Mobility in 2× rulesets

Purpose
The purpose of this article is to explain what happens to game balance when the mobility of units is multiplied.

Background
Longturn rulesets use doubled movement rates.This improves the pace of the games. Doubled movement also helps when more players result in much larger maps. The speed at which Workers finish their tasks is also doubled, improving game pace. Under 1× movement, maps would feel too large and games would move too slowly.

As 2× movement starts becoming a new norm, its effects on game balance deserve to be studied.

If the movement rates of all units are doubled, is this fair and balanced? The short answer is "no."

The Power of Mobility
Mobility is a key characteristic of a unit's useful power. Slow units are less effective because of their shorter range. They can react to fewer incidents and have less opportunities. Thus, units with more mobility are more powerful.

If one doubles the movement rate of a unit, what really happens to its mobility? A unit with 1 move has a choice of 8 possible tiles. With 2 moves, it has a choice of 24 possible tiles. 24/8 = 3×. If this were a simple case of a unit on a chessboard, its power just tripled. If the size of the chessboard is larger and every other unit has its power tripled, that should be fine. But what happens in a real longturn Freeciv game?

Reached Area under different movement multipliers
In the table above, 2× movement gives Mounted and Motor units much more gain to reachable area than it gives to Foot units. Movement multipliers from roads and railroads increase this phenomenon much more than what is shown in the numbers above. Because road placement is situational, there is no way to quantify it.

Unfair Mobility Advantage gained under 2× rules
In the table above, a value of 0% is the baseline for no relative gain in "mobility power" under 2×. If there is a positive value, this means the transition to 2× movement has made these units more powerful relative to other units. When movement multipliers such as roads and railroads are in use, the "unfair advantage" is far greater than the numbers shown above. For example, in MP2 rules, the upper limit to the "unfair advantage" is +44% for Motor units on railroads.

Consequences to Game Balance
For years, people played 2× rulesets under a mistaken belief. Every unit got the same 2× multiplier, so most people thought game balance remained the same. However, some players noticed that Foot units were considerably less useful in 2× rules. The mathematics above quantify some of this, but it's far from the full story. Strategy games are a combination of mechanics, tactics, and timing that is impossible to quantify. The biggest weaknesses turn out to be qualitative differences that result from these complex strategic composites.

Qualitative differences are a little more subjective, but still describe objective phenomena. The following is a list of some of the qualitative differences that result from 2× movement.
 * 1× Foot units were multipurpose offense / defense. Lesser mobility was compensated by cost effectiveness, making them good value for many front line attacks. Increased defensive coverage compensated their lesser offensive mobility. They were useful for "front line cannon fodder" as cheaper first attackers used to weaken strong defenses. A choice to make a Foot unit gave pros and cons. You got more overall value=(Attack+Defense)/(Shields spent), defensive coverage, and opportunities for attrition-value exchanges. You were more effective in fixed theatres and border wars, with less vulnerability. You paid for this by being less effective when blitz, pure offense, or mobility were more important.
 * 2× Foot units lost relative mobility, and are more specialized for static defenses: border forts, choke points, and city defense. They have less value per shield spent. This are overpriced compared to 1×. Thus, players make less of them and have less static defense. Play style gets changed. More mobile offensive units are made and these units face less static defenses. Offensive units start being used for "pre-emptive aggressive defense" and in "reactive counterstrikes." Making more Foot units now forces players into a more passive defensive style of play which is "strategically predictable" to enemies. Brilliantly mixing Foot units into offensive campaigns is replaced by Foot units being the thoughtless no-brainer choice for static defenses..


 * 1× Mounted units felt historically accurate. Cheaper multipurpose Foot units were enhanced by the extra mobility and opportunism of Mounted units. Two separate Foot armies could exert influence on two different regions, while a Mounted division could react to a crisis or opportunity that developed in either region. On strongly defended tiles that killed the first attacker, a cheap Foot unit could hit first, then a Mounted unit came in for the kill. Foot units' ability to achieve superior attrition resulted in deep tactics of position, timing, and range. Mounted units perfectly fit their historic roles: mobility, opportunism, blitz, breach insurance, double coverage, rapid reinforcement, and pure offensive strength.
 * 2× Mounted units gain an edge comparable to what Mongols had in real history. Everyone is now a Mongol. Mounted/Foot ratios higher than 1.0 are more common. So are battles with mounted units charging all over killing each other, with few foot units in sight. Foot units passively wait in cities for Mounted units to pick the right time and conditions to come kill them.


 * 1× Motor units and 2× Motor units have a similar analysis to what was already said about Mounted units. The dynamic effect is even stronger.
 * 1× and 2× Air and Missile units have a similar analysis to all the above, with the effect even more emphatic.

Areas of adjustment to bring 2× games back into balance.

 * The largest discrepancy area was in Air and Missile units getting the greatest gains in Mobility Power Index.
 * A substantial discrepancy area is in Foot units' major loss of effectiveness relative to Motor and Mounted units. Foot units need enhancements to bring things back in balance.

Corrections
The net effect of introducing all these counters is a much more balanced game with respect to Air and Missile power. If these new elements overcorrect or did not correct enough, they can be tuned by micro-adjustments to cost, attack/defense strength, etc.
 * Air and Missile units
 * Missiles given 1.5× instead of 2× movement.
 * Anti-Aircraft Artillery introduced (counter)
 * Mobile SAM introduced (counter)
 * Armor II introduced (counter)
 * Escort Fighter introduced (counter)
 * Vigil Interception introduced

Surprisingly, after the above enhancements to Foot units, they're in many cases still less effective than in 1× rules. Nevertheless, they are definitely better than before these changes were made. To characterize how these changes still fail, one can notice a few things. 1) Most of them depend on specific commitments to achieve them (Wonders, techs, form of government.) 2) fixing the ridiculous imbalance of infinite rail speed had a strong side effect: Foot units which could formerly travel just as far as Mounted and Motor units, were altered to travel at ½ or ⅓ speed on rails. A "great equalizer" that came from railroads was removed, right around the time that 3 strong gunpowder Foot units would have a "Golden Age of Foot units." 3) In the case of Alpines, Marines, and Paratroopers, they cost as much or more than Mech.Inf. Finding useful roles for units that are slower, weaker, AND more expensive than Mech.Inf. isn't easy.
 * Foot units
 * Agoge of Sparta introduced. (Enhances movement, attack strength of phalanx/pikemen)
 * Upkeep can be changed to 1 GOLD after tech discovery.
 * Communists pay less for Riflemen (Cheaper)
 * Marines were buffed (Stronger)
 * Marines are more mobile (can travel in Helicopter)
 * JTIDS introduced (Enhances vet level, promotion odds)
 * Many Foot units get Special Unit Attacks
 * Train and Truck introduced.

Possible Further Corrections

 * Undo the removal of "The Great Equalizer" somehow. Make Foot units equal on rails to other unit types.
 * More options to make small increases to the range of Foot units.
 * Cheaper or more accessible options to increase the range of Foot units.
 * Alternative compensations: special bonuses or abilities for different Foot units.
 * Cheaper costs for Foot units, either by default or accessible through acquired bonuses.