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the only problem in your case was that you just compared the numbers and thought your forces were on par. a few thousand light infantry and pikes will not stop an equal number of heavy cav and inf. you'd need to outnumber them.
Are Spearmen+Infantry considered in same group?
Now that said pound for pound (1:1 ratio) pure heavy cavalry army will destroy just about any regular army, but it's a different story if you face it with numerical advantage and mix the heavy cavalry with an actual army (tactics highly favor pure or mostly pure armies, as are the holy orders). A retinue of heavy infantry like the Norse one could make a good counter for exemple.
That's not total war...
Now I'm having another problem, the Saxons attack me and have more archers and light cavalry than me, and although I have more heavy infantry, apparently the morale goes down very fast by a long phase of harassment.
I've got the DLC but barely ever use it, when I'm small I use extra money in mercenaries rather than retinue and when I have the money I'm too strong to need a retinue :)
You already suggested the right counter on your own: commanders with morale defense is what you need. Defense helps too but not so much. Especially if you face tribal Saxons they will route a couple days after melee phase begining.
Their only general use is filler for meeting a minimum number to siege quota or warding off a faction from firing.
If you have an ass-load of them, you can potentially break the enemies morale before the Melee phase (doesn't work well vs HC as they have several tactics that immediately shift the battle to melee phase), but if you don't, you're gonna have a bad day as they'll fold like wet tissue once the pikes/hi/hc/lc can bring to bear against them.
Pikes have massive defense but only average attack strength in the melee phase, while HC are one of the strongest melee phase units (only elpehants are higher iirc). So while they can take the brunt of the HC's damage, they need some else to handle the attacking or they'll get worn down eventually, like say Heavy Infantry who are a bit stronger attack-wide.
Now that said, if you have enough pikes and the enemy has a certain percentage of cav relative to their total troop composition, your commander (above 8 martial, 16+ for higher weight) can potentially choose the Stand Fast (Force Back also works) tactic which will utterly destroy them usually.
OH and never put a sub-8 martial in charge of your armies. getting bad tactics can utterly destroy you on fights you should've easily won.
Can I extend the harassment phase if I have much more light cavalry than the enemy? because although my enemy has 300 HC, I have almost 5000 LC, my problem is the HC, less than 100
They're pretty junk for everything else (they're sort of nice in Skirmish phase, not Archer good, but one of the better Skirmish phase units).
But if you're ping-ponging the enemies, sicne they immediately rout if their morale is too low, a large amount of LC will cause massive casualties, where as very little LC barely dints the enemy in Pursuit phase.
Unfortunately, there's no real way to stop the enemy from skipping Skirmish Phase if they have enough HC and a suitibly skilled Commander to roll one of the charge tactics consistently.
having the Longbow Volley tactic from a English or Welsh Commander can potentially break the enemy into pursuit phase, but you need a lot of archers for that, and it gets by-passed completely if a Charge is used since you only get 6 days of attacks before charge forces the phase shift which is less likely to break the morale before they can rip your guts out in melee phase.
As far as i can see, the only tactic that can shorten melee phase is Retreat and Ambush, which requires an Altaic Commander, flat and reasonably open terrain, and at least 20% horse archers (30% and Martial 10+ for extra weight), which forces the combat to switch to Skirimish phase and gives your LC, HA, and archers a pretty big boost in damage.
And are massively beefed up versions of the normal units.
the standard retinues that everyone gets are 50% stronger than non-retinue troops of the same type.
The cultural retinues are MUCH stronger than their regular type, though it varies from nation to nation. The Africans especially have a ludacrisly strong LI cultural retinue that is ALMOST as strong as heavy infantry but they're cheap and they get a ton of them for their cap-cost.
All of the cultural tactics are brokenly OP (even after nerfing the crap out of them, they're still the strongest tactics by far), but require you to structure your whole army around around and have the right culture of commander in charge.
I don't really like retinues though because they're too strong and the ai almost never uses them, which means you're basically cheating if you do build them heavily.
The way faction revolt chance considers only the size of their leige's forces, not their strength, means that a large enough LI retinue will make factions NEVER trigger.
This in turn renders the entire opinion system moot, meaning you can be as tyrannical as you like -
your vassals' factions will never revolt.
Of course this broken mechanic can occur with any retinue type, but LI retinues hit this tipping point much much sooner, with a much lower financial & technological cost.