I'm sick today laying in bed and was thinking about a problem which came up in the new unit thread here. But I'm not feeling well and so am not thinking as clearly as I should...
I've seen Henry Cobb's formula for rating units and this is really nice work. But it is calibrated against existing ratings and so it doesn't extend so well to unconventional attributes like the proposed Cyclops unit which potentially adds 1 to friendly attack rolls.
It seems at the core the value of a unit is how well it contributes to win conditions. That is all. But win conditions seem to always involve survive and destroy and so the following attributes are always valued:
1. Destroys enemy units
2. Prevents friendly units from being destroyed
3. Survives itself
4. Contributes to other scenario objectives
Consider a simple scenario where each side gets the same number of AU and they fight until one side has no units left. The average unit on the winning side destroys one enemy unit. The average unit on the losing side destroys less than one enemy unit. So if an AU destroys one enemy AU before itself being destroyed you could say it was at least break even.
Consider some hypothetical units:
1. Destroys an enemy AU of the enemy's choosing on turn 1 but then simultaneously self destructs. This unit must be worth exactly 1 AU because then it reduces each force by 1 AU which is balanced. Note I carefully said the enemy gets to pick the unit it loses.
2. Same but a random enemy is removed. This is worth slightly more because it adds randomness to a carefully optimized enemy layout...it increases disorder.
3. Same but the player gets to pick which enemy AU is removed. This is worth a bit more still.
4. Now the unit self destructs as before but it eliminates the enemy unit on the last turn of the game, again the enemy choosing which is lost. This is clearly worth less than 1 AU because the eliminated unit was able to contribute during the entire game, when it on average was able to destroy close to 1 friendly AU.
5. The same as 1 but instead of self destructing the unit has D2 A0. The only way this could change W/L, however, is if it was the only unit left at the end, meaning two other units simultaneously wiped each other out. This is extremely rare (ramming attacks, perhaps). So it changes little. If it were D3 one infantry would need to overrun it to destroy it so that could result in a stalemate. If there were a time limit on the game then the D2 would have more value. This is an interesting case because it highlights that attack strength always has value but defense strength only has significant value toward victory chances with attack strength (or the ability to reach other goals like consuming time). Additionally while D2A0 may not affect the chances of winning, if its team does win, it will increase the VP balance. So it has some value.
6. A special unit which if it eliminates an AU within range is able to instead choose any AU on the board to destroy. This is obviously worth more. Assume it doesn't destroy more AUs than without the power but it is able to contribute more to victory by eliminating the most valuable AU given the present configuration. Note in reality this might increase it's chance to stay in range of targets but that's not what I'm focusing on here: instead I'm focusing on that choice of targets has value in addition to simply number of targets.
Case 1 is obviously worth 1 AU. A typical unit is worth less by virtue of destroying its enemy AU later than the beginning of turn 1, more by virtue of being able to survive to contribute to VP, more by increasing the disorder in the enemy configuration (it destroys a unit other than the one the enemy would choose to lose).
Cobb points out movement acts as an enhancement to attack and defence. For attack it allows the unit to destroy units more often and also to provide more choice over which are destroyed. On defence if helps the unit stay out of range.
I guess the ultimate test would be to have a computer version of the game. Take a balanced game, same units on each side, and replace a single heavy tank (for example) with something whose value should be tested. Now play 10000 games, alternating which side goes first, randomizing certain factors like total number if units, unit selection, terrain, and unit placement, doing each with each side moving first. If the side with the experimental feature win 49%-51% of the time, then that tested thing is worth approximately the same as the heavy tank it replaced. On the other hand if the game is rebalanced by replacing 2 heavy tanks the tested thing is worth that much. Since SJGames seems to be working on a computer version maybe they can do this sort of experiment.
Without the simulator we need to rely on simpler experiments like playing a few test games and seeing how many enemy AU the test feature eliminates. But my test cases above show how and when an AU is eliminated also affect value.
I've seen Henry Cobb's formula for rating units and this is really nice work. But it is calibrated against existing ratings and so it doesn't extend so well to unconventional attributes like the proposed Cyclops unit which potentially adds 1 to friendly attack rolls.
It seems at the core the value of a unit is how well it contributes to win conditions. That is all. But win conditions seem to always involve survive and destroy and so the following attributes are always valued:
1. Destroys enemy units
2. Prevents friendly units from being destroyed
3. Survives itself
4. Contributes to other scenario objectives
Consider a simple scenario where each side gets the same number of AU and they fight until one side has no units left. The average unit on the winning side destroys one enemy unit. The average unit on the losing side destroys less than one enemy unit. So if an AU destroys one enemy AU before itself being destroyed you could say it was at least break even.
Consider some hypothetical units:
1. Destroys an enemy AU of the enemy's choosing on turn 1 but then simultaneously self destructs. This unit must be worth exactly 1 AU because then it reduces each force by 1 AU which is balanced. Note I carefully said the enemy gets to pick the unit it loses.
2. Same but a random enemy is removed. This is worth slightly more because it adds randomness to a carefully optimized enemy layout...it increases disorder.
3. Same but the player gets to pick which enemy AU is removed. This is worth a bit more still.
4. Now the unit self destructs as before but it eliminates the enemy unit on the last turn of the game, again the enemy choosing which is lost. This is clearly worth less than 1 AU because the eliminated unit was able to contribute during the entire game, when it on average was able to destroy close to 1 friendly AU.
5. The same as 1 but instead of self destructing the unit has D2 A0. The only way this could change W/L, however, is if it was the only unit left at the end, meaning two other units simultaneously wiped each other out. This is extremely rare (ramming attacks, perhaps). So it changes little. If it were D3 one infantry would need to overrun it to destroy it so that could result in a stalemate. If there were a time limit on the game then the D2 would have more value. This is an interesting case because it highlights that attack strength always has value but defense strength only has significant value toward victory chances with attack strength (or the ability to reach other goals like consuming time). Additionally while D2A0 may not affect the chances of winning, if its team does win, it will increase the VP balance. So it has some value.
6. A special unit which if it eliminates an AU within range is able to instead choose any AU on the board to destroy. This is obviously worth more. Assume it doesn't destroy more AUs than without the power but it is able to contribute more to victory by eliminating the most valuable AU given the present configuration. Note in reality this might increase it's chance to stay in range of targets but that's not what I'm focusing on here: instead I'm focusing on that choice of targets has value in addition to simply number of targets.
Case 1 is obviously worth 1 AU. A typical unit is worth less by virtue of destroying its enemy AU later than the beginning of turn 1, more by virtue of being able to survive to contribute to VP, more by increasing the disorder in the enemy configuration (it destroys a unit other than the one the enemy would choose to lose).
Cobb points out movement acts as an enhancement to attack and defence. For attack it allows the unit to destroy units more often and also to provide more choice over which are destroyed. On defence if helps the unit stay out of range.
I guess the ultimate test would be to have a computer version of the game. Take a balanced game, same units on each side, and replace a single heavy tank (for example) with something whose value should be tested. Now play 10000 games, alternating which side goes first, randomizing certain factors like total number if units, unit selection, terrain, and unit placement, doing each with each side moving first. If the side with the experimental feature win 49%-51% of the time, then that tested thing is worth approximately the same as the heavy tank it replaced. On the other hand if the game is rebalanced by replacing 2 heavy tanks the tested thing is worth that much. Since SJGames seems to be working on a computer version maybe they can do this sort of experiment.
Without the simulator we need to rely on simpler experiments like playing a few test games and seeing how many enemy AU the test feature eliminates. But my test cases above show how and when an AU is eliminated also affect value.
Determining unit values
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