes are from the same tee this limits the number of combinations. I submit that the correct number of permutations equals:


(3^18) + (3^18)

OR

(3^18)x2 = 774,840,978

 

[DavidSauls]

Sorry to disagree, and I'm going to take this in a slightly different direction, but let's start by sticking to 1 tee at a time. If each tee has 3 combinations (ABC) then 2 holes have 9 combinations:
AA AB AC
BA BB BC
CA CB CC
so that is 3^2, or a formula of (Possibilties)^(#holes)

I may be wrong, though, so please feel free to correct any errors.

P.S.- I know there are 2 tees but I'll get to that in a little bit. It should be disregarded for the moment... will explain that...

Let's use hole numbers and letters for pin placements:

1 hole course

You can play 1A, 1B, 1C

2 hole course

You can play:

1A, 2A
1A, 2B
1A, 2C
1B, 2A
1B, 2B
1B, 2C
1C, 2A
1C, 2B
1C, 2C

That's 9 options for 2 holes.

For a 3 hole course, you have 27 options:

1A, 2A......and 3A, 3B, or 3C (3 choices)
1A, 2B.....etc.
1A, 2C.....etc.
1B, 2A
1B, 2B
1B, 2C
1C, 2A
1C, 2B
1C, 2C

 

[Olorin]

Let's use hole numbers and letters for pin placements:

1 hole course

You can play 1A, 1B, 1C

2 hole course

You can play:

1A, 2A
1A, 2B
1A, 2C
1B, 2A
1B, 2B
1B, 2C
1C, 2A
1C, 2B
1C, 2C

That's 9 options for 2 holes.

For a 3 hole course, you have 27 options:

1A, 2A......and 3A, 3B, or 3C (3 choices)
1A, 2B.....etc.
1A, 2C.....etc.
1B, 2A
1B, 2B
1B, 2C
1C, 2A
1C, 2B
1C, 2C

Exactly!
This equals: 3^1, 3^2, 3^3...
which fits the formula (# of combinations)^(# of holes)

 

[Steve West]

But.....to be more specific.....for a sanctioned event, if in the same round, one division plays the same course except a different tee on one hole, it is officially (PDGA) a different layout. The TD enters it as a different layout in the TD Report.

Yeah, but....

I think I read somewhere that when TDs try to do that to manipulate ratings, the PDGA smushes it back into one layout somehow.

As someone up there said, not very far into the 774,840,978 "layouts" that only vary by one tee or target, you would get really bored of the repetitive play. As bored as if you were only playing a few different courses.

 

[DavidSauls]

Scarpfish pointed out the conundrum: Though there are 700 million, shall we say, variations of the layout, you can play every variation of every hole in just a few rounds.

I didn't know the PDGA might combine the rounds. We no longer run a singles tournament, but when we did, we had exactly this: One hole with a different tee for different divisions. It's only about 50' shorter and, for most players, only slightly easier. We did it to avoid a water carry, for the smaller number of players for whom it would matter greatly. It was sometimes an issue when there weren't enough propagators for the divisions playing the shorter tee.

 

[Olorin]

You could conceivably play all the hole segments in as little as two rounds.

To be more precise...
If you only play the standard one disc for a round you can play the 6 combinations for each tee and basket in... 6 rounds (assuming that the basket are ever set up in all A, all B, or all C).
But if the baskets are ever set up in all A, all B, or all C then you could throw from both the short and long tee on each hole and play every hole's combination in 3 rounds.

 

[Cgkdisc]

Scarpfish pointed out the conundrum: Though there are 700 million, shall we say, variations of the layout, you can play every variation of every hole in just a few rounds.

I didn't know the PDGA might combine the rounds. We no longer run a singles tournament, but when we did, we had exactly this: One hole with a different tee for different divisions. It's only about 50' shorter and, for most players, only slightly easier. We did it to avoid a water carry, for the smaller number of players for whom it would matter greatly. It was sometimes an issue when there weren't enough propagators for the divisions playing the shorter tee.

That wouldn't be considered "best practice" if we had such a document listing them. First, we don't combine rounds on two different layouts if identified in the TD report, even if just one hole is changed. However. you run the risk of players being upset when the fewer number of props on the shorter layout sometimes produce a higher rating for the same score. This happens randomly maybe 1/3 of the time just due the normal statistical fluctuation in SSA the smaller the number of props on essentially the same course.

So the recommendation would be to have at least 4 shorter tees if you need one for sure. Remembering one different tee can sometimes be harder to remember than when you have to check more often during the round to make sure you're on the correct tee. Now, if the short tee is only the forward drop zone with penalty if chosen, then everyone gets rated on the same layout.

 

[DavidSauls]

Well, in our case, it's not practical to have 4 or more shorter tees. The players do a good job remembering the one hole....because the weaker divisions don't want to throw over the water. One look at the pond jogs their memory.

We offered a shorter tee on another hole once, but the affected division came to me and unanimously asked to use the longer one.

A moot point for us now, because our only tournament doesn't have ratable rounds, so that consideration is removed.

 

[DavidSauls]

....admittedly, it's not a "best practice." Sometimes we have to compromise.

 

[Cgkdisc]

....admittedly, it's not a "best practice." Sometimes we have to compromise.

Having a shorter tee on a hole like that is a better practice so no problem with that.

 

[Disczealot]

Never use average and par in the same sentence.

Also, I need to correct myself. While using up a couple of thousand pencils writing out the complete formula, about 2.3rds of the way through I figured I could save tons a paper by writing on both sides. I forgot to add the backs.

So, using the first tee/target combo on each hole gives you one full layout. Each new target adds 1/36th of a layout. So, from the short tees you get [1+ (2*18)/36 layouts] or 2.

Each long tee you play adds 1/36th of a layout, so you get (18/36ths) more by playing the longs.

So you get 2.5 layouts, not 3.

Wouldn't each new target add 1/18th of a layout?

I don't understand how you would get 2.5 layouts....

If you want 100% different layouts(with playing all new holes), why isn't the formula simply 2*3=6?

3 rounds from short and 3 from long with all pins in A, then all pins in B, then all in C.

Am I missing something?