League Ranking Formula

score = SQRT (n * b * b / e) / (f + 1.0)

The Guiding Principles

• The higher you finish, the more points you should get
• Larger tournaments are harder to win than smaller tournaments
• Higher buy-in tournaments are taken more seriously than smaller buy-in tournaments
• Profitability counts
• Point structure should mimic payout structure
• Encourage participation

Finishing position

This is the most obvious, but sometimes it is worth mentioning the obvious. I wanted each person to be awarded more points than if they had exited the tournament one position earlier. In general, if you consistently finish higher than someone, then you probably have more skill.

Tournament size

Again, obvious. Given the same player skills levels, larger tournaments are harder to win than smaller tournaments.

Buy-in cost

We noticed that the larger the buy-in the more serious people took the tournament and therefore the harder it was to do well.

Profitability

Who is probably the better player: the person who wins 10 tournaments without rebuying even once, or the person who wins 10 tournaments but has to rebuy every single time? And if you can’t decide, then look at who is more profitable.

Inventing the Formula – Weighting the Factors

Once I had those identified, I had to decide how to weight them. I looked at each individually …

Finishing position

If the 2nd person out gets one more point than the 1st person out, is it really fair to only give the winner one more point than the runner up? NO!!! My experience was this: It was really easy to be the first one eliminated. Just about as easy to be the second one out … or the third one out … or fourth. But each position got a little bit harder. And when you got close to the money, a lot harder. And as the awards for each additional finish went up, it got even harder…and the difficulty didn’t increase linearly…it increased exponentially. The points for finishing position within a tournament should follow a nice accelerating curve. Notice that this is also how good payout structures are done. That is not a coincidence.

Tournament size

Does the winner of a 20-player tournament deserve twice as many points as the winner of a 10-player tournament? NO! Why? Because even though the field is twice as big, you don’t face twice as many people. The 10-player tournament might have 10 people at the same table, but the 20 player tournament would start with 2 tables. You’d face 10 initially, but you’d be consolidated when it gets down to 5 at each…so you really only face 15 on average. So, the formula should follow a nice decelerating curve when taking tournament size into account.

Buy-in cost

Pretty much the same argument as tournament size. It’s harder to win a $100 buy-in tournament than it is a $25 buy-in tournament … but there’s no way it is 4 times harder. Again: Decelerating curve.

Profitability

And again, the same argument. Someone who wins without rebuying does not deserve twice as many points as someone who wins via a rebuy. They deserve more, but not twice as much. Again: Decelerating curve.

So, I knew about what I needed to do, but I still had a question to answer: What does the first person out get? Some options …

Negative points

I actually considered a system where all the points for a tournament would add up to 0 … but ruled that out because I didn’t want people to be penalized for playing within the context of a league. Your score should never decrease.

Zero

Considered this also, but in the spirit of encouraging participation, I thought someone who played and failed deserved more points that someone who didn’t play at all.

So, we’re left with everyone gets at least something. But now think about this: Does the first person out in a 100-player tournament deserve the same points as the first person out in a 10-player tournament or a 5-player tournament? That one was tough to answer, but I decided that, on average, someone who consistently goes out first in a 100-player tournament probably sucks a little more. So, again … decelerating curve.

So, let’s take a look at the formula again …

score = SQRT (n * b * b / e) / (f + 1.0)

Having size (“n”), cost (“b”) and profitability (“b / e”) inside the square root function gives us that nice decelerating curve I wanted for these factors.

Dividing by the finishing position (“f”) gives us that nice accelerating curve I wanted. I added the “+ 1.0” to make it a little less drastic.

Here are some examples using Buy In: 25, Players: 10