How does the points system for the game 'disc pool' work?

Answer 1

Yes, I realize I'm answering my own question. I thought it would be interesting to share the information I've come across.

For those not familiar with the game of disc pool, check it out on miniclip.com

For those that ARE familiar with the game, this answer will provide vital information concerning ranked games and how points are determined.

Basically, when you play a ranked game, you either win or lose: when you win, you gain points; when you lose, you lose points. Simple as that. This value usually hovers around 16, but can vary a lot. I couldn't understand why my girlfriend would lose a staggering 21+ points a game, but only win a paltry 11 or 12 points. The key in calculating the points gain/loss lies in the difference between players total points. For example, someone (let's call him Mutt) just starting out has 1600 points. Suppose they play someone (say, Jeff) with 1700 points. If Mutt beats Jeff, he can expect to win more than 16 points, because he's beating out someone 'better' than him, according to their total points. If he were to lose, though, he'd lose LESS than 16 points, because the expected outcome is for him to lose anyway.

Before I show you the formula, know that, at all times, this formula applies:

(1) |W|+|L|=32

where W is the points you would have gained had you won, and L is the points you would have lost had you lost your game. It was this realization that led me to find, in a game of even strength, the points gained or lost are 16.

Now, here is the rough formula for finding the first value needed to determine the point loss/gain in a game:

(2) T= D/(22+(|D|/75)),

where D=Opponent's_Total_Points - Your_Total_Points

Note the absolute value brackets.

If you win your game, add T to 16: that will be your point gain, and the opponent's point loss.

If you lose your game, -(16-D) and that will be your point gain (since it will be positive, I speak of 'gain' of a negative, which is equivalent to the loss of a positive.)

As I mentioned, this formula works well for smaller values of D, where the players are relatively even-strength. It works right up to at least a difference of 258 points.

It does not work, though, for a value such as 426, which yields a -3,+29 situation or T value of 13. By my formula, this T value would be 15, and almost 16, meaning that a few more points difference would yield a -0,+32 situation, which would be unfair.

Many more points would produce the ridiculous situation of both players gaining points regardless of who wins, albeit in vastly different quantities. Also, this would violate the formula (1).

Of course, the designers of the game surely had this in mind, and found an elegant way of abiding by (1). A rewrite of the above formula:

(3) T= D/(22+(|D|/E)),

where E is a function inversely related to D.

With E decreasing and D increasing, this would eliminate the problem of run-away point gains, always satisfying (1).

Of course, I have not found a satisfactory way of determining E or else I would have posted it. I am still working on finding it precisely.