In case you were curious (some numbers)
by slugthog · in ThinkTanks · 10/09/2003 (12:42 pm) · 45 replies
Everyone knows that lights dominate in nearly every TTanks game. For those who are interested I did some back of envelope calculations to find out just how much they dominate.
The only three parameters I had to work with were cross-sectional area, speed and rate of fire but these were adequate to generate some ball park numbers.
Cross-sectional area and speed can give a fair approximation of how easy it is to hit a target. Rate of fire gives a sense of the amount of damage done.
I don't have real figures for these so I used a Mk 1 eyeball approximating device then normalized each parameter. I tried to hedge all guesses against lights so that I wouldn't over estimate their dominance. Here my base numbers:
Heavy Medium Light
X-Area 3.00 2.00 1.00
Speed 2.00 5.00 7.00
Burst Rate 4.00 5.00 6.00
I used an impulse basis of 4, four time units fort, and calculated the number of shots fired from-to each platform. The two extremes give the clue. In the time it takes a light to close with a heavy the heavy fires 16. In the time it takes a heavy to close with a light the light fires 84 times.
Using a base probability to hit of 0.25 and adjusting for speed and area the expected number of hits from a light to a heavy is about 31.5 while expected hits from heavy to light is 0.57. With a bit more number mashing I generated a relative firepower table:
Relative Firepower:
H M L
H 1.000 15.625 55.125
M 0.064 1.000 3.528
L 0.018 0.283 1.000
So a light tank has about 55 times the firepower vs a heavy
slugthog
The only three parameters I had to work with were cross-sectional area, speed and rate of fire but these were adequate to generate some ball park numbers.
Cross-sectional area and speed can give a fair approximation of how easy it is to hit a target. Rate of fire gives a sense of the amount of damage done.
I don't have real figures for these so I used a Mk 1 eyeball approximating device then normalized each parameter. I tried to hedge all guesses against lights so that I wouldn't over estimate their dominance. Here my base numbers:
Heavy Medium Light
X-Area 3.00 2.00 1.00
Speed 2.00 5.00 7.00
Burst Rate 4.00 5.00 6.00
I used an impulse basis of 4, four time units fort, and calculated the number of shots fired from-to each platform. The two extremes give the clue. In the time it takes a light to close with a heavy the heavy fires 16. In the time it takes a heavy to close with a light the light fires 84 times.
Using a base probability to hit of 0.25 and adjusting for speed and area the expected number of hits from a light to a heavy is about 31.5 while expected hits from heavy to light is 0.57. With a bit more number mashing I generated a relative firepower table:
Relative Firepower:
H M L
H 1.000 15.625 55.125
M 0.064 1.000 3.528
L 0.018 0.283 1.000
So a light tank has about 55 times the firepower vs a heavy
slugthog
About the author
#2
10/09/2003 (1:00 pm)
You didn't take into account the ability of the tanks to dodge. Heavies have much tighter turning radiuses and can out turn a circling light. They can also dodge bullets more effectively.
#3
X-Area 3.00 2.00 1.00
Speed 2.00 5.00 7.00
Burst Rate 4.00 5.00 6.00
Your base probability of a hit is kinda low. Heavies are big and easy to hit. Put the probability of the lights shot landing higher than the heavies, thus:
H vs L prob of hit: .70 approximately taking into account the heavies added maneuverability and length of volley.
L vs H prob of hit: .95 approximatley taking into account the size of the heavy, the volley of the light, and the speed of the light.
Now use some numbers to figure out which tank will die first based on tank armor and volley shots. Assuming your numbers to be correct:
About 9 1/2 volleys of light ammo to kill heavy.
4 volleys of heavy ammo to kill a light.
With tanks within easy firing/hitting range, about 20 lengths apart:
.95(9.5) = 9.025 SO if accuracy table correct the light will kill the heavy in 9.025 volleys BUT
.70(4) = 2.8 + light armor factor(~.25 of heaviy armor) + distance of charge=
The heavy will kill the light as the light passes it, taking about 70% of its health in damage.
This does not take into account any dodging or powerups. Someone calculate how quickly the tanks will die with powerups.
Ben(SA)
10/09/2003 (1:06 pm)
Heavy Medium LightX-Area 3.00 2.00 1.00
Speed 2.00 5.00 7.00
Burst Rate 4.00 5.00 6.00
Your base probability of a hit is kinda low. Heavies are big and easy to hit. Put the probability of the lights shot landing higher than the heavies, thus:
H vs L prob of hit: .70 approximately taking into account the heavies added maneuverability and length of volley.
L vs H prob of hit: .95 approximatley taking into account the size of the heavy, the volley of the light, and the speed of the light.
Now use some numbers to figure out which tank will die first based on tank armor and volley shots. Assuming your numbers to be correct:
About 9 1/2 volleys of light ammo to kill heavy.
4 volleys of heavy ammo to kill a light.
With tanks within easy firing/hitting range, about 20 lengths apart:
.95(9.5) = 9.025 SO if accuracy table correct the light will kill the heavy in 9.025 volleys BUT
.70(4) = 2.8 + light armor factor(~.25 of heaviy armor) + distance of charge=
The heavy will kill the light as the light passes it, taking about 70% of its health in damage.
This does not take into account any dodging or powerups. Someone calculate how quickly the tanks will die with powerups.
Ben(SA)
#4
10/09/2003 (1:07 pm)
LC and Dan got their posts in before me, but mine answers LC's question at least.
#5
The second factor contributing to light dominance is Force Multiplication. a force multiplier is something that makes a sides units more valuable than their apparent base value. In the case of TTanks the force multipliers are speed, range and respawn rate. Since range and respawn rate are equal for all platforms speed it the only force multiplier
Speed determines how long it takes a unit to return from the respawn point to the point of conflict.
Here's another little table for your edification:
Respawn multiplier = speed/speed
Heavy Medium Light
H 1.00 2.50 3.50
M 0.40 1.00 1.40
L 0.33 0.71 1.00
This suggests that 3.5 lights can return to the battle in the time it takes one heavy to return. This gives the lights a force multiplier of, you guessed it, 3.5. And, in fact, in the time 4 heavies respawn and return to the point of conflict 14 lights will have done so.
Multiplying the respawn factor of 3.5 by the light's relative firepower of 55.125 we get about 193. Which means that the light is about 193 times as effective as a heavy in the game.
BraveTree has adjusted rate of fire, speed and armor on all platforms in an attempt to neutralize this imbalance. They have done moderately well in normalizing the firepower imbalance but they haven't yet addressed the force multiplier issue.
From my first cursory examination of the underlying Torque engine I think that the following modifications might be possible.
1) Give each platform a different range. Absolutely normalized values would be in the range of Inverse(burstRate * speed) which yields proportions of:
Heavy Medium Light
5.25 3.13 1.00
2) Uneven reapawn times. Delay the respawn times of the faster platforms in the same proportions.
slugthog the longwinded
10/09/2003 (1:14 pm)
For any who haven't already drifted off.The second factor contributing to light dominance is Force Multiplication. a force multiplier is something that makes a sides units more valuable than their apparent base value. In the case of TTanks the force multipliers are speed, range and respawn rate. Since range and respawn rate are equal for all platforms speed it the only force multiplier
Speed determines how long it takes a unit to return from the respawn point to the point of conflict.
Here's another little table for your edification:
Respawn multiplier = speed/speed
Heavy Medium Light
H 1.00 2.50 3.50
M 0.40 1.00 1.40
L 0.33 0.71 1.00
This suggests that 3.5 lights can return to the battle in the time it takes one heavy to return. This gives the lights a force multiplier of, you guessed it, 3.5. And, in fact, in the time 4 heavies respawn and return to the point of conflict 14 lights will have done so.
Multiplying the respawn factor of 3.5 by the light's relative firepower of 55.125 we get about 193. Which means that the light is about 193 times as effective as a heavy in the game.
BraveTree has adjusted rate of fire, speed and armor on all platforms in an attempt to neutralize this imbalance. They have done moderately well in normalizing the firepower imbalance but they haven't yet addressed the force multiplier issue.
From my first cursory examination of the underlying Torque engine I think that the following modifications might be possible.
1) Give each platform a different range. Absolutely normalized values would be in the range of Inverse(burstRate * speed) which yields proportions of:
Heavy Medium Light
5.25 3.13 1.00
2) Uneven reapawn times. Delay the respawn times of the faster platforms in the same proportions.
slugthog the longwinded
#6
I do account for "ease of hitting". The numbers I posted are abstracted from an Excel spreadsheet. I will eMail you a copy if you wish.
To balance firepower using only armor a heavy would need 55 times the armor of a light.
@ Dan
Ability to dodge is as much a function of the player's skill as it is the platform's maneuverability. I will admit that I simplified a lot to keep the discussion in the range that most players can understand.
@Ben
The base "to hit" value is arbitrary. I chose 0.25 because when I was at what I considered a moderate skill level I hit about a quarter fo the things I aimed at. I modify this value by speed and area in my calculations hence I include your fudges. If you wish a copy of the Excel spreadsheet I will eMail it to you.
@All
Again I abstracted these values from a more complex table of values. Any who wish are welcome to my original basis.
slugthog
10/09/2003 (1:26 pm)
@LC 50I do account for "ease of hitting". The numbers I posted are abstracted from an Excel spreadsheet. I will eMail you a copy if you wish.
To balance firepower using only armor a heavy would need 55 times the armor of a light.
@ Dan
Ability to dodge is as much a function of the player's skill as it is the platform's maneuverability. I will admit that I simplified a lot to keep the discussion in the range that most players can understand.
@Ben
The base "to hit" value is arbitrary. I chose 0.25 because when I was at what I considered a moderate skill level I hit about a quarter fo the things I aimed at. I modify this value by speed and area in my calculations hence I include your fudges. If you wish a copy of the Excel spreadsheet I will eMail it to you.
@All
Again I abstracted these values from a more complex table of values. Any who wish are welcome to my original basis.
slugthog
#7
Ben(SA) - Is longwindedness contagious?
10/09/2003 (1:32 pm)
Are you trying to make all units equal? The great thing about this game is the challenge playing different tanks provides. If BraveTree incoroporated your suggestions, any and all advantages to playing as light, medium or heavy would be taken away. Leave the imbalances. A heavy will kill a light charging it 99% of the time, whereas, in my case, I can take out a heavy so long as you circle, shoot, and so on. Leave the respawn quirks, heavies aren't designed to charge back into the middle of the fray. Just watch LC50 play. He's the best heavy battlemoder I know. Who cares about respawn times? Lights are supposed to be strike, charge, quick kill, quick die vehicles. Mediums are ideally supposed to combine the heavy and light in a package. And finally, heavies are slug machines in a couple of ways, speed and strength. The numbers are fine, but one important factor is HUMAN SKILL. That can make all the difference in the game.Ben(SA) - Is longwindedness contagious?
#8
If they are equally accessble then their net effect on the game is zero.
If are not kequally accessible then speed is the only controlable factor that deterimes their accessibility. In that case power-ups increase the advantage of lights.
slugthog the semi-precise
10/09/2003 (1:32 pm)
Since power-up are randomizers we can consider that, either, they ar equally useful for all platforms or that there usefulness is a function of their accessibility (how easily a platform can gain access to a power-up).If they are equally accessble then their net effect on the game is zero.
If are not kequally accessible then speed is the only controlable factor that deterimes their accessibility. In that case power-ups increase the advantage of lights.
slugthog the semi-precise
#9
-- a light hitting a standing heavy at full speed will knock it into the air and back three tank lengths, while a heavy hitting a standing light at full speed will not even budge it. This is used to great effect by lights that constantly bump heavies as they fire at them.
-- a light tank crossing a speed arrow pointing in the opposite direction will "spin out" briefly on the arrow and then continue forward; a heavy doing the same thing will be shot backward several lengths. It seems the backward arrow takes into account the speed of the light tank, but it doesn't account for the weight of the heavy
-- a light and a heavy pushing each other head-to-head with no bumping will result in the heavy being pushed backwards. If a light and heavy push against each other such that the light is going forward and the heavy backwards, they stay in place and/or the light is slightly moved backwards.
-- knocking and stealing the scrum seems to be off kilter between lights and heavies,too, but I haven't been able to test enough to know which is light/heavy trouble and which is due to other factors in the game I know little of due not to playing lights as much yet.
10/09/2003 (1:34 pm)
Interesting stuff. Makes my head spin and I don't fully understand it, but it seems to jibe with much of what I feel tooling around in a Heavy. Don't know how you might add in the physics problems to the equations, if they matter:-- a light hitting a standing heavy at full speed will knock it into the air and back three tank lengths, while a heavy hitting a standing light at full speed will not even budge it. This is used to great effect by lights that constantly bump heavies as they fire at them.
-- a light tank crossing a speed arrow pointing in the opposite direction will "spin out" briefly on the arrow and then continue forward; a heavy doing the same thing will be shot backward several lengths. It seems the backward arrow takes into account the speed of the light tank, but it doesn't account for the weight of the heavy
-- a light and a heavy pushing each other head-to-head with no bumping will result in the heavy being pushed backwards. If a light and heavy push against each other such that the light is going forward and the heavy backwards, they stay in place and/or the light is slightly moved backwards.
-- knocking and stealing the scrum seems to be off kilter between lights and heavies,too, but I haven't been able to test enough to know which is light/heavy trouble and which is due to other factors in the game I know little of due not to playing lights as much yet.
#10
If they are equally accessble then their net effect on the game is zero.
If are not kequally accessible then speed is the only controlable factor that deterimes their accessibility. In that case power-ups increase the advantage of lights."
Slugthog
Powerups can be quite damaging for heavies. The easiest time to take out a heavy is when it has bounce back, just pow pow pow and bye bye. The heavies greatest asset besides its armor is the natural strength of its gun.
Lights can be killed and kill with area effect and speedy is just a more powerful bullet.
Ben(SA) - Fires another one off...
10/09/2003 (1:37 pm)
"Since power-up are randomizers we can consider that, either, they ar equally useful for all platforms or that there usefulness is a function of their accessibility (how easily a platform can gain access to a power-up).If they are equally accessble then their net effect on the game is zero.
If are not kequally accessible then speed is the only controlable factor that deterimes their accessibility. In that case power-ups increase the advantage of lights."
Slugthog
Powerups can be quite damaging for heavies. The easiest time to take out a heavy is when it has bounce back, just pow pow pow and bye bye. The heavies greatest asset besides its armor is the natural strength of its gun.
Lights can be killed and kill with area effect and speedy is just a more powerful bullet.
Ben(SA) - Fires another one off...
#11
So was said about heavies. Could you teach me this? I've played the heavy a lot and don't seem to have this down yet. Especially since a heavy is slow to start moving (which makes it a challenge to block speeding lights who can stop and go much quicker :) -- and THAT particular trick I'm not complaining about because it seems like something that should be...)
The argument about turning radius and such is fine until you're up against two lights piloted by skilled players like Ben who, as he said, can take out a heavy by circling and firing. So much for turning radius.
Now, I don't want to be accused of wanting to make all the tanks too similar or so evenly matched that there is no real strategies. However, at a certain point, strategy is outclassed by excellent play and the quirks...
10/09/2003 (1:39 pm)
>They can also dodge bullets more effectively.So was said about heavies. Could you teach me this? I've played the heavy a lot and don't seem to have this down yet. Especially since a heavy is slow to start moving (which makes it a challenge to block speeding lights who can stop and go much quicker :) -- and THAT particular trick I'm not complaining about because it seems like something that should be...)
The argument about turning radius and such is fine until you're up against two lights piloted by skilled players like Ben who, as he said, can take out a heavy by circling and firing. So much for turning radius.
Now, I don't want to be accused of wanting to make all the tanks too similar or so evenly matched that there is no real strategies. However, at a certain point, strategy is outclassed by excellent play and the quirks...
#12
Definitely true. I generally stay away from the powerups. Sometimes I will pick one up if folks are far away and hope to get a speedy fire (for long distance sniping) or area effect (for wading into a bunch of lights and letting loose area effect blasts at ground zero -- the lights are usually gone before me :) ) If folks are far enough away, I can usually get another powerup or get rid of bouncebacks before they come to kill me, but if I'm caught with them they can be effective if aimed just right... fairly difficult -- not impossible.
10/09/2003 (1:42 pm)
>Powerups can be quite damaging for heavies. The easiest time to take out a heavy is when it has bounce back, just pow pow pow and bye bye. The heavies greatest asset besides its armor is the natural strength of its gun.Definitely true. I generally stay away from the powerups. Sometimes I will pick one up if folks are far away and hope to get a speedy fire (for long distance sniping) or area effect (for wading into a bunch of lights and letting loose area effect blasts at ground zero -- the lights are usually gone before me :) ) If folks are far enough away, I can usually get another powerup or get rid of bouncebacks before they come to kill me, but if I'm caught with them they can be effective if aimed just right... fairly difficult -- not impossible.
#13
Ben(SA) - Still going...
10/09/2003 (1:43 pm)
Heavies can't so much dodge as just sit in place and peg away at a light tank. Their greater maneuverability allows them a 360 turn in place very quickly. The few times I have played heavy, I noticed this especially. It's a very powerful ability.Ben(SA) - Still going...
#14
No, I don't desire to make the platforms equal. What a boring game that could be.
What I would like to see are adjustments made that make all of the platforms viable choices in the games.
As it is, SCRUM/TEAM SCRUM are, for the most part, light only games.
BATTLEMODE/TEAM BATTLEMODE are light dominated about 4 to 1 with the one being a heavy and, very rarely, a medium.
Now some of this is the result of the force multiplier effect of the lights that allows them to be used in a banzai assault tactic.
From a game economics perspective , lights are very, very cheap making them an obvious logistical choice. Heavies are signigicantly more expensive but still valuable in some situations. Mediums hover between valueless and not-quite-worthless.
And yes "long windedness" is contageous but it can be made less "whelming" by use of paragraphs.
sluggy the pedantic
10/09/2003 (1:44 pm)
@BenNo, I don't desire to make the platforms equal. What a boring game that could be.
What I would like to see are adjustments made that make all of the platforms viable choices in the games.
As it is, SCRUM/TEAM SCRUM are, for the most part, light only games.
BATTLEMODE/TEAM BATTLEMODE are light dominated about 4 to 1 with the one being a heavy and, very rarely, a medium.
Now some of this is the result of the force multiplier effect of the lights that allows them to be used in a banzai assault tactic.
From a game economics perspective , lights are very, very cheap making them an obvious logistical choice. Heavies are signigicantly more expensive but still valuable in some situations. Mediums hover between valueless and not-quite-worthless.
And yes "long windedness" is contageous but it can be made less "whelming" by use of paragraphs.
sluggy the pedantic
#15
Ben(SA) - Signing off
10/09/2003 (1:47 pm)
The only tank I think needs a LOT more equalizing is the medium. I have seen three players, including sluggy, who use a medium in battlemode.Ben(SA) - Signing off
#16
You have brought up a point that is significant in the play of the game. Momentum also known as mv^2.
The reason that lights have such a devasting effect on heavies is that, although the relative masses of the two platforms are reasonable, the base mass of all platforms is just too low versus their speeds.
In the real world tank masses are in the range of 10^9 while tank speeds are in the range of 10^1. Hence mv^2 in the real word is in the range of 10^11 for all platforms (mass dominates speed).
Whereas, in TTanks masses appear to be in the range of 10^2 and velocites in the range of 10^1 so mv^2 is in the range of 10^4. Speed dominates mass.
slugthog the dimensional analyst
10/09/2003 (1:56 pm)
@MichaelYou have brought up a point that is significant in the play of the game. Momentum also known as mv^2.
The reason that lights have such a devasting effect on heavies is that, although the relative masses of the two platforms are reasonable, the base mass of all platforms is just too low versus their speeds.
In the real world tank masses are in the range of 10^9 while tank speeds are in the range of 10^1. Hence mv^2 in the real word is in the range of 10^11 for all platforms (mass dominates speed).
Whereas, in TTanks masses appear to be in the range of 10^2 and velocites in the range of 10^1 so mv^2 is in the range of 10^4. Speed dominates mass.
slugthog the dimensional analyst
#17
Localizing respawning is a good solution. On the other hand, delayed respawing servers a second advangage of making banzai assaults less profitable.
As regards the M-16 you are mostly correct. Rate of fire is a major reason it was adopted by the USArmy, as were its light weight versus the then standard M-14 and the light weight of the 6.55 round versus that of the .303. Lighter weapons and ammunition meant that a soldier was able march farther and carry more ammunition.
As regards rate of fire, the M-16 was converted from automatic fire to burst fire because soldiers tended to waste too much ammuniton on automatic fire.
slugthog the tacticly perverse
10/09/2003 (1:59 pm)
@FleaLocalizing respawning is a good solution. On the other hand, delayed respawing servers a second advangage of making banzai assaults less profitable.
As regards the M-16 you are mostly correct. Rate of fire is a major reason it was adopted by the USArmy, as were its light weight versus the then standard M-14 and the light weight of the 6.55 round versus that of the .303. Lighter weapons and ammunition meant that a soldier was able march farther and carry more ammunition.
As regards rate of fire, the M-16 was converted from automatic fire to burst fire because soldiers tended to waste too much ammuniton on automatic fire.
slugthog the tacticly perverse
#18
You're right Ben, I do use a medium in battle mode. I favor a "shoot & scoot" strategy in BATTLEMODE. Although, because of its speed, the light it the best platform for "shoot & scoot" I have a perverse desire to "make mediums viable" and use it instead. Perhaps because when I was a sprout I got to ride in a Sherman and I "liked" it.
Come to think of it the Sherman was a lot like the medium in TTanks except that it had a more speed versus its opposition and held up quite well against German light tanks and scout cars.
Some time I'd like to put together a squad of mediums, with maybe a light as an FO, and see what kind of damage we could do in TEAM BATTLEMODE.
slugthog the reminiscent
10/09/2003 (2:16 pm)
@BenYou're right Ben, I do use a medium in battle mode. I favor a "shoot & scoot" strategy in BATTLEMODE. Although, because of its speed, the light it the best platform for "shoot & scoot" I have a perverse desire to "make mediums viable" and use it instead. Perhaps because when I was a sprout I got to ride in a Sherman and I "liked" it.
Come to think of it the Sherman was a lot like the medium in TTanks except that it had a more speed versus its opposition and held up quite well against German light tanks and scout cars.
Some time I'd like to put together a squad of mediums, with maybe a light as an FO, and see what kind of damage we could do in TEAM BATTLEMODE.
slugthog the reminiscent
#19
shooting is tarred by (at least) 2 variables. clip quantity and strength. individual heavy shots are muy powerful, but they are so difficult to hit with, i liken them more to trash can than pill box. let them fire the same number of shots as a light with their current power and we'll have something to reckon with.
10/09/2003 (3:28 pm)
Quick hit: before i try and read the density above, my contribution:shooting is tarred by (at least) 2 variables. clip quantity and strength. individual heavy shots are muy powerful, but they are so difficult to hit with, i liken them more to trash can than pill box. let them fire the same number of shots as a light with their current power and we'll have something to reckon with.
#20
as for the light-as-throw-away comment: this harkens back to the initial change in game engine physics ( especially speeding up of light bullets etc ) which made death much more common. i speak for the old-timers i think when i say we are still not totally pleased with the changes. i think this thread and its geometric growth evidences that. the thrill of the chase has been greatly compacted; if you dont remember/weren't around, ill try and find the thread.
...
@ flea: modifier: reload times :). maybe heavies reload slower, then erupt like bejesus; an added strategic element.\\\...
...
HEY SLUGGY: ***NICE*** CONTRIBUTION TO THE COMMUNITY.
10/09/2003 (3:45 pm)
Slug i agree with in regard to ben getting snagged on evenness. the only reason players go with the medium or heavy is for the challenge of it i reckong. this shouldn't be why one picks their weapon, because it implies an immediate handicap. im not picking up a bow and arrow when the other guy is going for his uzi because i like the added challenge.as for the light-as-throw-away comment: this harkens back to the initial change in game engine physics ( especially speeding up of light bullets etc ) which made death much more common. i speak for the old-timers i think when i say we are still not totally pleased with the changes. i think this thread and its geometric growth evidences that. the thrill of the chase has been greatly compacted; if you dont remember/weren't around, ill try and find the thread.
...
@ flea: modifier: reload times :). maybe heavies reload slower, then erupt like bejesus; an added strategic element.\\\...
...
HEY SLUGGY: ***NICE*** CONTRIBUTION TO THE COMMUNITY.
LC50
LC50