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Stat increases depend on the Learning of the tutor. You get penalties at <8, <6, <4, <2. You get bonuses at >11, >14, >17, >20.
Then, half the time the tutor increases the stat of his/her education, per point. The other half it increases randomly one stat of the ward, per point.
On average a Tutor will increase each ward 2 or 3 points if he/she has Learning Stat between 8 and 11. If a Tutor has Learning of at least 21 it increases on average 6 stat points each ward.
In the end you should pay attention to the Learning of the Tutor and his/her education.
Was wondering if you have any kind of idea on how much the difference between a tutored child and a normally educated child turn out. I can't really tell in my games yet if it has helped that much
By either having a ward, having focus on scholarship or focus on theology... then it is a matter of luck.
It helps if you have either of the focci as it turns the event a bit more frequent.