8 SNG set probabilities

[AleoMagus]

Wow. Check this out

http://www.aleomagus.freeservers.com/spreadsheet

the 'confidence comparison.xls' file

Regards
Brad S

[Irieguy]

Wow. I love it when I believe something for a long time and then find out that I'm flat wrong.

A normal distribution. Who woulda thunk it?

Irieguy

[w_raedy99]

It sounds like you are doing these things in Excel so I am not sure if Excel supports anything more precise than double-precision floating point.

If you were doing it in Java, you could use a solution called BigDecimal. Note: I am a Java programmer and if you could show me the calculations, I could very likely write a program to do it as well. Java even has packages that would allow you to produce the graphs as well.

There are other solutions too. Depending on how good of a programmer you are, you can always do bit manipulation to use two double-preicision floating point numbers to act as one or a similar idea.

Hopefully this will be helpful,
Will

[tallstack]

Hi Will,

Thanks for the info. I used Visual Basic for this, and then exported the won/lost and probability data into Excel for graphing. VB is the the only language that I know anything about, and I am definitely not a strong programmer. If you would like to see the code then just send me a PM and I will forward it to you. It is only about 100 lines of code so you would abe able to get it working in Java in no time I am sure.

It the end, it looks like the results for SNG sets higher than about 50 games smooth out to look normally distributed anyways. So there may not be any need to go higher.

If you know of a variable type with a higher range in VB, then please let me know and I will change the code. Basically, it would need the capacity to store a number about 10^2500 to get to 1000 games.

Dave S

[eastbay]

[ QUOTE ]
Wow. Check this out

http://www.aleomagus.freeservers.com/spreadsheet

the 'confidence comparison.xls' file

Regards
Brad S

[/ QUOTE ]

Absolutely beautiful work, Aleo. The result with the evidence should be recorded for all time in the FAQ.

eastbay

[tallstack]

Very nice!

The more I think about this, the more surprised I am that it fits so nicely after just 50 games. It seems to be about the only thing that does converge after 50 games [img]/images/graemlins/laugh.gif[/img]

Great work, Brad!

Dave S

[stupidsucker]

could someone explain the 'confidence comparison.xls' file to me? I understood the other file, but this one I didnt get.

[AleoMagus]

Any past calculations that some of us have done regarding confidence estimates (like my confidence calculator in the SNG spreadsheet) have all been based on Normal distribution assumptions.

This has generally been considered a good estimate, but the idea has been tossed around a few times that maybe SNG results do not obey a normal distribution. The discrete nature of SNG results (only a few distinct possible outcomes) seemed to indicate that in some ways it might not make sense and the actual distribution might be quite different.

Anyways, the combinatoric calculations here are not estimates at all, but are exact results based on summing all possible outcomes from a small sample of SNGs (like 8-50).

The comparison essentially shows us that while the Normal distribution is still an approximation, it is, in fact, a VERY good approximation. The two graphs look almost identical. They are so alike that I do not intend to do any further combinatoric calculations for larger SNG samples. The usual Normal distributuion calcualtions are much simpler and apparently give us virtually identical results. In a strict mathematical sense, they are not equivalent, but they are so close it is unimportant for our purposes.

This has been surprising to me. Call me a sceptic, but I just didn't expect it to match up nearly this well. This is a pleasing result however, as it takes a lot less work to do these kinds of calculations with the usual stats.

Just to illustrate:

a 1000 SNG sample has 4^1000 distinct outcomes (roughly speaking, that's a 1 followed by 600 zeroes). There are of course tricks to make this easier to compute, but it is still very calculation intensive. Using the normal distribution calcualtions is as easy for a 1000 SNG sample as it is for a 10 or 1000000 Sample.

Regards
Brad S