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: Dr. Neau's Tournament Formula  ( 15271 )
Dr. Neau
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Dr. Neau is a player of the pokers


« : Mar 07, 2013 at 17:20 »

Over the years, there has been periodic discussion on the board about various formulas people use for their league.  Usually, someone suggests using the formula I came up with in 2005...then there is banter about the pros and cons.

Nutn asked me to put together a writeup on it that we can direct people to.  Enjoy ;)

The Formula

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

      where

   n = number of participants in the tournament
   b = standard buy-in cost for the tournament
   e = the individual player’s total expense (buy-ins + add-ons + rebuys)
   f = the individual player’s finish

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

Origins
I started running tournaments in January, 2004.  From then until July, 2005, my friend and I hosted 12 tournaments.  They ranged in size (6 players to 17 players), buy-in cost ($30 to $60), rebuys (some tournaments allowed none while others allowed multiple) and add-ons (some tournaments allowed none while others allowed a small bump before the first break).

People would often ask “Who is the best player?”  I found that a pretty difficult question to answer...
•   Was it the player with the best average finishing position? Maybe, but how do you compare someone who played all 12 tournaments and had an average finish of 4th to someone who played a single tournament and finished 3rd?  And shouldn’t the size of the tournament be taken into account?  Clearly, 2nd in a 6-player tournament isn’t as meaningful as 2nd in a 17-player tournament.
•   Was it the most profitable player?  Maybe, but is a luckbox who wins one tournament really better than someone who plays twice and finishes 2nd both times but makes less money due to the payout structure?

Inventing the Formula - Factors to Consider
In August, 2005, we decided it was time to start a league.  We planned 6 tournaments over the next 6 months with a final championship that would consist of the top players throughout the season.  I did a lot assessing of various formulas that I could find (if I remember, some of those included WSOP, Card Player, WPT, etc.)  I read various articles from pros on what they thought the qualities of a good point system were.  Based on all of that information, my experience trying to assess the best player from our tournaments and the fact that we needed to choose the players for a championship, I looked at the factors I wanted my system to take into account:
•   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)

      where

   n = number of participants in the tournament
   b = standard buy-in cost for the tournament
   e = the individual player’s total expense (buy-ins + add-ons + rebuys)
   f = the individual player’s finish

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.

League Considerations
Since this was within the context of a league where we were trying to decide who got to play in the championship, it is probably worth mentioning a few other points that had more to do with how someone’s total score for the season was calculated.
•   Only count the top X scores - The reasoning here was really based on me.  Since I ran the league, I could easily make every single tournament.  I didn’t feel it was fair to have 10 of my scores count while someone else who had various conflicts and could only make 6 tournaments only had 6 scores count.  Was I a better player because I could make more tournaments?  NO!!!  We settled on counting the top 5 scores from each player.
•   Minimum participation requirement - Along with that, we didn’t think it was fair for someone to play 1 or 2 tournaments out of ten and qualify for the championship and exclude someone else who played all 10 tournaments and contributed to the league pool all season.  For that reason, we’ll list your scores in the league standings, but you don’t qualify for the championship until after you’ve played X tournaments (usually half).
•   Calculation – No it isn’t a system where someone can easily think, “Okay, if I finish 1st, I get 10 points…if I finish 2nd, I get 9 points…”.  For that reason, I have a league website with a calculator for the formula…so anybody at any time can go there and figure out what they would need to do in the upcoming tournament to meet their goals.

A Little More History
So we started using this formula for our league in September of 2005.  I incorporated it into my software as an optional formula for people to use.  It started popping up on HPT in various threads over time (first mention I can find is Wedge in December of 2005 saying he’s using it).  It’s actually been quite amusing over the last 7 years to see that life that it has taken on and how polarizing it can be.  And I do sometimes think about the fact that after I’m gone, the one lasting legacy outside my family will probably be this formula.  How long will it live?

Putting It to Work
As well as running a league for the last 8 years, I've participated in a few others.  It really drives me nuts when the league manager is slow to get information out about tournament results, league standings, etc.  I've really made an effort with my league to keep people as up to date as possible.  I send an email the next morning with results and current standings.  I update the website at the same time.  In the invites, I always make sure to include a link to the website where the results, standings and point calculator are.

Doing all of this can be a lot of work if you are doing it by hand or having to retype a lot of information into a spreadsheet.  To that end, I've put a lot of effort into my software, Dr. Neau's Tournament Manager, so that it does a lot of the work for me.

First, the software lets you create and save your formula so that it can be your calculator:



Once you've done that, the software will automatically calculate scores dynamically throughout your tournament.  You can view that at any time on the roster or the player properties dialog, but what's more important is that the players themselves know the current standings when they need to.  You can either display those in a widget at all times (along with payouts, blinds, etc.), or maybe you find it helpful to display a full-screen view of the standings periodically during breaks:



Within the context of a league, you might also need help calculating the standings.  How many tournaments does someone need to play to qualify?  How many scores for each player will count.  Do you want to exclude anyone from the standings due to ejection from the league?  The software also helps you there:



When you need to get the league standings out of the software into something else (email, web page), you have the ability to export a report to PDF or Excel: http://drneau.com/appImages/LeagueStandings.pdf

Managing a league can be a lot of work...make it easy on yourself.




* rodney.jpg (2.84 kB, 83x71 - viewed 5111 times.)
« : Mar 08, 2013 at 13:28 Dr. Neau »

(not a real doctor)

Concentrate on winning your tournament...let Dr. Neau manage it.

http://drneau.com
Martini
Regular
***
: 9999



« #1 : Mar 07, 2013 at 18:18 »

Thanks for posting this so there is a definitive thread to link to. Can this be linked from the sidebar as well? For whatever reason Google and the built in search have trouble finding older content buried in forums.

(not a real alcoholic beverage)
nutN2Lewz
Administrator
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*****
: 3670



« #2 : Mar 08, 2013 at 06:22 »

Can this be linked from the sidebar as well?


Do you mean adding it to the HPT menu items on the far left side of the page? I will certainly link to this post from my 'Poker Leagues' page and Google will pick that up no problem. I guess I could also include Dr. Neau's entire post on my 'Poker Leagues' page. What about it Dr. Neau, should I insert your entire post on that page?

Good luck, nutn
Dr. Neau
Regular
***
: 9678


Dr. Neau is a player of the pokers


« #3 : Mar 08, 2013 at 08:59 »

Go for it.  While you're at it, it should probably be the first thing people see when they cruise to hpt.com!
« : Apr 14, 2015 at 09:15 Dr. Neau »

(not a real doctor)

Concentrate on winning your tournament...let Dr. Neau manage it.

http://drneau.com
Martini
Regular
***
: 9999



« #4 : Mar 08, 2013 at 11:17 »

Can this be linked from the sidebar as well?


Do you mean adding it to the HPT menu items on the far left side of the page? I will certainly link to this post from my 'Poker Leagues' page and Google will pick that up no problem. I guess I could also include Dr. Neau's entire post on my 'Poker Leagues' page. What about it Dr. Neau, should I insert your entire post on that page?

Good luck, nutn


Just a link somewhere on a static page on the main site. Yes, on the http://www.homepokertourney.com/poker-leagues.htm page in the points systems section would be a great place to find it.

(not a real alcoholic beverage)
Dr. Neau
Regular
***
: 9678


Dr. Neau is a player of the pokers


« #5 : Mar 08, 2013 at 11:23 »

OMG!  Nutn suggests a linear point system!!

(not a real doctor)

Concentrate on winning your tournament...let Dr. Neau manage it.

http://drneau.com
Wedge Rock
Global Moderator
Regular
****
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CC&GTCC # R-7604


« #6 : Mar 08, 2013 at 11:50 »

And I do sometimes think about the fact that after I’m gone, the one lasting legacy outside my family will probably be this formula.

Sad the 4ceps' prize pool distribution model doesn't also bear his name...  I've been using that for 8 years too.

Wedge Rock (not a real rock)



Guilty of over-using ellipses...
nutN2Lewz
Administrator
Regular
*****
: 3670



« #7 : Mar 08, 2013 at 13:58 »

Go for it.  While your at it, it should probably be the first thing people see when they cruise to hpt.com!


The first thing people see when they visit HPT is a cartoon image of me naked in a barrel.

Good luck, nutn
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