So I was watching an AFL game the other night. Actually, it was a bit more than the other night, it was a few weeks ago, at Rottnest, at a bar which managed the unholy trinity of being really seedy, too expensive, and still being filled with screaming kids, and I mean literally screaming. By the end of the match my eardrums felt more like ear cymbals.

But I digress. At some point in the night my mind started to wander, as it happens, to the scoring system of AFL. In case you've been living under a rock (or alternatively, just don't follow this particular code of football like 99% of the world's population- and hey, I don't really exactly 'follow' it as such either) AFL uses an arcane scoring system where, rather than 'goals' and 'points' being interchangable terms as in most games, they instead refer to two distinct scores; a 'goal' being worth 6 'points'. These are written like so:

2 3 15

which means 2 goals, plus 3 behinds, equals 15 points.

(You probably already know this.)

At that point (ha.), for some inexplicable reason, and despite being totally devoid of maths for the best part of six months, my brain goes, "Hey, that looks like a sum!", and refused to leave this concept alone until I proved that, in fact, AFL score is unable in any way able to be confused with any kind of basic mathematical numberthing. Except I was wrong.

Obviously, addition and subtraction are right out. What remains of my rapidly disintegrating maths skills tell me this. Except for 0 0 0, in no case is 6a + b = a + b. Subtraction is the same, for the same reason. And I was all ready to discard multiplication too, when I remembered a score from a few years ago:

7 7 49

Uh, hmm. That's definitely both a footy score and a multiplication sum. This did not appease my brain, far from it. My brain now wants to know how many other cases of this could exist. Now, we've already tried the honest-to-god algebraic approach, and I feel like writing some useless python, so let's brute-force this sucker.

```
#!/usr/bin/env python
for goal in range(0,50):
for point in range (0,50):
if goal * point == (( 6 * goal ) + point ):
print str(goal) +" "+ str(point) +" "+ str(goal*point)
```

Which gives:

```
rocky@tal ~/Desktop $ python afl.py
0 0 0
2 12 24
3 9 27
4 8 32
7 7 49
```

Which is a lot more than I was expecting. And took a lot less time. Yay for processors, etc.

So what if there was a sport where scores multiplied? Kind of like in video games, with a... well, a multiplier. It'd give an interesting strategic tradeoff between going for bulk scoring or trying to increase your multiplier, which would obviously be harder. Multiplier can offer greater payoffs, but you have to have something to multiply first, and vice versa- it'd be a lot more difficult to win if your opponent was literally doubling their score with every goal. You'd either have to adopt a system whereby the multiplier only affects only future point-scores, or have a situation where you have a game which both swings from one team to another very fast and has extremely high scores, and/or have one team get totally destroyed.

Now that I've written about that, brain, can I finally go to sleep? Thanks, much appreciated. Night.

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