NTBB2014 Explained

[plasmoid]

Hi all,
back in january I posted the NTBB2014 rules (as well as the NTBB2014 Bretonnians).
They can (as always) be found here: http://www.plasmoids.dk/bbowl/NTBB.htm

However, I also wanted to post some thorough explanations about why NTBB2014 turned out like it did. Then Work got in the way. A lot.
But now summer is here, and I've finally finished my write up. You can read it here:
http://www.plasmoids.dk/bbowl/NTBB2014x.htm

Finally, if you just want the lovely reference sheets, you can grab it here:
Rules: http://www.plasmoids.dk/NTBB2014.pdf
Inducements: http://www.plasmoids.dk/Inducements%20NTBB2014.pdf

Enjoy
Martin

[dode74]

Hey Martin. You need to take another look at your confidence intervals for the Tournament Play data. Under 10k samples will not give you a CI95 range of +/-0.0052. The majority of those margins will be +/-1 minimum.

Also, did you only use means from Box? If so that's rather inconsistent.

[sann0638]

That's what I thought

[plasmoid]

Hi Dode,
I went with the formula for binomial distribution that you showed me.
It doesn't just factor in sample size, but also the deviation from the 50% mean.

And as stated up front, I know that these numbers do not entail that the sample used would match a global population. AFAIK rule of thumb is that you'd a 20K(?) sample for that.

Cheers
Martin

[plasmoid]

PS - and no, I didn't use Means from the box. I'm not that incompetent.
As stated I removed the mirror matches. At the top end there are a lot of those. Sadly.
(BTW, on the subject, it is a characteristic of the Swiss format to pull the stats towards 50%, as bad teams play against bad teams, and good teams against good teams. I could only remove the mirror matches, but the trend would surely suggest that the powerteams are even more powerful than the stats can show).

Cheers
Martin

[dode74]

I went with the formula for binomial distribution that you showed me.
It doesn't just factor in sample size, but also the deviation from the 50% mean.

I suspect something has gone wrong, then, because those margins are far, far too small.

PS - and no, I didn't use Means from the box. I'm not that incompetent.

I didn't say you were incompetent
You said on your website that you "went through the data in 100 point TV increments, writing down all performance means. If a mean was outside of the tier boundaries, then I checked the adjacent means also - and if several neighboring means were either too low or too high, then I calculated the statistical inaccuracy with a 95% confidence interval." To me this means that you just looked at the means, and only if the means were outside the tiers did you bother with the 95CI.

it is a characteristic of the Swiss format to pull the stats towards 50%, as bad teams play against bad teams, and good teams against good teams. I could only remove the mirror matches, but the trend would surely suggest that the powerteams are even more powerful than the stats can show

Not sure what the Swiss format has to do with Box, but I think you're going a bit to far to state what you are saying. You could weight the rounds of the swiss format to try to account for this if you wish, but without evidence that what you say is happening is actually happening I think you're working from intuition and assumption there.

[plasmoid]

Hi Dode74,

I suspect something has gone wrong, then, because those margins are far, far too small.

Well, my mathspeak is not good, so you'll have to pardon me, but I read on the site that it was easiest just to do the calculation step by step. What I did was:
(1 minus Mean) times Mean. (so, for Undead/NAF: (1-0.564) x 0.564 = 0,2459...
Divide that by the number of games played. (0,245904/9050 = 0.00002717)
Take the Square root of that. (0.005213..)
That's the CI, which should be Applied to "both sides" of the Mean. (0.5640 +/- 0.0052)
?

You said on your website that you "went through the data in 100 point TV increments, writing down all performance means. If a mean was outside of the tier boundaries, then I checked the adjacent means also - and if several neighboring means were either too low or too high, then I calculated the statistical inaccuracy with a 95% confidence interval." To me this means that you just looked at the means, and only if the means were outside the tiers did you bother with the 95CI.

I think I've fairly clearly posted under 2 headlines: NAF stats and Box stats.
The quote is from the Box stats bit.
And yes, I only went into the CI calculation if there was a string of Means outside of the tier-boundaries.
If the Means were inside, then I figured the CI could not put them completely outside.
Make sense?

Not sure what the Swiss format has to do with Box, but I think you're going a bit to far to state what you are saying.

You asked about the NAF data, which is where Swiss applies.
If you think I'm overstating it here, then you'll be happy to know that I didn't let it affect the data in any way.

Cheers
Martin

[dode74]

This might make it easier: http://www.surveysystem.com/sscalc.htm
Use the Find Confidence Interval bit and use a population size of a couple of million.

The quote is from the Box stats bit.
And yes, I only went into the CI calculation if there was a string of Means outside of the tier-boundaries.
If the Means were inside, then I figured the CI could not put them completely outside.
Make sense?

Thanks for clarifying. Might be worth putting that in the Box stats bit (which was the bit I was referencing, since I asked if you only used means from the box).

You asked about the NAF data, which is where Swiss applies.

No, I was asking about the box data. The NAF data is clearly displayed. Misunderstanding there, clearly

[VoodooMike]

Dode and plasmoid doing stats! But which javascript page app can we turn to authoritatively!?

http://www.youtube.com/watch?v=23SVHUPrUJ4#t=1m53s

It pocksaclips, full of pain!

[stick_with_poo_on_the_end]

Mm mm. Confidence Intervals!

[plasmoid]

Hi Dode,
does indeed look like a misunderstanding. You said:

Hey Martin. You need to take another look at your confidence intervals for the Tournament Play data. Under 10k samples will not give you a CI95 range of +/-0.0052. The majority of those margins will be +/-1 minimum.

Also, did you only use means from Box? If so that's rather inconsistent.

I took the second question as a continuation of the first. So - did I use Box-Means in the NAF data. Otherwize I couldn't tell what you meant by inconsistent(?)

But, to clarify:
For Tournament data, I used NAF data.
For TV-Matched online, I used Box data. (As stated). And worked with it as stated.
Make sense?

As for the CI calculation - you know this is not my home turf.
Back in 2013 when I asked for your help, you sent me the link you just referenced above, and then a link to a website. Do you remember which one, or can you find out? I'd like to read it Again to look for the mistake.

The site you linked to now seems (to me) to not only test the CI within the sample, but also calculate whether we can be sure that the sample matches the larger population. I'm not claiming that it does. In fact I explicitly state that I do not know.
What I'm after is just the CI-calculation for the sample I'm looking at.
AFAIK, that's what the other website showed.
...But I could be wrong here.
Looking at other sites it seems quite possible that I've managed to leave out a 1.96 multiplier. That would (almost) double the CI - which lines up with what you suggested. That would mean a lot of recalculating (sigh) and fewer teams requiring a change for NTBB - which would suit me fine.

Cheers
Martin

[dode74]

What I'm after is just the CI-calculation for the sample I'm looking at.

The CI tells you the likely range of the population mean based on the sample mean and SD. A sample itself does not have a CI outside the context of the population since the CI is the confidence that the population mean lies within the range given. The sample mean is just the mean.

Yes, you missed out the 1.96, which is a multiplier used to assess where the z-score for a 95CI comes in (if you wanted 99CI then you would use 2.58 - see this table: find half the required CI as a decimal in the table and the axes give you the multiplier); as it is currently your range is simply one SD either side of the mean. You also didn't factor the MoEs up to percentages on your table, which could be confusing. Instead of 0.0052 (for Undead) stating 0.52 would be easier to follow as it is in the same units as the rest of the table. You correctly added the (miscalculated) upscaled MoE to get the range, but the table needs to all be at the same units to make sense to the reader, imo.

[plasmoid]

Thanks. Have started reworking the data.

On a side note - if this calculation includes sample's relation to the total population, then what is an ANOVA(??) for?
Cheers
Martin

PS - in NAF stats and Box stats, Undead are still broken

[dode74]

Analysis of Variance (ANOVA) is for comparing multiple means to each other. This is a reasonable explanation: https://explorable.com/anova

It can be used to see if multiple races are comparable (i.e. have different means) with each other. As it is there is a standard already set (the tier) and you are only looking to see whether that standard is met, hence a 95CI for a race is reasonable.

[plasmoid]

Thanks