Victory Or Defeat

One of the of the hardest things to do during a competition is work out the b****y score. It's especially difficult at the end of a hard fought game that's just "gone the distance" and it seems to get harder as the day goes on.

In Field of Glory (FOG) games are scored out of twenty with a five bonus points for breaking your opponent army so you'd think it would be simple; wouldn't you? Well you'd be wrong. Look at this typical example of a helpful cross reference chart (click image for readable version):



I had a quiet half hour today so I sat down and tried to figure out why this is so confusing.

Firstly, I was struck by how confusing the instructions were. They read like an excerpt from a Marx Brothers sketch. Take for example the following guidance:

"Cross reference ... your own attrition point losses against ... your army size = points gained (G)."
"Cross reference ... [your] opponents attrition point losses against ... their army size = points lost (L)."

So we end up with instructions to:

• Use your losses to look up your gains.
  
• Use your opponents losses to look up points lost that are actually your gains too.

Have you spotted that the total number of points before bonuses isn't just the sum of the two numbers G and L? Are you still awake?

What they are trying to is actually very straightforward:

1. Calculate the proportion of your attrition points remaining relative to your army size.
   
2. Calculate the proportion of your opponent's attrition point losses relative to their army size.
   
3. Add the two numbers together.
   
4. Round and multiply by 10 for convenience.
   
5. Work out any win bonuses.

Things are confusing partly because the language is logically inconsistent as shown above, because the number of attrition points remaining isn't the same as the number of battle groups remaining, and partly because the "official" calculator tries to use the same table to do two different calculations or lookups.
The table isn't a simple proportion lookup table. It multiplies everything by ten for you but if you look up 5 losses for a 13 BG army you get 6.2 which is 10*8/13 not, as you might have expected, 10*5/13 = 3.8. The table neatly switches the result to points remaining without you having to do any subtraction. So far so good.

Things come unstuck when is comes to points gained from your opponent losses. Looking up their losses now gives you the wrong proportion as you no longer require the inversion provided by the table. This is why, when working out the total score, you have to subtract this number whilst adding 10. For example, if you look up 6 losses from an 11 BG army you get 4.6 which is 10*5/11 not, as you require, 10*6/11 = 5.4. Subtracting 4.6 from 10 gives you the right answer.

There's a final arithmetical twist which the table handles for you. When an army is broken you can end up with more attrition points than the army size and so the proportions have to be constrained between 0 and 1, or 1 - 10, or 0 - 100% however you prefer to think about it.

So there you have it. Opposite proportions are used to calculate the scores and one table can't handle that without some extra arithmetic. Expressing this in words only seems to have compounded the situation. My preferred solution is to remember this:

1. What I have left = (army size - attrition points lost) x 10 / my army size
   
2. Losses I have inflicted = attrition points x 10 / opponent's army size
   
3. Add the two numbers together.
   
4. Opponent's score = 20 - my score.
   
5. Award 5 bonus points for breaking an army.

It involves a bit of arithmetic, and I will have to remember to adjust 1 & 2 for any army breaks, but it seems a far clearer and logical set of instructions. Now all I have to do is remember this at the end of my next competition game.