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HATTRICK - Confusion and Withdraw: the Formulas



For general aspects of these issues let me refer you to an exhaustive article posted in _eNeRGy_ blog http://www.nrgjack.altervista.org/wordpress/2008/11/30/overconfidence-e-confusione, here I will cover only the mathematical formulas issues.




CONFUSION

GM-Mjoelnir posted in the global forum a table with the% of losses detected for the confusion:


Now, these values ​​are discrete, that is related to the integer. But confusion has the decimals, it can be seen from the fact that they are often cited in the match report: "the team went from passable level to the
passable level", because it has changed from 6.8 to 6.2 and decimals are not mentioned.
So it would be interesting to a formula that approximates the values ​​of confusion even for
decimals .

The formula that I calculated from the above data (keeping in mind that "
passable" is not 6.0 but 6.5, the average of all those mentioned in the report) is as follows:

CONFUSION LOSS % = 0.55 * (8.5-level)^2 + 3*(8.5-level)

the table is


The graph shows that this is a good approximation:


I add a note, following the
zorro33 comment: what shown above is used to calculate the % loss from confusion, while to see the overall effect on the ratings you shoud calculate, if I remember correctly, the weighted average between the number of minutes without confusion and those with confusion (applying the loss calculated above).

So, for example, if confusion has occurred at the 40th minute, at a "weak" level (loss of about 21%) and the final evaluation will be "
insuff very low " (5.125) then I set as "VALfinal" the final rating and "VALnoconf" the rating without confusion, I see that

VALfinal = VALnoconf *(minutes of conf/90) + VALnoconf*(1 -% loss by confusion) * (1 - minute of conf/90)

5.125 = VALnoconf*(40/90) + VALnoconf*0.79*(1 - 40/90)

gathering VALnoconf

VALnoconf = 5.125 / [(40/90) + 0.79*(1 - 40/90)]

VALnoconf = 5.125 / 0.883 = 5.801

that's insuff very high,
so with the confusion we lost two sublevels

the formula and identify the value without confusion (in the case of a single
confusion event) is

VALnoconf = VALfinal / [(min of conf/90) + (1 -% loss by confusion) * (1 - minute of conf/90)]




WITHDRAW

FIRST HYPOTHESIS

I took the average values ​​in the table posted in the link mentioned above:



if it happens at the 15th minute, I'll have backing off for 75 minutes, if I it happens at the 30th, I'll have for 60 minutes ... I looked at how many minutes of withdraw and I noticed that if I divide the number of minutes by the variation % I get almost a constant number


whose average value is 4.25
so we can assume that

% VARIATION by WITHDRAW = (90 - minute when happens) / 4.25

the variation will of course be positive
for the defense and negative for the attack.



GM-Homerjay
HYPOTHESIS

I only found out later (mea culpa) that in http://www.fantamondi.it/HTMS/index.php?page=realizzazione&lang=it GM-Homerjay said:

"We assume therefore that the loss in attack and defense are
fixed % factors and that the final ratings are weighted averages of those of every minute of the game. Estimating the minutes of the withdraw and by setting the factor of gain / loss on defense / attack at 20% we succeed in considering the withdraw in the ratings"

so a fixed
20% loss for attack and 20% gain for defense.
The formula is

% VARIATION by WITHDRAW = 20% * (90 - minute when happens) / 90

it is like putting "4.5" instead of 4.25 in the
above formula (and 4.5 = 90/20)

The table shows that the estimated values ​​are good


and that is the graph







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