TPRS.

I'm going to take a shot at explaining the formula in totally non-math terms.

First of all, let me say that the math is actually a lot more simple than it looks once the whole thing is algebra-ized.

Second of all, in a perfect world, we'd be able to penalize players for entering tournaments and not finishing in the money. That way we'd have a good idea what peoples' actual win/loss records were. In poker, though, that's impossible. Nobody actually has a list of everyone who enters a given tournament. The only records are of the people who cashed in the tournament. So, all we can do is add up someone's money finishes. That's not really a measure of skill, it's just a measure of how much someone achieved. So, someone who plays 100 tournaments is always going to rack up more points than someone who plays 10. That's just how it has to work.

Okay, now, the way you come up with a player's score is by adding up all of their cashes. But, not all cashes are equal. To compare different cashes, we use three criteria:

1) How big the field was (how many people entered the tournament?)
2) How "deep" the cash was (1st? 3rd? 10th? 50th?)
3) How expensive the tournament was (was the buy-in $100? $1,000? $10,000?)

These are basically the same three criteria everybody uses. I thought about other stuff to incorporate, but really, that's it. The buy-in is basically a measure of how tough the field is (i.e., how good the average player in the tournament was). Everything else is self-explanatory, pretty much, right? And almost every system just somehow quantifies (converts into points) those three things, and then multiplies them all together. And that makes a lot of sense. That's what you should do: find the product. And that's what our formula does.

Our formula is different in how we convert the three factors into points.

First of all, let's say we didn't do any kind of conversion at all. Let's say we just multiplied the three of them together. Well, what you'd get would basically be the amount of money won. If you made $50,000, you'd get X points, and if someone else made $100,000, they'd get 2X points. It would be pretty linear and direct. Here's the problem with that: according to that system, Joe Hachem would be the most successful tournament player of all time. Now, does anybody here actually think Joe Hachem's record is more impressive than Phil Ivey's? Or John Juanda's? No. So, clearly, we have to fuck around with the formula a little bit.

So what we did was, we came up with three different functions, one for each of the three criteria.

1) How big the field was.

What we did with this one was used a function that curves down a little bit, so it looks like the first half of a hump. So, a 100-person field gets about twice as many points as a 50-person field, but a 1000-person field only gets maybe 1.75-times as many points as a 500-person field. And a 4000-person field gets like 1.5 as many points as a 2000-person field. I'm not sure exactly how fast it slows down. But the point is, when the fields get HUGE (like the WSOP main event), the finishes become pretty unreliable. So we grade them down a little bit, proportionally. That doesn't mean that winning a 5000-person tournament is less impressive than winning a 1000-person tournament, it just means, the scale slows down a little bit. The actual function we used is, where x is the field size, y = x - x^2/200. It works out to about what we want.

2) How "deep" the cash was.

For this one, we just use whatever percent of the total prize pool the person won. So like if they win the tournament, and they get 40% of the prize pool, we multiply the whole score by 0.4. If they finish 20th and get 2%, we multiply the whole score by 0.02. We think this makes sense. And, let's imagine there's a tournament with a really bad money distribution. Like if they gave 90% of the money to the winner. Well, we still give the person who wins a 0.9. Our feeling is, good players should be playing for the win in that tournament, because of the way the money is distributed. On the other hand, if the winner only got 10%, and 10th place also got 10%, why should the winner get more points than the person in 10th? Good players would just be playing to make the final 10, since that's where the money is. I think our logic makes sense.

3) How expensive the tournament was.

Okay, ask yourself: is the average player in a $10,000 tournament really exactly twice as good as the average player in a $5,000 tournament? I mean, really, two whole times as good? Is the average player in a $2,000 person tournament really twice as good as the average player in a $1,000 person tournament? Twice? Just using a linear, straight scale for this seems really dumb. That's just not how it works in real life. And there's also this other issue of: money gets less valuable when you have more of it. Think about it. Think about what $1,000 means to you, versus what it means to a millionaire. On that same note, think about the difference between a $2,000 tournament and a $1,000 tournament, versus the difference between an $11,000 tournament and a $10,000 tournament. Obviously the difference shrinks as the buy-in grows, right? And the difference between a $101,000 tournament and a $100,000 tournament would be even less. So, we use a function that looks like a curve. The function is y = ln(x+1) where x is the buy-in. It's a logarithm, and the math of it doesn't really matter, it just works out to what we want it to.

So that's it, basically. We plug each of the three factors into their respective functions, we get three numbers, we multiply them together. That's the score of a cash. And then we add up all of someone's scores, and that's their ranking. It's pretty simple.

The only other thing is this "rolling" function. Basically, if we're doing Player of the Year, or Player of the Month, or Player of All Time, or whatever, we don't need the rolling function. But let's say we're trying to come up with the best player today. Well, then, we figure that more recent cashes should count more than cashes that happened a while ago. Does that make sense? I mean, someone who wins the World Series of Poker today ought to be ranked higher than someone who won it ten years ago, just because things change. So we just have this system where, as cashes move further into the past, they count less towards somebody's rating.

And that's it.