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	Rugged defense Information

Interpretation of the score formula

We leave apart the bonus part which is just bonus or malus points that are given to favour or discourage specific playing behaviours or types of matches.

There are two interpretations.

1. You can see size(i) as the intrinsic scenario point value, and outcome(i) as the percentage (from 100% to 0%) of those points you will receive according to the outcome of your match. Then win pct is the percentage of the maximum points you could have received, had you achieved an OV on all your matches.

   100% means you are an excellent player and 50% an average player.

   The score function then applies this win pct to the sum of points of all scenario you played.

2. size(i) ranges around 1 for all different scens, and size(i)=1 for a scenario i representing the average size among all scenarios we have in the database.

   See outcome(i)=(100,83,67,50,33,17,0) not as a percentage but only as a coefficient set representing the levels of victory by a numerical value. outcome(i)=(6,5,4,3,2,1,0) can do just as well, or even outcome(i)=(3,2,1,0,-1,-2,-3). Only we chosed the set to be symmetric as are the levels of victory.

   win pct is then just a weighted average of the different outcomes you achived on your matches. It's value is like a cursor indicator summarizing your average outcome somewhere between OV and OD. Also, being weighted by size(i), win pct gives more weight to the outcome of a more complex scenario : have you played a size 2 scenario and achieved an OV (100 x 2 ) ? this is counted the same as if you had achieved two OV on a size 1 scenario ( 100 x 1 + 100 x 1 ).

   Seen like this, win pct values a risk component associated with a more complex scenario. If you win, you win more in one time but if you loose you loose more in one time : an OD on a size 3 scenario is counted the same as 3 successive OD on a size 1 scenario.

   Suppose you play three times the same scenario with the same opponent, maybe if you do bad the first time (surprise effect), you do better the second, and maybe even better the third time, so it is unlikely you would have received 3 successive OD. Well if you play a complex scenario, think that the outcome will be counted as if you repeated this same outcome on a less complex scenario. And symmetrically. This is what is meant by risk component.

   The right part of the formula (voir Definition) is just like the total number of matches you have played, but weighted by the scenario size just as win pct.

   Again this is as if you had played this number of times the average size scenario. But this time there is no outcome involved, it is enough you played it. So this is seen as the risk free component of the formula : this part gives points whatever.

   For the interpretation, we see that the risk component of the score formula is much more valued (power 2) than the risk free component (power 1). Play at your own risks !