Yet Another Combat Suggestion: Balancing Attack and Defence

Hey guys,

This is my first post, be nice.

I've read quite a few suggestions to tweak combat, adding options or changing the rules and I decided I'd spam the forum with my own little idea. The objective of the post would be to suggest a change in the balance to improve the use of defence.

So, what wrong with the balance?

Well, as I played the game and read posts on the forum, there seems to be a penchant for focussing on the attack and first strike. As I heard, the combat system will undergo a change in the 1.2 Patch with the defender receiving a 'parting shot' meaning that destroyed ships will be able to fire back. Some claim this will shift the focus a bit more to defense, but I believe this change will make the attack even more important. I will try to keep this instinctive and brief but there quite a bit of math behind it.

As things stand now, the randomizers used in the game to determine the result of attacks and defences are equally distributed (ie. every number has the same chance of coming up). No problem, right? We just take the mean to determine the effectiveness of our design.

Well, that works...in large samples. Let's take the example of a single six-sided die. If I asked you what I would roll, would you answer 3.5 (the mean of a single die), or would you say any number is just as likely to pop up and therefore, it's a completely wild guess?

Hint: you can't roll a 3.5.

Now, what if I said I'd roll 2 dice and add the results together? What would you say? 7?
7 is the most likely number to turn up. Let's compare the odds of 7 turning up compared to say, 2.

2's easy, it just has one chance: 1, 1.
7 has more chances: 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1.

Wait a minute. With one die, every result is just as likely to pop up, but when I roll two dice, that isn't the case anymore. Congratulations, you have discovered the 'Central Limit Theorem'. I will spare you the details but it means that most probability distributions will change to a normal (bell-curve or Gauss distribution) distribution if you take repeated samples (such as throwing more than one die).

This is what those people who play theoretic battles do. They're assuming they have a large sample and will therefore roll an average result. However, I found that battles are small samples and therefore, the mean is not nearly as useful a guideline as one would believe it was.

The main snag here is called 'variance'. People know means but few know variance. It boils down to how predictable/stable your results are. Variance is also a(n important) measure of risk and I believe this is what's keeping the defensive systems from being as useful as they should be at face value.

You see, defences are all about limiting risk, blocking an attack and ultimately, trying to keep your ship and crew in one piece. Once the variance becomes too big, the use of defenses drops to zero. The variance increases as the potence of your tech increases and as such, defences become less usefull. I'll try to explain this but it's a little abstract.

Suppose you have a Frigate 16 HP, 4 attack, 4 defence and you're fighting an identical vessel. Now, half the time, you should penetrate your opponent's defences and damage him. Given the low yield of the equipment, you can do at most 4 damage (and so can he). Anyway, this means you will both need a few rounds (at least 4) to determine the last man standing. So, many rolls are taken and the results will lie closer to the mean.

Now, image the same Frigate but this time tricked out with 40 attack and 40 defence. Suddenly, a fluke roll will end the fight. In fact, it doesn't even has to be a fluke roll, just a lesser roll (say, 10) compared the a better roll (say 30) will kill off the ship. So, odds are that fights become plagued by a greater variance.

But what if it is so likely you'll lose your ship? I mean, sure, you can't block everything but if the result is a total loss, why bother? Just stack op on weapons and beat the snot out of him! And by stacking on weapons, your chances of taking the enemy out of the game improve drastically. The best defence is a good offence, right?

The Cure

So, how do we fix it? Introduce the normal distribution (which has a lower distribution than an equal distribution over a similar range). How? Well, that's the easy part actually.
Here are some options which should also be fairly easy to implement:

1) Roll a die for every weapon/defence on the ship and add them together. So a ship with ten plasma beams get ten rolls and has them added together. This makes use of the Central Limit Theorem. Thing is, as you stack of equipment, you will encounter less variance (more rolls) compared to more variance (higher ranges) as the game progresses. You dampen the variance increase you would otherwise find.

2) Introduce a normally distributed variable and use that one instead of the one being used now. This one is trickier. You see, you have to dictacte a mean and a variance to the computer, but you can't really set clear boundaries (unless you're using cut-offs), so if you're not careful, crazy rolls are possible although they are very unlikely (in the order of 0.01% or less).

3) Just keep on rolling as you are used to but roll X times for the same ship and take the mean. This is the Central Limit Theorem yet again. This gives designers the greatest control over the variance. The more rolls they allow, the smaller the variance.

4) Beef up the hit points of the hulls. This is a fairly simple thing to do (players can do it just the same). The drawback is that you would need a large increase to make sure defences are useful in the end-game since the ranges are so high.

Word of caution:

Although variance is a measurement of risk, I feel that some variance is needed to keep things interesting. Many tactical games (PC and boardgames) make use of dice just to introduce something of a random element (and tension) in the game. There's a balance to strive for. To little variance creates a boring game, too much creates a dibillitating effect where gambling is encouraged.