Ohhh.. though you can see right information at eu4wiki, you perfectly failed to know exact information.
Cavalry has 0.00 fire bonus at mil tech 1-10.
Cavalry has 1.00 shock bonus at mil tech 2-7, 2.00 at 8-16.
Infantry has 0.25 fire at 1-6, 0.35 at 7, 0.60 at 8-13.
Infantry has 0.50 shock at 2-4, 0.65 at 5, 0.95 at 6-10.
So, at 2-7, cavalry has 0.00/1.00.
ar 8-10, cavalry as 0.00/2.00
At 2-4, infantry has 0.25/0.50, at 5, infantry has 0.25/0.65, at 6, infantry has 0.25/0.95, at 7, infantry has 0.35/0.95, at 8-10, infantry has 0.60/0.95.
Western tech cavalry has 3 pips at 1-9, 8 pips at 10-13.
Wedtern tech infantry has 2 pips at 1-4, 3 pips at 5-8, 5 pips at 9-11.
So, tell me. Exact what 'sum of modifiers' did you see? Do you earn benefit from 0.05 more shock bonus for cavalry before 8? Can't you see 0.25-0.60 fire bonus for infantry? Can't you see that infantry has same pips at 5-8 and 2 more pips at 9? Don't you know that cavalry is 2.5 time expensive than infantry??????????
PLEASE, don't say anything if you know nothing and don't have will to find exact information.
You seem confused about how the modifiers work together. You said:
If we play Western European nations, cavalry has no meaning at 5-9 level, especially at 6, 7 level.
At level 5, assuming even terrain/general bonuses, infantry does an average of 4.5*.25*B (where B is the base damage per die roll value) damage in the fire phase, and 5.5*.65*B in shock.
Cavalry will do no damage in the fire phase, and average 5.5*1*B in shock.
Total damage 4.7*B for infantry, 5.5*B for cavalry, cavalry does ~17% more damage.
At level 8, it becomes (4.5*.6*B+5.5*..95*B)=7.925*B for infantry, and (0+5.5*2*B)=11*B for cavalry, cavalry does ~39% more damage.
Note that the percentages change significantly depending on generals. In the extreme case (a 6/0 general vs. a 0/6) you have the following:
fire advantage, shock disadvantage:
level 5, infantry averages (10.5*.25*B+1*.65*B)=3.275*B, cavalry averages (0+1*1*B)=1*B, with infantry doing ~228% more damage
level 8, infantry averages (10.5*.6*B+1*.95*B)=7.13*B, cavalry averages (0+1*2*B)=2*B, with infantry doing ~257% more damage
shock advantage, fire disadvantage:
level 5, infantry averages (.6*.25*B+11.5*.65*B)=7.625*B, cavalry averages (0+11.5*1*B)=11.5*B, with cavalry doing ~50% more damage
level 8, infantry averages (.6*.25*B+11.5*.95*B)=11.075*B, cavalry averages (0+11.5*2*B)=23*B, with cavalry doing ~107% more damage
But wait! Notice that in this fight with very lopsided generals, the side with the shock advantage is doing 50% to 100% more damage with its infantry than the infantry of the side with the fire advantage. And the cavalry of the shock advantaged side is doing 225% to 250% more damage than the infantry of the fire advantaged side in both cases!
So that means that under conditions that lend themselves to winning battles against even numbers of troops at these tech levels (i.e., not at a shock disadvantage), cavalry can do significantly more damage than infantry. And if we look back at the case of being even in leadership, we see that an army with 25% cavalry will do ~4% more damage overall at level 5 (compared to an all-infantry army) and ~10% more damage overall at level 8. That means that (given equal luck with the dice) an army with cavalry will tend to defeat an army without cavalry at these tech levels.
It's true that techs 6-7 are particularly painful for cavalry, but saying cavalry has no meaning at levels 5-9 is patently false. Outside of the level 6-7 dead zone, cavalry can still make the difference between winning and losing a battle.
Edit - forgot to add in the effects of shock pips in a couple places. Funnily, fixing the numbers makes things look even better for the cavalry.