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
#42
This is just a short post(I know you don't believe me) on balance in team games.
There is a common misconception that when a game is unbalanced (more players on on team than on the other) that the advantage to the larger team is linear. That is to say, that if there are 4 on one team and 5 on the other team that the larger team has a 20% advantage, i.e. 5/4=1.2.
In fact the difference is the ratio of the squares of the size of the teams. If you need a reference for this I can dig it up or you can Monte Carlo it yourself. In the same example, 5 on 4, the real advantage is:
5^2/4^2 = 25/16 = 1.56.
That extra player really provides a better than 50% advantage.
So, another of Granpa Sluggy's tables. I treat all players as equally skilled. I use half values to represent bots. My choice is arbitrary. I know that all bots are not equal. And yes, I know that player skill can make a significant difference. This table simply represents an estimated base advantage of team unbalance. And, trust me, it's in the ball park.
vs 5.0 4.5 4.0 3.5 3.0
5.0 1.00
4.5 1.23 1.00
4.0 1.56 1.27 1.00
3.5 2.04 1.65 1.31 1.00
3.0 2.78 2.25 1.78 1.36 1.00
2.5 4.00 3.24 2.56 1.96 1.44
At the extremes the values are a bit risky in application, particularly in scrum but it's interesting to note that 5 versus 2 and a bot confers a four to one advantage.
So what's it worth? Well, if you want to have a reasonable idea of the final score in a game, multiply the smaller team's score by the appropriate value from the table, or by the ratio of the squares of the sizes of the teams. In a 5 on 4 game if the final score is 11 to 8 the adjusted score would be : 11 to 12.48. The smaller team actually won by nearly a point and a half.
There is one more application of this relationship. That is alliances in non-team games. An alliance in a non-team game can be thought of as a collection of 2 on 1 situations yielding a 4X multiplier for the alliance versus each of the other players. In fact the advantage is not quite as large but it is significant. For the poker players among us, imagine if you were in a poker game in which two of your opponents formed a conspiracy to support each other's betting. Would you be surprised if the pair of them walked away with a larger than expected portion of the winnings?
In a non-team game the actual winner is the non-allied player with the highest score.
slugthog the mathematically imbalanced
10/12/2003 (3:12 pm)
Okay this is the last one for a while.This is just a short post(I know you don't believe me) on balance in team games.
There is a common misconception that when a game is unbalanced (more players on on team than on the other) that the advantage to the larger team is linear. That is to say, that if there are 4 on one team and 5 on the other team that the larger team has a 20% advantage, i.e. 5/4=1.2.
In fact the difference is the ratio of the squares of the size of the teams. If you need a reference for this I can dig it up or you can Monte Carlo it yourself. In the same example, 5 on 4, the real advantage is:
5^2/4^2 = 25/16 = 1.56.
That extra player really provides a better than 50% advantage.
So, another of Granpa Sluggy's tables. I treat all players as equally skilled. I use half values to represent bots. My choice is arbitrary. I know that all bots are not equal. And yes, I know that player skill can make a significant difference. This table simply represents an estimated base advantage of team unbalance. And, trust me, it's in the ball park.
vs 5.0 4.5 4.0 3.5 3.0
5.0 1.00
4.5 1.23 1.00
4.0 1.56 1.27 1.00
3.5 2.04 1.65 1.31 1.00
3.0 2.78 2.25 1.78 1.36 1.00
2.5 4.00 3.24 2.56 1.96 1.44
At the extremes the values are a bit risky in application, particularly in scrum but it's interesting to note that 5 versus 2 and a bot confers a four to one advantage.
So what's it worth? Well, if you want to have a reasonable idea of the final score in a game, multiply the smaller team's score by the appropriate value from the table, or by the ratio of the squares of the sizes of the teams. In a 5 on 4 game if the final score is 11 to 8 the adjusted score would be : 11 to 12.48. The smaller team actually won by nearly a point and a half.
There is one more application of this relationship. That is alliances in non-team games. An alliance in a non-team game can be thought of as a collection of 2 on 1 situations yielding a 4X multiplier for the alliance versus each of the other players. In fact the advantage is not quite as large but it is significant. For the poker players among us, imagine if you were in a poker game in which two of your opponents formed a conspiracy to support each other's betting. Would you be surprised if the pair of them walked away with a larger than expected portion of the winnings?
In a non-team game the actual winner is the non-allied player with the highest score.
slugthog the mathematically imbalanced
#43
Hey thanks for the new post. The math on this thread is giving me a workout I'm just not getting from Algebra II.
Ben(SA)
10/12/2003 (3:17 pm)
Nice. It does check out that way. And I agree with you in none team game alliances. Those have been very damaging to me, there being that one extra player you can't kill. And he's really not helping you since ultimately your score is individual. This is why SA's fight each other in most battlemodes. Hey thanks for the new post. The math on this thread is giving me a workout I'm just not getting from Algebra II.
Ben(SA)
#44
I like numbers. Some of my best friends are numbers. The number 31 and I dated all through high school back in the..., well we won't go into that, just let it be known that 31 was a much younger number in those days.
Back-of-envelope calculations are used to verify hunches we may feel about a relationship. When I do back-of-envelope calculations I try to keep my calculations and the results simple enough for someone with just a smattering of Algebra to understand. I use small integers, whole numbers, because thy are a scale nearly everyone can visualize. I choose intuitive probabities, 1/4 or 1/2, for the same reason.
After seeing my conclusion folx often respond with, "Well, duh, everyone knows that." That's true. These calculations have been about things that everyone knows. All I have done is put them in a form that allows us to understand exactly what it is were are talking about, provide fodder for our discussion, hint at the scale of the imblalance and perhaps offer BraveTree a leg-up on solution.
slugthog the egregious
P.S, Oh yeah! And maybe convince some of you to invest in a dictionary. ;^)=====
10/12/2003 (4:06 pm)
For those who are intimidated by numbers.I like numbers. Some of my best friends are numbers. The number 31 and I dated all through high school back in the..., well we won't go into that, just let it be known that 31 was a much younger number in those days.
Back-of-envelope calculations are used to verify hunches we may feel about a relationship. When I do back-of-envelope calculations I try to keep my calculations and the results simple enough for someone with just a smattering of Algebra to understand. I use small integers, whole numbers, because thy are a scale nearly everyone can visualize. I choose intuitive probabities, 1/4 or 1/2, for the same reason.
After seeing my conclusion folx often respond with, "Well, duh, everyone knows that." That's true. These calculations have been about things that everyone knows. All I have done is put them in a form that allows us to understand exactly what it is were are talking about, provide fodder for our discussion, hint at the scale of the imblalance and perhaps offer BraveTree a leg-up on solution.
slugthog the egregious
P.S, Oh yeah! And maybe convince some of you to invest in a dictionary. ;^)=====
Torque Owner slugthog
I don't know which files you mean. I approximated the tank speeds from my experience in the game and from the graphic that is displayed in the selection window.
In fact I hedged my estimates to reduce the light's apparent advantage.
sluggy the approximate