My Lionhead Rabbit Is Making Strange Noises

Hattrick - The "Random" in ' Allocation of Shares

the hot topic " random," a guarantee of inflamed debates in the various threads that are permanently open about it in the forums.

How will those who have seen the last column on the right with past articles, the topic I have already devoted a few posts

http://acandio.blogspot.com/2010/04/hattrick-nuovo-motore- e-random.html
http://acandio.blogspot.com/2010/04/hattrick-nuovo-motore-e-random-parte-2.html
I realize quite technical and complex and

http://acandio.blogspot.com/2010/08/hattrick-tattica-strategia-random.html

Now I draw inspiration from an exchange of ideas with his friend to put down some account Laiho looking di essere il meno tecnico e complesso possibile. Restringo l'analisi al solo confronto tra i centrocampi e all'assegnazione delle azioni.
Vediamo cosa ne vien fuori.

****

Il confronto che spesso vien fatto è tra "Vecchio" motore, antecedente a gennaio 2010, e "Nuovo" motore, seguente a tale data. Si tratta di una distinzione impropria.
Il motore infatti è sempre quello: si basa su un'estrazione aleatoria, solo che è stato modificato il loro numero (da 10 a 15 secondo gli studi effettuati) e le conseguenze dell'estrazione stessa (in 10 casi su 15). Quindi cambio la dicitura da "Vecchio" e "Nuovo" motore, in "PRE" e "POST" modifiche. It seems more consistent with reality.

Now, the point is, these changes have affected sull'aleatorietà (random) assignment of shares?
Let's do the math that will explain step by step.




1) PRE Changes


start from the base, a value for the DC and one for Team 1 Team 2, suppose that the first and the second is worth 9 8. Possession will be of 56.25% for the first team and the likelihood of the shares will be 58.74% for the same team (I given the formulas used, where P3 and Q3 are the cells of the values \u200b\u200bof the two CC)

Before these changes were generated 10 actions. Each action was assigned to Team 1 or Team 2, based on probabilities calculated with the formula in the example is P3 ^ 3 / (P3 Q3 ^ ^ 3 + 3)
So, given the value of cell "Probability the action is assigned to Team 1, "which in my spreadsheet is in cell P10, I can repeat the process for 10 shares in that if the random value generated by Excel is less than the value in P10 then the action is assigned to the Team 1, if it is greater, is assigned to Team 2. The formula is IF (RAND () <$P;1;2)

Here:

see that various actions are assigned to teams.
A total of 7 to 1 and 3 teams for the team 2. The report, "Action Team 1 / 2 Action Team" is 7 / 3 = 2.33 that is 233%

course, the experiment can be repeated at will, and you find the sheet attached at the end I repeated for 1000 simulated games.

After that step is to count how many times has a number of actions for each team

then I'll have 1000 games, in this simulation, 26.6% of matches with 6 shares team 1 (and therefore 4 for the team 2), 21.4% 5 games with the action team 1 (and then the team with 5 to 2), etc. ...
If you consider the distribution of the actions I see that I

• no case of "0 shares on Team 1 and Team 2 to 10, with the corresponding value of" Action Team 1 / 2 Action Team "of 0 / 10 = 0.0% 1 in 1000
• matches "an action for Team 1 and Team 2 to 9, with the corresponding value of" actions of a Team / Action Team 2 "1 / 9 = 11.1%
• 11 cases in 1000 lots of "action for Team 2 to Team 1 and 8 2", with the corresponding value of "actions of a Team / Action Team 2" equal to 2 / 8 = 25.0%
• 53 cases in 1000 lots of "action at 3 Team 1 and Team 7 to 2, with the corresponding value of "actions of a Team / Action Team 2" of 3 / 7 = 42.9%

etc. All this can be seen in this table (# DIV / 0! refers to the case of the 10 actions team 1 and team 2 to 0 and 10 / 0 gives that error):

2) POST Changes

With the changes were introduced in early 2010 Shares " exclusive ".
In a nutshell, the first 10 shares were extracted and "or was it mine or was yours"
15 hours they are extracted, with 5 as the first "or is it me or is yours" (Shares "Municipalities"), 5 "or is my or none "and 5" or is yours or anyone "(Shares" Exclusive ")
So for the actions

• COMMON formula remains IF (RAND () <$U;1;2), ie either team 1 or team 2
• EXCLUSIVE formula becomes SE (RAND () <$U;1;0) for those only for the team and a IF (RAND () <$U;0;2) for those only for the team 2

The paper is easily modified as follows:

Solite 1000 games and the usual simulated collection of data which gives the following table

So far so simple, but now comes a point: how many shares has the team does not tell us how much one has Team 2. Before it was simple: the team had a 7? then the two had three. Now if a team has 7 team 2, it could have any number from 0 to 8.
So the simple table view with only those above 11 cases of values \u200b\u200b"Team1 Actions / Action Team2" becomes much more complex: the values \u200b\u200bare now 57 !

Here is the scoreboard

Now: how to compare them with previous values, Pre changes?

proceeds with a comparison to clarify the matter.
It 's like if we were analyzing the heights of a group of people.
We used a simple thing like:

we now find ourselves with a table of this type

It 'clear that a plot histograms or frequency curve would say very little because of the dispersion of the values \u200b\u200bin the second.

I might be rusty in statistics, the rest are past several years, but the only thing that comes to mind to make a comparison between the two cases is a descriptive statistical analysis: the distribution function. Essentially we look at "How many cases where there is already a given phenomenon", ie not "How many have a certain height," but "How many are under a certain height." The previous tables become

and in the second case

now a comparison is possible (of course the first table will proceed "step"), but we'll have an idea:

see that the curves are the same road (due to the fact that the values \u200b\u200bin the second table I have obtained "spreading" of those values \u200b\u200bin the first neighbors), the red curve of the first steps to carry out data definition, but essentially there are variations. The blue curve is just the red curve, more detailed, but the same phenomenon.

If, however, 77 people were in the more detailed table a different distribution and they were all quite high (eg. only 40 out of 77 less than 180cm), then in that case we have two very different curves:

Now, armed with this knowledge, we return to consider our distributions pre and post changes, you see in the data sheet "Compare" Excel file attachment. Similar to what we just saw above we consider the cases of "% of Shares Team1 / Team2" not exceeding a certain value and then we get curves of this type

Or even better, considering the values \u200b\u200bin ' X axis time scale as




curves, as seen above, describe exactly the same phenomenon.

Curve "POST Changes" or "New " engine does is describe in more detail than before. The noticeable differences in terms of "Change in% of the allocation of Shares to Team 1 from those allocated to Team 2" are just nell'addolcimento of the curve in its approach to the shape of the distribution function of a standard Gaussian


Reduction of "random" then? The answer is, "depends on what you mean by random.
If "random" we mean a "statistically noticeable removal from an assignment equitable actions (meaning that fair on the Gaussian) " then the answer can only be positive, in terms seen above, due to softening of the curve.

are Gaussian curve in order to explain this concept better :

It 'obvious that the blue curve, the POST changes, following more closely the Gaussian creates situations in reality less aberrant than before. For example, take the value in the X axis of 150 , ie 150% share of the team 1 vs. team 2 (the team has a one and a half times the shares allocated to the second team, changes in the PRE was the case "6" to a team and "4" to the team 2). The distribution
"fair" in the Gaussian is 500 games, the red curve was "636" matches, while the blue one becomes "578" lots, closer to fair value.
Without passing value for value is evident that the blue curve is generally closer to the green and then achieve an overall lower number of aberrant cases to the equator.

HERE
file

http://sites.google.com/site/andreactools/home/AZIONIVECCHIOENUOVO.xlsx?attredirects=0&d=1




****

Since the mail I am receiving add a final note: there is no reduction of the situations "extreme", but a more equitable distribution "in the middle and
example
the team has a DC that is 9.5
the team has the second DC is 8
probability of action for the team 1 is 62.61% of shares
chance for the team 2 is 37.39%
an equitable distribution would be to assign the 62.61% / 37.39% = 167.46% of shares on a team than the team version 2

PRE changes can assign
4 to 6 on the first and second
7 = 150.00% in the first and the second 3 = 233.33%
can not be closer to the ideal 167.46%

version
POST changes, however, can assign the first and 5 to 8
5 seconds = 160.00% in the first and the second 3 = 166.67
7% in the first and the second 4 = all
175.00% 167.46% values \u200b\u200bcloser to the ideal
In this is the most equitable




from a point Numerically

• PRE changes: if the actions of a team are X then those are two of the team (10-X)
• POST changes: if the actions of a team are X then those Team 2 is a number ranging from 0 and Min (10, 15-X ) , with the constraint that the sum is at least 5 (the joint actions which have to be assigned)
  

This flexibility of action for the team 2, you get closer to the fair value of the allotment of shares which is given by " probability of action for the team a" / "likelihood of action for the team 2"

formulas for calculate this function are well known and, pointing with CC1 and CC2 values \u200b\u200bof the two midfield
cc1 ^ 3 / (cc1 cc2 ^ ^ 3 + 3) / cc2 ^ 3 / (cc1 cc2 ^ ^ 3 + 3) which simplifies
in

cc1 ^ 3 / cc2 ^ 3

this is the fair value of the allotment of shares

is a continuous line ... more easy to approach when the actions of the team 2 may vary between 0 and 15-X (the curve best 'sweet sight above) than when they blocked a 10-X (and read "step").
Or, put another way, I was only in the PRE changes values \u200b\u200bby 11 (0.00% 11.11% 25.00% 42.86% 66.67% 100.00% 150.00% 233, 33% 400.00% 900.00% # DIV / 0!) to approximate a continuous curve, while changes in the POST I 57 well, so it is much easier to have a value close to the fair.

PS. take a look at ' CONTENTS of the blog, there are several items that may be of interest.




Andreace (team in Hattrick ID 1730726)

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