I have often heard it said that a boar steal is a decisive event in the game, as it not just represents a loss of around 300 food to one player, but also a gain of 300 food to another player. If the result of stealing a boar were 600 food, you'd think it would be a truly game-breaking event. However, I have seen in general that players often come back after a boar steal, and even sheep stealing is rarely fatal for the aggrieved party's chance in the game. The question then is, how much does laming really set you back? In this post, I'll look at boar and sheep stealing, and I come to the conclusion that neither of these are decisive, with stealing two sheep being worth a switch of 68 food, while a stolen boar is worth around 210 food or so, as long as the lamed player responds in the right way.
Right off the bat, what happens in the early game is players find their starting food and start collecting from them. Once they've run out of natural food sources, they turn to farms, which cost wood. Now suppose you lose a boar to your enemy: you now have to transition into farms earlier, but as long as your villagers aren't idle, you'll still be collecting resources, just at a lower rate. To evaluate how much in the way of potential resources you've lost, you need to find out how long it would have taken you to extract the resources from the missing animal, and then compare that the resources you extract from an earlier transition into farms. So, suppose an animal has food f, a gather rate r, a decay rate d and is worked on by n villagers. Then if it takes a time t to deplete the animal completely, we have:
nrt=f-dt
Or
t=f/(nr+d)
The villager-seconds spent between all the villagers is
nt=f/(r+d/n)
Now we have to figure out how quickly food from farming would have gathered in that time. The average gather rate must take into account moving around on the farm, so supposing a villager has a pathlength l, a capacity c and velocity v, then one round trip requires
c/r+l/v
seconds to complete. The average gather rate is then the food gathered divided by this time; the food gathered is simply c. So:
a=1/((1/r)+(l/cv))
The Genie Editor reveals that farmers gather at a rate of 0.53 food per second. Meanwhile, before wheelbarrow, the capacity is 10 and the velocity is 0.8 tiles per second. The pathlength is an experimentally determined quantity, but it's roughly equal to 9 tiles. Putting this together means roughly
a=0.33
So if your opponent steals your boar or sheep, then we can match this value against the farming rate. Sheep have a base gather rate of 0.33, so losing sheep isn't much of a setback. If you lose a boar however, their gather rate of 0.41 means you gather less resources. For a boar with 340 food depleted by 9 villagers with a decay rate of 0.40, this is worth 748 villager seconds or 307 food from the boar. Converting this into farm time, we gather 246 food, which is 61 less than your opponent. Since he has a third boar, the steal means he's gathered 122 more resources than you by the time the boars run out, presuming he hasn't has significant idle time.
However, all I have examined here is the gather rate due to farming. I haven't taken into account the cost of wood to make the farm, nor the time taken to build it. The farming gather rate taking into account the wood investment now needs the total villager seconds invested over the lifetime of the farm. If the farm has food f, requires wood w, the average wood gather rate is g and the time to seed a farm is y, then the villager seconds invested in a farm is:
f/r+(f/c)l/v+w/g+y
For an average gather rate
a'=1/((1/r)+(l/cv)+(w/gf)+(y/f))
Broadly speaking, losing a boar forces you into a drush build, as you lack the speed to mount an effective rush under most circumstances. What this means is you build farms as you would intend for a drush, but these run out earlier, in the feudal age, when you have double bit axe and horse collar, but maybe not wheelbarrow. Therefore, I'll base it off these 2 upgrades. The average wood gather rate is
g=1/((1/r)+(l/cv)
Which combining a base rate of 0.39 with double bit axe gives g=0.38. Seeding a farm requires 18 seconds and costs 60 wood, so putting in all this information gives:
a'=0.27
Returning to sheep and boars, if your opponent steal two sheep and successfully guides them back to his base, then 8 villagers on two sheep with gather rate 0.33 and decay rate 0.25 yields 554 villager seconds or 183 food. The equivalent investment in farms yields 149 food, for a difference of 34 food. Doubling that (since your loss is your opponent's gain) gives 68 food. For a boar steal, the adjusted farm rate gives 202 food, so that's a difference of 105, which when doubled becomes 210 food. All in all, a boar steal is a massive nuisance, but nowhere near as decisive as people often think. The only occasion to worry is when a Mongol steals your boar, because then they deplete a boar in 516 villager seconds, gathering 317 food. In this time, their lamed opponent can only gather 139 resources. Taking the difference, which is 178, and doubling it means a swing of 356 food. In this situation, the game can be effectively over before it's really begun.
On top of that, one of the best ways of mitigating against a boar steal is to send your villagers out to hunt deer, when they otherwise would be too busy gathering from the boar. On the face of it, this may seem to be window-dressing, but a surprisingly large number of players don't bother taking their deers, even when they're close. I would estimate that sending your villagers out and milling a patch of deers (when your opponent doesn't) can slash the resources lost in a boar steal by half. 100 resources or so isn't that bad. It's often said that players often play less well after successfully stealing a boar; I think it's that the economic edge gained isn't as large as they thought, so they tend to overestimate how far ahead they actually are. If the lamed player knows the right response, this can be fatal.
Finally, I would say the best response to laming is prevention. The current meta favours build orders with 4 sheep gathered slower, then bringing in the boars. This means the second boar often comes in around six or seven minutes into the game, which is a long window of opportunity for an enemy scout. Extracting more intensely from sheep and aiming to bring in boars after the second sheep can reduce the second boar's arrival to around four and a half minutes. Considering most laming takes place later than this, taking a forward boar first, and keeping the scout as a sentinel around the other boar can significantly improve your odds of not being lamed.
Right off the bat, what happens in the early game is players find their starting food and start collecting from them. Once they've run out of natural food sources, they turn to farms, which cost wood. Now suppose you lose a boar to your enemy: you now have to transition into farms earlier, but as long as your villagers aren't idle, you'll still be collecting resources, just at a lower rate. To evaluate how much in the way of potential resources you've lost, you need to find out how long it would have taken you to extract the resources from the missing animal, and then compare that the resources you extract from an earlier transition into farms. So, suppose an animal has food f, a gather rate r, a decay rate d and is worked on by n villagers. Then if it takes a time t to deplete the animal completely, we have:
nrt=f-dt
Or
t=f/(nr+d)
The villager-seconds spent between all the villagers is
nt=f/(r+d/n)
Now we have to figure out how quickly food from farming would have gathered in that time. The average gather rate must take into account moving around on the farm, so supposing a villager has a pathlength l, a capacity c and velocity v, then one round trip requires
c/r+l/v
seconds to complete. The average gather rate is then the food gathered divided by this time; the food gathered is simply c. So:
a=1/((1/r)+(l/cv))
The Genie Editor reveals that farmers gather at a rate of 0.53 food per second. Meanwhile, before wheelbarrow, the capacity is 10 and the velocity is 0.8 tiles per second. The pathlength is an experimentally determined quantity, but it's roughly equal to 9 tiles. Putting this together means roughly
a=0.33
So if your opponent steals your boar or sheep, then we can match this value against the farming rate. Sheep have a base gather rate of 0.33, so losing sheep isn't much of a setback. If you lose a boar however, their gather rate of 0.41 means you gather less resources. For a boar with 340 food depleted by 9 villagers with a decay rate of 0.40, this is worth 748 villager seconds or 307 food from the boar. Converting this into farm time, we gather 246 food, which is 61 less than your opponent. Since he has a third boar, the steal means he's gathered 122 more resources than you by the time the boars run out, presuming he hasn't has significant idle time.
However, all I have examined here is the gather rate due to farming. I haven't taken into account the cost of wood to make the farm, nor the time taken to build it. The farming gather rate taking into account the wood investment now needs the total villager seconds invested over the lifetime of the farm. If the farm has food f, requires wood w, the average wood gather rate is g and the time to seed a farm is y, then the villager seconds invested in a farm is:
f/r+(f/c)l/v+w/g+y
For an average gather rate
a'=1/((1/r)+(l/cv)+(w/gf)+(y/f))
Broadly speaking, losing a boar forces you into a drush build, as you lack the speed to mount an effective rush under most circumstances. What this means is you build farms as you would intend for a drush, but these run out earlier, in the feudal age, when you have double bit axe and horse collar, but maybe not wheelbarrow. Therefore, I'll base it off these 2 upgrades. The average wood gather rate is
g=1/((1/r)+(l/cv)
Which combining a base rate of 0.39 with double bit axe gives g=0.38. Seeding a farm requires 18 seconds and costs 60 wood, so putting in all this information gives:
a'=0.27
Returning to sheep and boars, if your opponent steal two sheep and successfully guides them back to his base, then 8 villagers on two sheep with gather rate 0.33 and decay rate 0.25 yields 554 villager seconds or 183 food. The equivalent investment in farms yields 149 food, for a difference of 34 food. Doubling that (since your loss is your opponent's gain) gives 68 food. For a boar steal, the adjusted farm rate gives 202 food, so that's a difference of 105, which when doubled becomes 210 food. All in all, a boar steal is a massive nuisance, but nowhere near as decisive as people often think. The only occasion to worry is when a Mongol steals your boar, because then they deplete a boar in 516 villager seconds, gathering 317 food. In this time, their lamed opponent can only gather 139 resources. Taking the difference, which is 178, and doubling it means a swing of 356 food. In this situation, the game can be effectively over before it's really begun.
On top of that, one of the best ways of mitigating against a boar steal is to send your villagers out to hunt deer, when they otherwise would be too busy gathering from the boar. On the face of it, this may seem to be window-dressing, but a surprisingly large number of players don't bother taking their deers, even when they're close. I would estimate that sending your villagers out and milling a patch of deers (when your opponent doesn't) can slash the resources lost in a boar steal by half. 100 resources or so isn't that bad. It's often said that players often play less well after successfully stealing a boar; I think it's that the economic edge gained isn't as large as they thought, so they tend to overestimate how far ahead they actually are. If the lamed player knows the right response, this can be fatal.
Finally, I would say the best response to laming is prevention. The current meta favours build orders with 4 sheep gathered slower, then bringing in the boars. This means the second boar often comes in around six or seven minutes into the game, which is a long window of opportunity for an enemy scout. Extracting more intensely from sheep and aiming to bring in boars after the second sheep can reduce the second boar's arrival to around four and a half minutes. Considering most laming takes place later than this, taking a forward boar first, and keeping the scout as a sentinel around the other boar can significantly improve your odds of not being lamed.