Short question - long answer!
As far as I know, troops moving through enemy-controlled territory lose cohesion faster (the manual doesn't tell us how much faster...). Moreover, a stack which enters a totally (at least 94%) enemy-controlled region switches to "offensive" command-posture (unless the stack is cavalry/irregulars/support only; p. 61). Troops moving in "offensive" command posture also lose cohesion faster (again the manual is not clear on the extent of cohesion loss). Last but not least, troops that are out of supply and fail to fourage lose cohesion faster.
With lower cohesion, troops move more slowly.
Whether an enemy stack loses speed depends on:
1. The amount of rest. When the stack moves all the 15 days of the round, it loses a lot of cohesion. When it only moves 10 days and rests during the remaining 5 days, then the elements in the stack will recover cohesion during these 5 days! The speed of cohesion recovery depends on a number of factors (loyalty in a region, special abilities, national morale, etc.etc.). Note that if your troops have a movement-order, they can only rest during the last days of the turn - there is no option to "delay" the movement-order and thereby rest at the beginning of the turn.
2. The quality of the elements in the stack (in terms of their maximum cohesion value; see english manual p. 34). The speed of movement depends on the actual cohesion points of the elements in the stack compared to their maximum cohesion points. An element of grenadiers with 80 cohesion points out of 115 is at ca. 70%. Thus, it moves 15% slower (100-70=30; 30/2=15). If you take a rather poor element of line infantry (max. cohesion 80) instead, which has moved the same distance and therefore has lost the same amount of cohesion points as the grenadier-element (35 points), you will see that it moves even 22% slower: 45 out of 80 points is 56 %. 100-56= 44; 44/2=22.
For a stack, you have to consider the average values of all elements in the stack. So, to return to our example, a stack consisting only of the two elements mentioned above would have its speed reduced by ca. 15%. Basically this means that better troops (with high cohesion value) will lose less cohesion/speed (in % of their max. cohesion) than poorer troops. Here, grenadier-batallions (a "unit" of grenadier elements only) have an advantage over "normal" batallions (a "unit" of 4 elements of normal infantry and 1 element of grenadiers). Grenadier-Batallions are able to march for a longer period of time (several game turns) without losing too much cohesion (and thus becoming slower and less effective in battle). Also remember that max. cohesion is affected by e.g. national morale!
3. The speed coefficient of enemy troops. I noticed that Prussian infantry troops do not only fight better (they have a RoF of 3!), but also have a 115% speed-coefficient, whereas my austrian troops only have 100%, gnarl!!!

I guess this is the austrian "Gemütlichkeit"

.
PS: And you can hope for the enemy to do stupid things like entering difficult terrain when your're close to him - he will need some time to enter a region with difficult terrain while you quickly enter the "clear" region that the enemy is currently trying to leave.
Other tips: Optimize your speed!
4. Be sure that your forces are led by active commanders! Inactive commanders in command of a stack give a -35% penalty on movement speed! This really ruins your day! To prevent this, always take two commanders with you in case one of them fails his activation test. Remove the inacitve commander from the stack if he would otherwise take over command (due to his rank/seniority). Alternatively, take only one good (i.e. high strategic rating) commander with you.
PS: I noticed that the trick with two commanders doesnt work. The active general switches to inactive if you try that

. It seems you need to have quality, not numbers... poor Austrians!
5. Be careful with cavalry stacks and commanders. Form cavalry brigades, do not leave the commander and the cavalry as seperate units in a stack. The stack moves at the speed of the slowest unit in the stack, which is the commander (light infantry!). When you form a brigade, then the commander also moves at the speed of the cavalry. Also remember that artillery and supply wagons slow down your infantry in bad weather or when you don't move along roads. Pontoneers are only needed when crossing rivers without bridges - otherwise they may slow down a cavalry force!
6. Under-commanded forces (stacks lacking command points) move slower (5% per missing CP). Make sure that there are enough CP/commanders in the stack. But beware when it comes to cavalry-stacks: sometimes it is better to take e.g. a -10% movement penalty due to under-commandment, than to have more seperate commander-units (light infantry speed) in the stack. The decision depends on the terrain to be covered, as terrain affects light infantry and cavalry differently. You have to try it out from case to case.
7. Consider a forced-march. You can order a forced-march with any active commander. The chance of success depends on his strategic rating (ca. 50-70%). But be sure to catch the enemy, as a forced-march costs a lot of cohesion. So when the enemy escapes, you will be at a disadvantage due to your lowered cohesion (=speed).
8. You could create two
columns: one cavalry, the other infantry/artillery etc. Catch the enemy with your cavalry column and be sure that the infantry column is only one region away so it can march to the sound of the guns! Hope for your infantry force to arrive in time - otherwise your cavalry might be shot into pieces. Moreover, your cavalry stack needs some power so that it doesn't withdraw too quickly. This plan is rather difficult to carry out, and it needs at least two columns (i.e. 2 **-commanders). Without
columns /
armies, it is extremly difficult and unlikely to delay an opposing force by giving battle with a cavalry-advance-guard. The battle would have to last full 6 rounds in order to delay the enemy for only 1 day! Hardly any cavalry-force endures 6 rounds, let alone the costs!
9. Check the tool-tips of regions! Sometimes the map makes you believe that there is a road in a region, but the tool-tip says "no".
10. Use commanders with the corresponding abilities (e.g. "fast mover"). Also commanders giving more CP are useful for small cavalry forces. (You don't need to put more commanders (light infantry-speed!) into the stack in order to reduce the under-commandment penalty.) For longer marches, any abilities that enhance cohesion recovery (e.g. "admired commander") or max. cohesion (e.g. "brave"), or both (e.g. "charismatic") are good. It would be interesting to know whether small breaks during a longer march of several turns pay off in the end (in terms of time).
(
11. Oh, I'm sure you do, but do you target the enemy stack (Interception-Order)? When it moves thorugh your territory, the enemy stack should't be able to slip out of your sight easily, as you've got a detection value of 2 in each of your loyal/controlled regions.)
For all that was said above: keep the influence of the different factors in mind! E.g. a stack which is at 70% of its max. cohesion (on averge) would get a movement-penalty of 15%. This can easily be canceled out by a commander with "fast mover"-ability (speed enhanced by 15%!). Also, I don't know whether all the factors I've mentioned above are cumulative or how they interact with each other. E.g. there is a natural cap (50%) for movement penalties due to low cohesion, or (35%) due to under-commandment. Also, you need to keep in mind that a slight penalty/bonus of 10% might often not be enough to gain enough time to take effect in game terms (1 day).
Good Luck!
PS: Also remember that cohesion is an important factor in combat. An element with low cohesion is very likely to rout once it gets hit! When a lot of your elements rout, the other non-routed elements get more of the enemy's attention - which is really bad

. This becomes especially catastrophic when most of the enemy elements get to fire before your elements (range/initiative). If I'm correct, a low-cohesion cavalry force will not have much of an impact on an infantry force: all infantry elements will shoot prior to close-combat phase and thereby they will probably rout lots of low-cohesion cavalry elements. So only few cavalry elements will reach close combat in round 1. The cavalry will not deal many hits and is likely to withdraw rather quickly.
Remember: when you deal hits to an enemy element, it will lose cohesion! So a stack that has been severly damaged in battle moves very slowly and needs to rest.
[SIZE="1"]
If you feel tricky or simply crazy enough, you could try to encircle the enemy stack before forcing it to battle. An enemy stack cannot withdraw to a region where it has less than 6% control (p. 61). When the enemy penetrates your territory, it is likely that he will create a 1-region-wide "path of control" where he moves along. If you have sufficient troops at your disposal, you could try to move units in the enemy-controlled regions that are adjacent to the region where the battle is going to take place. Dragoons and Husars are good at this task, for they have a police-value of 2 and they're quick, so they will reach the region quickly and can police the region for several days. If the enemy's control was low enough (depending on the size of his force and the period of time the force spent in the region) and the number of your polive-force big enough, then you could manage to reduce the enemy's control to less than 6% before the battle takes place. But this is all very very hypothetical. I've never tried it out. With two columns it is a nice option, as the police-force and the attack-force still support each other in battle. I guess you need to be a clairvoyant in order to get it right though![/size]
