I have a problem with the new proposed system as it is written in kfsw's recent thread. It may be a better judge of effort than straight point differential but it is a far worse measure of contribution. This is good on a youth soccer team where everyone gets trophies but is undesirable in a competitive video game. Below I have outlined a modification to the point differential system (a version of which I have proposed in a previous post) which would eliminate a good portion of the variance due to defense in order to make it more palatable to everyone.
There are two components to getting "unlucky" on defense over a given time period: getting attacked more than average, and performing below expectation on these attacks. My system nearly eliminates the affect of bad luck from the first component, creating a more reliable version of the point differential metric.
This is accomplished in four easy steps, easily automated with a spreadsheet:
1. Determine the average number of defenses per member for a period (easy to find directly from kfsw's stats)
2. Guess at a baseline number for expected point loss per defense (doesn't need to change each period, should probably be around 13 points per battle).
3. For each player, subtract the actual number of defenses from the average number of defenses.
4. Multiply the result of step (3) by the result of step (2) and add this number to overall point differential. Voila!
Here is an example to illustrate why this is better than straight point differential. Imagine 3 players:
Player 1: +1000 points, 120 defenses
Player 2: +1000 points, 100 defenses
Player 3: +1000 points, 80 defenses
To adjust player 1, we take 120 defenses minus the average of 100 defenses and multiply this by 15 (from step 2, rounded for ease) to get and adjustment of +300 (15 * 20).
No adjustment is made to player 2 because he fought an average number of defenses.
To adjust player 3, we take 80 defenses minus the average of 100 defenses and multiply this by 15 to get and adjustment of -300 (15 * -20).
The result:
Player 1: +1000 points, 120 defenses FINAL SCORE: +1300
Player 2: +1000 points, 100 defenses FINAL SCORE: +1000
Player 3: +1000 points, 80 defenses FINAL SCORE: +700
Quick Q and A:
Q: We can't actually know the expected point loss per defensive battle, won't that mess everything up?
A: A tiny bit, but not enough that it matters. We have good information giving us a narrow range of values that this number is centered around. If we are off by say 4 points, which I think is a very high value, and the person fought 20 extra defensive battles, this would still only amount to a double digit difference in point differential which is usually going to be inconsequential.
Q: Let's say we get attacked by MoM and I get targeted 20 times while Fred gets targeted 2 times. Then we get attacked by Atlantis and I get targeted 2 times while Fred gets targeted 20 times. We would show the same number of attacks, but MoM's attack is a lot stronger than Atlantis so it's totally unfair!
A: First, it's extremely unlikely that a differential this large in defenses would happen. Second, even in this extreme scenario, the adjustment is still not very large compared to overall score (100 to 150) and far smaller than any error likely to arise from using stamina and number of surges as primary metrics.
Q: You can still get unlucky on how you do in defensive battles so you didn't solve anything!
A: The affects of performing good or bad in defensive battles are less than people might expect. Using a binomial calculator (easy to find with google) you can confirm that if you have 60 defensive battles, and you are expected to win 20 of them, the combined odds of winning less than 10 battles or more than 30 is about .5%, or 1 in 200. 10 battles is unlikely to make a difference in overall rank unless you are already not contributing much.
