How many field combinations played?

[tig567899]

If we take audience selection into account, then the defense at position 3 is limited to 2 options.

Taking this into consideration, we have 1*6*2*4*2.

For example, if category A was selected as the 3rd defense, then it would be unavailable for any of the other positions.

This gives us 96.

Squaring 96 gives us 9216... which is precisely half of the number presented. I don't know where that extra 2 came from. If anyone could care to enlighten me, that'd be welcome. From what I see if 10980 combinations were played we've played more combinations than are available. Just my take on the issue.

[kiasam111]

That's such a clean and easy way to include the audience selection - I love it It also means that your number is more accurate than mine #goteam

I've calculated my numbers again using 9,216 combinations (thanks!) and an Arithmetic Series, but this is based on a shaky interpretation of the 90% found in the FRC Blog.

An average event has 100 matches, and 90% of those have unique field combinations (90 matches).

Therefore Event 1 - 90/9216 = 0.98%

At Event 2, 90% of the field combinations have been used before (at Event 1) and 10% haven't. (I think..)

Therefore Event 2 - 0.98% + (0.98%*0.1) = 1.078%

Similarly, at Event 3, 90% of the field combinations have been used before (at Event 1 and 2) and 10% haven't.

Therefore Event 3 - 0.98% + (0.98%*0.1) + (0.98%*0.1) = 1.176%

From this, we can see a pattern is emerging. For each event, we add (0.98%*0.1), therefore we can create a generic formula to represent the projected percentage of defensive combinations used at any given event.

Therefore Defensive Combinations = 0.98% + (n-1)(0.98%*0.1)

This fits the generic form of an Arithmetic Progression, where Term n = a + (n-1)d, where a is our first term (0.98%), n is the event number, and d is the common difference (0.98%*0.1).

Using this, the 121st event would be term 121 (n=121).

Therefore, Defensive Combinations used by the 121st event would equal
0.98% + (121-1)(0.98%*0.1) = 0.98 + 120(0.098)
= 0.98 + 11.76
= 12.74%

So this means that after the 121st event, roughly 12.74% of the defensive combinations have been played. Does that make sense??? Happy to explain further. This is so much fun!!!

[Hitchhiker 42]

Originally Posted by kiasam111

An average event has 100 matches, and 90% of those have unique field combinations (90 matches).
.
.
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At Event 2, 90% of the field combinations have been used before

The way I interpreted their numbers was that each event had 90% of the matches use different fields than any other in that event. So I'm not sure how to check how many are popping up across events, but if it's totally random which defenses get selected (which it's not), I'll assume each field combo has an equal shot at selection (100 matches per event, 121 events assumption), so, each event has a (however uniques matches played)/(total field combos) chance to repeat a match. I'll attach an excel file in a moment to explain.

[Hitchhiker 42]

The excel file attached should show my calculations as well as my explanation for how I worked it out... I narrowed it down to (of course with all the simplifying assumptions) 43% matches possible played.

[kiasam111]

Originally Posted by Hitchhiker 42

The way I interpreted their numbers was that each event had 90% of the matches use different fields than any other in that event. So I'm not sure how to check how many are popping up across events, but if it's totally random which defenses get selected (which it's not), I'll assume each field combo has an equal shot at selection (100 matches per event, 121 events assumption), so, each event has a (however uniques matches played)/(total field combos) chance to repeat a match. I'll attach an excel file in a moment to explain.

This makes more sense! Not sure what I was doing before

The spreadsheet also means we can extrapolate!! Hooray!

Not sure how helpful this will be, but TBA has the total number of matches played as 11162 right now (found here)

[kiasam111]

The spreadsheet also means we can extrapolate!! Hooray!

Speaking of extrapolation, it would take 3918 events to play 90% of all combinations. As far as I can tell, at this point it becomes a limiting sum.

[Hitchhiker 42]

Originally Posted by kiasam111

This makes more sense! Not sure what I was doing before

The spreadsheet also means we can extrapolate!! Hooray!

Not sure how helpful this will be, but TBA has the total number of matches played as 11162 right now (found here)

Thanks. I can adjust the average matches/event to 92.25... That shifts it down to 40.9% field combos played.


Also, I edited my previous post explaining how many possible field combos there are (thanks for the catch, it should've been (6*4*2)^2).

[Van.Augur]

Time to play devil's advocate:

If you want to be exact, you might want to take into account that the rough terrain, according the rules, is a random layout of the steel cubes. There are an extremely large number of rough terrain defenses that could theoretically exist (keep in mind they aren't symmetrical when you rotate them 180 degrees), making the real number of possible unique defense layouts impractically large...
but still calculable

[EricH]

Originally Posted by Van.Augur

Time to play devil's advocate:

If you want to be exact, you might want to take into account that the rough terrain, according the rules, is a random layout of the steel cubes. There are an extremely large number of rough terrain defenses that could theoretically exist (keep in mind they aren't symmetrical when you rotate them 180 degrees), making the real number of possible unique defense layouts impractically large...
but still calculable

Nice try, go read the field drawings. All the rough terrain units were built the same. "Random" was in fact in quotes in the Manual. You only get one rough terrain defense, not one per combination...

[Hitchhiker 42]

Originally Posted by Van.Augur

Time to play devil's advocate:

If you want to be exact, you might want to take into account that the rough terrain, according the rules, is a random layout of the steel cubes. There are an extremely large number of rough terrain defenses that could theoretically exist (keep in mind they aren't symmetrical when you rotate them 180 degrees), making the real number of possible unique defense layouts impractically large...
but still calculable

Assuming, this, which it isn't (as per above post), you'd be completely limited by the number of built rough terrains.

[logank013]

Just to clarify the number of combinations possible, it was discussed in an earlier thread here

They seemed to agree on 18,432 possible combinations as well.

[Hitchhiker 42]

At this point, seeing the amount of times the following combination is played, this is probably not a good estimate.

Everyone always picks:

• sally port
• cheval
• ramparts
• rock wall

This seems to be most common, and because the excel file assumes each combo is equally likely, it zooms ahead with how many fields have been played.