Skill or Chance?

[MARCPELLETIER]

To calculate the probability, you just have to go here:

http://www.matforsk.no/ola/fisher.htm

you see four white boxes. In the two above, you write your winning-losing record. In the two below, you write the number of games divided by 2 (so that the sum of both squares make the total number of games you have played so far). You press compute, et voilà!!

[J-Pav]

[b:8ab4f29b4c]Marcus[/b:8ab4f29b4c]:

I've already argued on behalf of skill in 2005. I'm talking about 2006 only.

The formula I'd like to see would be a game theory formula which determines a game of chance (say, roulette), from a game of skill (say, poker). What results are required? Mathematically, is it .501 over x number of trials? What would be the standard deviation? Obviously, it has to be over a large number of trials, that's why I think 2006 is still too early to call.

If I argue that 2005 was a game of skill, and .530 (86-76) was an example of a skillful record, what proves that and over how many trials is necessary, give or take (+/-)? Once we answer this, then mathematically we should be able to start applying a basic formula to 2006. Where'd that [b:8ab4f29b4c]Ezampol[/b:8ab4f29b4c] guy go?

(From the I love me category, in 2005 I won (CHAMPS) in four consecutive autoleagues. I would love to know what the mathematical chances of this were, because I'm guessing it's a lot further right than six sigma).

That is, yesterday I knew it was [u:8ab4f29b4c]not[/u:8ab4f29b4c] luck. Today, I don't know if it is or it is not luck, but I can't explain why I don't know. Statistically, how do you tell the difference?

Maybe this route will be more fun than the philosophical one I started.

Where's [b:8ab4f29b4c]Ez[/b:8ab4f29b4c]?

[J-Pav]

[b:c5d20862ab]Marcus[/b:c5d20862ab]:

That formula has you at a 17% chance of chance in '06, and has Cummings at a 27% chance of chance.

What is this telling us?

[J-Pav]

This is my p value for chance in my entire 2005 season, if this thing is correct:

2-Tail : p-value = 0.000014102921916889161

[J-Pav]

And since this is a zero sum game, what about the guys who play sub .500 ball over many seasons? My 2005 season [i:3dfb8b36f1]reversed[/i:3dfb8b36f1] gives you the exact same figure, 0.00001. But as you approach .500, the p value moves to 1.00.

That is, a manager who plays .500 ball over x number of games has stats that equal pure chance. But obviously, that can't be a mathematical conclusion.

Something is wrong with the variables here...

[J-Pav]

AAAAAAAAAAAAAAHHHHHHHHHHHHHHHHRRRRRRRRRGGGGGGGGHHHHHHH.

[J-Pav]

All managers, all games = .500.

If we know the number of total games...

then we should be able to determine the point where a manager adds skill to a record (does the inverse hold true? negative skill?)

This will be some number above .500, but it must have to be within certain parameters to define it as no longer chance (and again, I'm guessing the inverse must have to hold true).

What is that number?
How many trials are necessary?
What does that p value have to equal to determine with x amount of probability that we are no longer talking about chance??

[cummings2]

J, I'm not a heavy duty math guy, for all I know what I'm about to write is kindergarten stuff for you Saber-heads.

However, here goes:

[color=blue:8e0ecb2541][i:8e0ecb2541]The formula I'd like to see would be a game theory formula which determines a game of chance (say, roulette), from a game of skill (say, poker). What results are required?[/i:8e0ecb2541][/color:8e0ecb2541]

Acording to J.A. Paulos:

[quote:8e0ecb2541]Conditional probability explains why Blackjack is the only casino game of chance in which it makes sense to keep track of past occurences. In roulette, what's occured previously has no effect on the probability of future spins of the wheel. The probability of red on the next spin as 18/38, the same as red on the next spin given that there have been five consecutive reds. Likewise with dice: The probability of rolling a 7 with a pair of dice is 1/6, the same as the conditional probability of rolling a seven that the three previous rolls have been 7s. Each trial is independent of the past.

A game of blackjack on the other hand, is sensitive to it's past. The probaility of drawing two aces in succession from a deck of cards is not (4/52 * 4/52) but rather (4/52 * 3/51), the latter factor being the conditional probability of choosing an ace given that the first card was an ace. Likewise, the conditional probability that that a card drawn from a deck will be a face card, given that only two of the thirty cards drawn so far have been face cards, is not 12/52 but a much higher 10/22. This fact- that (conditional) probabilities change according to the composition of the remaining portion of the deck in the basis for...[/quote:8e0ecb2541] (various counting strategies in blackjack)

Quoted from: John Allen Paulos, "Innumeracy"

Sorry if am repeating stuff you guys know about. I [i:8e0ecb2541]do not know[/i:8e0ecb2541] much about this, just pointing the quote since J's post above reminded me of this passage of the book.

Hope it helps...and if doesn't well...what can we do about it, eh? :wink:

[MARCPELLETIER]

[quote:13081e554f]
That formula has you at a 17% chance of chance in '06...

What is this telling us?
[/quote:13081e554f]

I am not sure what you refer too.

If you refer to my overall record,
then it is telling you nothing, because you include teams for which I had no control (the Beta-testing team)

For another time, I repeat: you cannot take all-teams records, because you include leagues that can't be compared (theme leagues, keeper leagues where sometimes you will intentionally play a losing season in order to help the building effort, beta-testing teams). That is why I don't like your first line of argument, where you say that you refer to overall records.

If you rather refer to my Tour record,
then it is telling you that the sample size is still too small, but it is looking towards demonstrating that my skills enable me to get better than chance.

[quote:13081e554f]I've already argued on behalf of skill in 2005. I'm talking about 2006 only.
[/quote:13081e554f]

As far as I can see, we have the same pricing system in 2006 than in 2005, if not in the details, at least in the overall structure. Same average price for both offense and defense, more or less 0.3M. Same bullpen vs SP set-ups.



[quote:13081e554f]
This is my p value for chance in my entire 2005 season, if this thing is correct:

2-Tail : p-value = 0.000014102921916889161[/quote:13081e554f]

This means that, for 2005, you were difinitively statistically significantly better than a .500 player.

[quote:13081e554f]And since this is a zero sum game, what about the guys who play sub .500 ball over many seasons? My 2005 season reversed gives you the exact same figure, 0.00001. But as you approach .500, the p value moves to 1.00.

That is, a manager who plays .500 ball over x number of games has stats that equal pure chance. But obviously, that can't be a mathematical conclusion.[/quote:13081e554f]

The test is a 2-tail test. This means that it calculates the probability of being different than .500 from both sides. In simple terms, your 2005 season reversed gives the same exact figure, because it is similarly distant from the .500 mark. As you approach .500, you get closer to the .500 mark, up to a moment where the p value gets equal to 1. That is, a manager who plays .500 over x number of game has stats that would be exactly the same as those expected from a random sampling of flipping a coin and getting head. A player like you who plays .530 over the course of 54 seasons has a distribution that cannot be obtained from such random sampling of coin flippings.

[quote:13081e554f]AAAAAAAAAAAAAAHHHHHHHHHHHHHHHHRRRRRRRRRGGGGGGGGHHHHHHH.[/quote:13081e554f]

You complicate your life way beyond reasonable questionnings. If you have a wife, or a child, it is time to take them in your arms and feel their love.

[quote:13081e554f]All managers, all games = .500.

If we know the number of total games...

then we should be able to determine the point where a manager adds skill to a record (does the inverse hold true? negative skill?)
[/quote:13081e554f]

Exact

[quote:13081e554f]
This will be some number above .500, but it must have to be within certain parameters to define it as no longer chance (and again, I'm guessing the inverse must have to hold true).

What is that number?
How many trials are necessary?
What does that p value have to equal to determine with x amount of probability that we are no longer talking about chance??[/quote:13081e554f]

First, we must take some probability criteria. In this experiment, I think that a value of p=0.05 is restrictive enough. That is, once we get results with a probability under 5% that such results would be obtained from a random sampling of coin flipping, then we can safely conclude that skills are in action.

The number (winning success) and the number of trials necessary are not independent from each other.

For one season, I have it that a record of 101-61 is a result that is likely to suggest skill (p value under 0.05).

For two seasons, I have the same probability for a 188-136 record (so basically two 94-68 records in a row).

For three seasons, 275-211 (.566) is a highly probable sign of skill.

If I maintain my Tour record (.544), I will need seven seasons before demonstrating statistically that there is skill under work.

That being said, 5% is quite restrictive. It is the number that devils of advocate usually choose (sometimes, they even choose 1%). In fact, as soon as your probability gets under 50%, it's a sign that there is something affecting your results other than flip coins. For a season, 89-73 is the mark that crosses under 50%---there lies that +/-8 wins of random distribution. A record of 172-152 after two seasons is the mark that crosses under 50% (so after two seasons, no more than +/- 5 wins of random distributions should be expected in the data).

[ANDREWLAITURI]

Cummings and lucky's posts got me to thinking (I know, I know, dangerous endeavor for me. :wink: ) that there is an easy way to define where the skill part comes into play over pure chance.

There is always the element of chance here. Why? Because we use dice.
The skill part of the game comes into play because we can skew the odds in our favor, ie. Choosing appropriate players, setting favorable L/Us, etc.

There is definately negative skills as well. In other words, if you make poor personnel choices and poor L/Us you have effectively skewed the odds against yourself and success. Oh you'll still win a few games here or there but you'll still lose much more than you'll win.

Placed with equal skill level players, the numbers will likewise tighten up much like if you're trying to win at poker or pool or any other game at which you and your opponents are equally skilled.

So to sum up, yes there is chance involved and chance will both win and lose you some games so as to effectively cancel itself out which leaves only skill. As in who skillfully skewed the odds in their favor better over the long haul of the season?

I think that made sense? First cup of coffee and all ya know. :roll: