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## April 28, 2005

### The maths of reality

I've always had an odd fascination with mathematical modelling of real-world probabilities. Many years ago I was involved in the National Ratings System for Scrabble in Australia. This is a method of ranking players in a way that the percentage chance of one beating another can be calculated directly from the ratings, and is mathematically correct. It is still being used today because it is a sound, solid ranking system.

More recently I've been getting into archery and discovered that here in Australia they use a ratings system that will accurately predict your scores under different distances and target sizes - even if you've never shot those ones before.

So, how does all of this relate to games ?

Yesterday I was playing with spreadsheets (lol) to calculate the odds of me shooting a perfect score (6x10's) from 30m, given my current ability. I realised that it would be very easy to take the formula that I was using and apply it to the accuracy of bows&arrows in a game, based on the players skill (RPG) or the equipment.

If the player shot their bow at the same spot, from the same distance, this formula would allow a "realistic" spread of arrows that has a real-world mirror. (deciding if an arrow did damage or not is a separate issue)

The player-ratings formula I mentioned earlier actually works really well in multiplayer competitions to correctly show relative skill levels between players, and to reward players appropriately from a match. I've used it to rank players in CounterStrike (using every kill, in order, to modify the rank) and it is suprisingly accurate (especially when compared to "kill counts" or "win counts" as a ranking method).

Most game developers don't care about this stuff, but sometimes it's simply because they don't even realise the information is out there. I'm always a fan of "correct" simulation in games (where possible) because I believe that the player can tell (at least subconciously) when something is 'believable' or not, whether it's in the battle or the rankings, or the physics of the ball in FIFA :-)

P.S. In case you are wondering, I've got about a 1/727 chance of shooting a perfect score at 30m with my current archery ability.

Posted by Zaph at April 28, 2005 02:02 PM

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