Song of Blades & Heroes: Math & Statistical Calculation

Hello,
this is not an usual post about 28mm 3D models/miniatures..
I started to play Song of Blades & Heroes, a very nice skirmish game, that you can play with any miniatures you have.
I've done for myself some tables with statistical calculation regarding SBH rules, that maybe are useful for someone else.

Below a table that show the probability to obtains successful rolls or turnover on activation tests, depending by Q+ score and number of dice.
Number in red are TURNOVER.



In the table above, in the bottom part is showed what change with the "Hero" special rule.
Is interesting to see, that the performance of a model with "Hero" is very similar (and often better, if you consider the importance of avoiding turnover) to the performance of a model with a Q+ better of 1 point.  (example Q+ 4 and Hero is similar to Q+ 3).

Note:
That consideration leads me to found a curiosity..
if you build by yourself the stats of your models using the formula ((Cx5 + "Special Rules")x(7-Q))/2
adding the Hero special rules and lowering the Q+ by 1, often could be a deal because your performance on activation tests are not worse and you gain the other benefit of the "Hero" rule.
Example:
98point Q+ 3  C 5
Leader, Heavy Armored, Mounted
could be:
96 point Q+ 4  C 5
Leader, Hero, Heavy Armored, Mounted
now that we are at Q4+ we can add also Shooter: Short reaching 99 point...

is convenient to add the Hero rule (cost = 15 point) and lowering the Q+ by 1, when:
if Q = 2+ =>> (Cx5 + S) should be >= 60
if Q = 3+ =>> (Cx5 + S) should be >= 45
if Q = 4+ =>> (Cx5 + S) should be >= 30
if Q = 5+ =>> (Cx5 + S) should be > =15
you can obtain this results resolving this expression below:
(Cx5 + "Special Rules")x(7-Q) >= (Cx5 + "Special Rules" + 15)x(7-(Q-1))

After the rule "Assassin", the Hero rule is one of the rule that if used without any constrain, allowed me, to obtain the things more unbalanced...probably we are going to create some house rules.

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In the Table below, the probability to win over an opponent, to double his roll, or to triple his roll.
In the Total C value, C and all the bonus/malus are included.

If I will do other tables or consideration  I'll update this post.
Endar