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Greninja Talonflame statistics


ZevKyogre

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Before reading this post, please review or learn from another site what permutations and combinations are, and you should know basic probability.

We have seen in Worlds that Talonflame's use has been limited to...Greninja decks. I have not seen them in any other matches, and I don't see any decklists that have Talonflame.

The new Talonflame from Steam Siege allows you to play the Stage 2, free-retreat, one-energy attacker down as your facedown active Pokemon - not on the bench, no use if it is picked up in Mulligan.

The opening hand has 7 cards, pulled from a 60 card deck: 60C7 = 386,206,920 different combinations. EXCEPT that some of those cards are duplicates obviously (2 BREAKS, 4 Frogadier, 4 Greninjas either as 1-3 or 2-2, energies, etc) and you have 4 Talonflame in the deck.

We don't care, believe it or not - it is still 386.2 million combinations possible. Cool!

How many combinations have at least 1 Talonflame, considering we have either 0, 1, 2, 3, or 4 Talonflame?

The answer is...not as simple as I originally posted. It actually depends on how many basics you have aside from Talonflame.

For 2 non-Talobasics (2 Froakies) - About 177 million give Mulligans. Another 54.7 million more give non-Talonflame starts. About 29 million give Talonflame + 1 other starter. 122 million give you one Talonflame, and the rest of the cards not playable. (This leads to an unfortunate situation where you could land your 2 Froakie in the prize cards, which you don't want.)

 

But ignoring Mulligans because you reshuffle your deck, you have 209 million combinations that I count for the stats.

About 1 in 4 - 26.2% chance of all 4 Talonflame being dead-weight in a deck.

 

BUT, if it works, you have a chance to set up Froakie, you have free-retreat, you have a chance to pick off a REALLY weak basic AND pick up any 2 cards you need (And then have them N'd next turn :o)

 

It is still better than having any other basic in the deck, where they might go out in play, and give you a dead hand with something cruddy like Regice, or Articuno, or worse - a free 2-prize hit off of Shaymin :(

 

(Can anyone with a better understanding of probability confirm that I didn't oversimplify by ignoring duplicates in the deck?)

 

(will post more stats as time goes on, and will make my excel sheets available)

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We ignore those because you redraw from 60 cards again.

But yes, Mulligan statistics need to be taken into account, because you don't want your opponent to be able to draw cards.

 

The Greninja/Talonflame decks typically run 6-8 "Basic" pokemon - they will include 2-3 Frogadier, and maybe 1 Jirachi (XY 67.)

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You're saying 60% of the time Talonflame won't be in your opening hand, but about 40% of 7-card hands aren't valid (not containing Talonflame or Froakie, assuming you run 4 and 3).  Then you've got about 66% chance of starting with Talonflame.

 

Formula:  1 - ( C(56,7) - C(56 - number of basics in deck, 7) ) / ( (C60,7) - C(56 - number of basics in deck, 7))

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You're saying 60% of the time Talonflame won't be in your opening hand, but about 40% of 7-card hands aren't valid (not containing Talonflame or Froakie, assuming you run 4 and 3).  Then you've got about 66% chance of starting with Talonflame.

 

Formula:  1 - ( C(56,7) - C(56 - number of basics in deck, 7) ) / ( (C60,7) - C(56 - number of basics in deck, 7))

 

No.

40% chance that you will get a valid opening hand without Talonflame. <<<---IS WHAT I INTENDED

(Though now I see, the statistics are a bit off, because that 60% chance is just that you will not get Talonflame - if you get Froakie without Talonflame, or if you mulligan completely, that's 40%.)

 

Again, we have to run the numbers and assume one of the 2-4 valid pokemon aside from Talonflame that can open will appear - that will show how good or bad Talonflame stats are.

 

 

Edit: The math behind this is difficult to put into Excel for confirmation.

I wish I could post the chart, but they won't let me :(

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i am not sure but i think graywh 's formula is correct and i dont think we should consider duplicates cause i think drawing 7 energy twice will still be considered as two possibilities.

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I DO HAVE MORE STATS NOW, thanks to Excel (and yes, everything sums up, I promise)

Assuming you run 4 Talonflame:

A 26% failure rate if you only have two non-Talonflame basics in the deck.
A 33.5% failure rate if you only have three non-Talonflame basics in the deck.
A 38.9% failure rate if you only have four non-Talonflame basics in the deck
A 42.95% failure rate if you have five non-Talonflame basics in the deck.

The Greninja deck that advanced to Masters Final has 3 Froakies, and no Jirachi / Regice / Aricuno / Seismitoad.
(My deck runs 2 Froakie, a Jirachi, and a Regice but that's a different story - no Talonflame.)

He runs a 47.5% chance that he will end up with Talonflame as his only legal starter.
He has a ~19% chance (a bit better than 1 in 6) to start with at least one Froakie on the bench to start, with Talonflame in the active position.

To mitigate the 50% chance of Talonflame + no Froakie (and to not look for Froakie, fearing N or a first-turn knockout,) he runs a thick amount of trainers including Dive Ball, Trainers' Mail, Sycamore, an "N" of his own, etc

If he only ran 2 Froakie (like I do, and I see why,) you run a 60% chance of seeing only Talonflame - and an unfortunate 4-5% chance to see all of your Greninja being deadweight as well unless you get a knockout, as both Froakie will be in the prizes.

If I may, I'm going to post a link to my Google Drive -  it is an Excel Spreadsheet.

(Well, I've made it public, but I can't find it myself on Google :()

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- and an unfortunate 4-5% chance to see all of your Greninja being deadweight as well unless you get a knockout, as both Froakie will be in the prizes.

That would be awful, but Talonflame's ability gives you the option to take a mulligan if you don't get a Froakie in your opening hand.

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So, just to let everyone know that if you are interested, the spreadsheet I used is now Public, on Google Sheets.

I don't think I'm legally allowed to post a link to it, so just look up "Talonflame Statistics - Public" or "Talonflame Spreadsheet" on your search engine, and it will be there.

There are 2 of them, unfortunately, because I'm not too bright. They both have the same numbers, just one actually HAS the formulas on all parts, whereas the other one does not.

 

 

The first sheet is just a concise spreadsheet of 4 Talonflame + up to 5 basics (which is what you will see in tourneys and competitive play.) The next sheets involve up to 10 basics, for statistical fun, and from 4 down to just 1 Talonflame (because someone suggested diminishing returns with too many Talonflame, why run 4 when you can run just 2?)

 

The math was actually simple, copy-pasting was time consuming. Kudos to graywh for noting the mulligan chances interfering with straight-simple calculations. It made the sum-check work out correctly, and allowed for adjusted statistics of success.

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So.. the purpose of this post is to show how bad talonflame is in a greninja deck? or not?

 

The purpose of statistics is to...present data analyzed. You draw your own conclusions.

 

But it shows how the chances change, going from 2-10 non-Talonflame basics, and why Cody ran the deck structure he did. It shows that YES, you can bank on it, but as Cody shows, it's not an end-all, be-all. If you have an all-or-nothing hope for Talonflame, the stats don't matter - you're running 4 Talonflame, but you need to balance - do we run 3 Froakie, can I add in Jirachi and still have the strategy work, etc.

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The purpose of statistics is to...present data analyzed. You draw your own conclusions.

 

But it shows how the chances change, going from 2-10 non-Talonflame basics, and why Cody ran the deck structure he did. It shows that YES, you can bank on it, but as Cody shows, it's not an end-all, be-all. If you have an all-or-nothing hope for Talonflame, the stats don't matter - you're running 4 Talonflame, but you need to balance - do we run 3 Froakie, can I add in Jirachi and still have the strategy work, etc.

 

Ahh ok I see what you are getting at, you are showing the chances of starting with talonflame in the opening hand that make it consistent, awesome :D

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