References and ranting
What you seem to be describing is a cavalry army Vs an infantry army which ain’t going to happen if it’s all in W Europe. Generally the rise of professionalism gives similar composition of armies in similar geography from say 1500.
If it is Horse vs Foot then the winner is the guy with the biggest granaries – normally the town.
A couple of corrections on some factual inaccuracies.
Canister (and I see no reason why any bagged grape would be different) has an effective range from 250m – about 600 for any battlefield artillery. Solid shot is up to 1200. The 250 is for a 3pdr. Shrapnel is about the same as solid and I think in all cases these numbers refer to point of first ricochet.
Reference
http://www.thepirateking.com/historical/cannon_smoothbores_early.htm
http://napoleonistyka.atspace.com/artillery_tactics.htm#_ratio_range_accuracy_artillery
http://www.napoleonguide.com/artillery_ranges.htm
http://www.napoleonguide.com/weapacc.htm
A smoothbore musket has a 50% hit rate at a battalion sized target at 50 yards and apparently falls off at 3% per m after that (12% if its windy). That’s against foot again would probably be more effective vs Horse as the tendency is to fire high, bigger target anyway. See the reference.
The reference for the battalion test is originally in Frederick’s instructions for major generals of infantry I think, he certainly ordered the tests, see also Nostworthy series on battlefield tactics or Paddy Griffiths.
The artillery argument though only really starts to apply on the battlefield regularly from around 1700 and once it does Horse is significantly more vulnerable that Foot. You can see it further off it’s taller so ricochet is more effective and horses lack patriotism and will not close up but tend to get disordered when dismembered.
Pikemen are not immobile – see the Swiss charging various Burgundian and French armies, English in later 100 years war, swedes like lunatics across everywhere and Spanish having to be held in place by repeated cavalry charges at Rocroi.
They are only immobile if constantly under attack by good Horse or ordered to hold in place.
The jinete quote is very selective. Jinetes used javelins basically which means they have to get to within maybe 40 yards. Not firing by Foot means that the Jinete is going to die when he gets to effective musket range range, firing at a distance during the approach means the foot is unloaded for 30 secs to a minute and subject to a shower of javelins and possible panic.
Panic is the main thing. There was an 18C Spanish general – a very elderly man who would demonstrate to his troops that he alone could hold off a horseman with nothing more than a walking cane.
Trying to make Horse even more effective is going to be really hard but the easy way is to have Horse trained in the way Frederick’s were which massively increases capability vs other Horse.
The main problem with the premise that in the 1500 – 1700 period for sure armies rarely had less than 30% Horse and sometimes 70% so how can you make it more dominant?
It’s going to be hard for four reasons. Firstly horses lack patriotism, no fodder=dead horse. Too much water=dead horse, too little water ….. you get the drift. Secondly cavalry can’t assault breaches. Thirdly horses eat more weight per day than men. Fourthly they are not as mobile operationally. Early period you may be able to argue but trained foot will easily outmarch cavalry over a period of weeks in any sort of terrain and can operate in terrain Horse cannot.
The real effectiveness of Jinete (and Hussars and Bashi Bazouks and Rajputs and Cossacks) is if you have no counter. That happened quite a lot and bluntly is decisive. But it’s nothing to do with what happens on the Battlefield and the counter is Mounted Xbows, Hussars, Bosniaks, Chasseurs a cheval and paying them off until you can hire them to work for you.