Dr Neau's Formula for mixed League (Rebuy & Freezeout) Mathematical Problem

[sagemal]

Hi all,

I've been using now Dr. Neaus Formula for our League since we started to host RA (Re-buy/Add-On) Tourney's, and we decided to use this Formula because of it's implemented Total Expense in the Formula. (Which gives you an advantage if you haven't re-bought heavy)

Now the Problem is that we made some FO (Freezeout) -tourney's again, wanted to use it in the same League and here's were the problem starts:

I think the step in points between RA and FO Tourneys is to big! 

Example:

35 $ RA with a average Buy-In of 105$ an 12 Players gives us the Following points for the first 4 Players:
1. 5,916 (total expense: 105$)
2. 3,416 (te: 140$)
3. 2,958 (te: 105$)
4. 2,366 (te: 105$)

100$ FO 9 Players
1. 15
2. 10
3. 7,5
4. 6

the used Formula (of Course Dr. Neau's!):
score = (sqrt(((a * b) * (b / c))) / (d + 1.0))

Has anybody an Idea how to adjust the Formula so a 35$ Re-buy and a 100$ FO would give us approximately the same amount of Points if we estimating an average 2 Buy-Ins and 1 Add-On? (I want to use only 1 Formula, possible?)

Or do I something wrong?

Any Help would give you a Free Buy-In @ one of our Hometourney's but be aware, were in Switzerland.

[Martini]

I have a suggestion for how to shoehorn the two types of tourneys into the same point range but I'm not sure how valid it would be. This is just off the top of my head and I haven't worked through many scenarios but here it goes...

For your RA tourneys, use the overall average total expense as your buy in amount and use the total expense as your buy in.

For example, in a ten person $35 RA tourney where basically everyone does a rebuy and an add-on such that the prize pool/number of players= $100:

a = 10 (tourney buy in count)
b = 100 (this is now the average player buy in expense or prize pool/num of players)
c = 105 (this is still the total amount a person put into the tourney)
d = 1 (player finish)

1st place would get 15.4 compared to the 15.8 he would get for winning a ten person $100 FO. The numbers are roughly equivalent.

This has the added side benefit of relating the player buy in to the total pool which the current formula does not. If nine out of the ten players rebought 10 times and winner only bought in once the current formula would give the winner the same amount of points as it would if everyone only bought in once even though the winner would win substantially more if everyone else did a bunch of rebuys. See the next example:

a = 10 (tourney buy in count)
b = 100 (this is now the average player buy in expense or prize pool/num of players)
c = 35 (player total expense)
d = 1 (player finish)

1st place would now get 26.7 points for first place because he only did the original buy in while the rest of the field was pouring more money into the prize pool. IMO it fairly adjusts his points to compensate for the fact that the other players had more chips to work with than he did.

It does add in the a quirk though in that it would now be possible for 2nd place to earn more points than 1st place depending on the buy ins. But from a return on investment standpoint, I think it is a reasonable trade off to have that happen.

[sagemal]

Hi Martini,

Thanks for your idea & explanation.

This sounds all quite great, this is a solution, but for me unfortunately it is only a workaround, as i use Dr. Neau's TM and as of now, and i generate all the Leaderboard's with it and so I'd have to calculate all Results again by hand

But i will look in Dr. Neau's  RankingMethodEditor if there is a possibility to use the prize-pool as a variable.

The quirk, you mentioned, that someone out out the Money can be on a better place, then someone in the Money is already in the formula as is. And for me that's o.k. As the Leaderboard is more skill-oriented not only Net-Gains/ROI

Thanks again for your help.

cheers sagemal

[sagemal]

Well...

It's possible, all necessary variables available

The Formula looks like this:
 

Code:

  score = (sqrt(((a * (b / a)) * ((b / a) / c))) / (d + 1.0))
 
    where
 
  a = Tournament Buy-in Count
  b = Tournament Gross Prize Pool
  c = Player Total Expense
  d = Player Finish
 
Score accumulation method:        Average
Score weighting method:           Equal
Score decay rate:                 0.0
Score number format:              Double
Minimum tournament participation: 50% of the tournaments

And yes, the leaderboard makes sense now.

The Board:


Legend
1. - 3. = 25RA
4. = 35RA
5. = 50FO

Thanks again for your help.

cheers sagemal

[Martini]

Great! I'm glad that the new formula works for you and that Dr. Neau's software can accommodate it so easily.

And the other thing I forgot to mention is that you should make point structure changes between seasons. Once you publish a points system you should stick with it to avoid the appearance of either benefiting or harming someone's standing on the leader board.

[Dr. Neau]

I'll add.

I v3, you'll be able to have a different formula for each tournament, if you wish.

[Martini]

@Dr. Neau
Hope I didn't bastardize your formula, especially since it introduces the concept of a a player potentially receiving more points than someone who placed higher. It did seem to work for his purposes even though it is a diversion from the standard formula.

Does v3 alter the formula any and does it incorporate total prize pool in any way? I recall another thread where you mentioned you were thinking of tweaking the formula.

[Dr. Neau]

@Dr. Neau
Hope I didn't bastardize your formula, especially since it introduces the concept of a a player potentially receiving more points than someone who placed higher. It did seem to work for his purposes even though it is a diversion from the standard formula.

Does v3 alter the formula any and does it incorporate total prize pool in any way? I recall another thread where you mentioned you were thinking of tweaking the formula.

Getting more points than someone who placed higher than you happens all the time for us.  Say the player in 4th rebought and added on whereas the player in 5th didn't.  5th place gets more points.

These are the variables currently available for ranking methods in v3:
- Player add-on count
- Player add-on expense
- Player bounty expense
- Player bounty net gain
- Player bounty revenue
- Player buy-in expense
- Player finish
- Player knockout count
- Player manual points
- Player net gain
- Player place revenue
- Player primary expense
- Player primary net gain
- Player primary revenue
- Player rebuy count
- Player rebuy expense
- Player secondary expense
- Player secondary net gain
- Player secondary revenue
- Player side bet expense
- Player side bet net gain
- Player side bet revenue
- Player total expense
- Player total revenue
- Tournament add-on count
- Tournament add-on revenue
- Tournament buy-in count
- Tournament buy-in revenue
- Tournament net prize pool
- Tournament rebuy count
- Tournament rebuy revenue
- Tournament total revenue

If anything, v3 gives you the ability to be more granular about what you want to reward.

I'm open for other ideas!

[sagemal]

Great! I'm glad that the new formula works for you and that Dr. Neau's software can accommodate it so easily.

And the other thing I forgot to mention is that you should make point structure changes between seasons. Once you publish a points system you should stick with it to avoid the appearance of either benefiting or harming someone's standing on the leader board.

Thanks again, The League is almost amongst friends, and they where informed, that the formula wasn't definitive. And the FO tournament was not yet published.

[Dr. Neau]

Thanks again, The League is almost amongst friends...

...except for that one guy who's a total bastard.