## 28 October 2008

### Hammer's Slammers: Game Mechanics

Oops.

This is a post I started working on some time ago, but held off because I was rethinking the problem. I was looking at it earlier today and must have accidentally clicked on "publish" instead of "save". Too late though, because Google already latched onto it and is trying to link to it, therefore I will add a few comments and put it out for show. This is also a test of the what sorts of graphs I can do in Google Documents (henceforth GD).

This was SUPPOSED to be a post about a way to put a value on units in the game, which can be used to help create balances scenarios in the Hammer's Slammers game I wrote about previously. The game includes such values already to help in designing your own scenarios. Ultimately this is a preliminary post to talking about Battle Value in Classic Battletech, but it needs more work.
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First and most obviously, It's not yet possible to have two different lines on a single graph using GD. I tried to work around this by making a single line with a few points that do not display, and ... well ... it's a mess. The X-axis is log-base-2 of the Attack/Defense ratio. This begs an explanation I haven't given yet - this ratio of attacker-to-defender strength which you look up on the Combat Results Table, roll the dice, and determine if the defending unit(s) are unaffected, disrupted, or destroyed. The Y-axis is the natural log of the odds of the units being disrupted (upper line) or destroyed (lower line), where the odds are the probability P, divided by 1-P, or odds = P/(1-P).
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The point of all this is that the battle effectiveness of units in Hammer's Slammers can described by a relationship which is roughly linear on a logarithmic scale. Statisticians like these sorts of relationships because there is a lot we can do to describe them. Unfortunately is just describes the effects of a single attack, and I really want to try to put a value on the unit in a game, not just in a single attack. To do that, I will need to discuss survival distributions, and that is a topic for another day.
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How is that for a broken post?