WSOP ME ROI estimation?

For fun I put in the payout structure from 2011 wsop into excel so I could see how ROI works out with different probabilities of finishing in spots.

- A perfectly average player returns (-6%) roi with an itm of 10%

- A player who gets itm 18% (like in Daut's sample) but has an even probability distribution of finishing in any itm spot returns 68% roi

- A player who gets itm 18% and is three times as likely to reach any final table spot as the person in point above who got 18% itm (with the extra probability of final table being taken out of the probability of mincash - a simplifying assumption), returns 214% roi

Now here's the problem, roi is ridiculously sensitive to minute differences in probability of finishing in the top spots. When we talk about a 5.3x increase in probability of final tabling between a theoretically perfectly average player (as in point 1) and a player with 18% itm who returns 214% roi (as in point 3), we're talking about an increase from 0.13% to 0.70% probability. In absolute terms it's a tiny difference yet leads to a huge change in roi.

Quick example, for Daut's sample size of 955 WSOPMEs played by a basket of good players, total buyins are $9.55mm. with 196% roi, total returns are $28.268mm. If we just remove one tournament result from this sample - Ben Lamb's final table finish for $4m, this reduces sample roi to 154%. The number of FT finishes in Daut's sample of 955 MEs is going to be in the low single figures. You can see where I'm going with this - this sample doesn't give us close to a clear idea of realistic ME rois. If we tried to get a 95% confidence interval around that 196% point estimate, it would be very wide indeed (an exercise i'll leave to those of you who are so motivated)

Payout data from 2011 wsop ME (i think it was 2011 but not sure
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This is intended to kick off discussion of the difficulty of ROI estimation in tournaments like the ME where we need a much bigger sample than we actually have before we can get narrow confidence intervals - and the implications for backing and staking "fair" markup. Can there even be such a thing as a normative idea of "fair"? Or is fair just what the market decides and what people are willing to pay / sell for?

0 votes

Daut:

How much does including a ME winner change the ROI?

Also seems you excluded not just ME winners but some other big wins to "not skew the data"

Doesn't that also skew the data though?

brief explanation for us math noobs pls

http://www.nsdpoker.com/2011/01/mtt-pros/

MTT variance article

seems like a sample of 1000 is approaching significance but not quite there yet?

The biggest issue with Daut's sample is that he is picking players who have already done well in that event. His sample is not independent. All his sample says is that a group of players who have gotten xxx% ROI in the main event and happen to have been winners have that ROI and are winners. Statistically speaking, that sample of players is meaningless, unless I miss something about his methodology for picking them.

For example, there could be players with higher than that ROI who happen to not have cashed.

There are players in that sample whose ROI is small and they should not even be on that list.

The sample is obviously skewed by a few extreme outliers.

o rly says the guy who hasnt seen my list....

i actually removed ivey after my original post because his ROI is both too high in reality and expectation to match the results of other players. new numbers: 948 main events, 168 cashes, 180% ROI

im picking all sorts of players. i picked tons of guys who went 0 fer 8 in the main event. i just picked a bunch of really good live and online players, wrote down their names, didnt remember that 1/5 of them at some point had a deep main event run and just added it all up.

examples:
brian rast 0 for 7
seidel 0/8
seiver 0/7
tricket 0/5
glantz 0/8
sauce 0/4
djk 0/3
genius28 0/5
robl 0/5
markholt 0/8
apestyles 0/7
me 0/7
bthere.com 0/5
cloutier 0/8
greenstein 0/8
arieh 0/8
hennigan 0/8
the toilet 0/6
joe cassidy 0/8
sowers 0/5
annette 0/3
oppenheim 0/8
singer 0/8
ville wahlbeck 0/7
torrelli 0/5
marchese 0/4
peachy 0/5


etc etc, lots of other guys who are 0/2 through 0/5

i left out gregy, duhamel, cheong, ivey, and some other final table players i cant think of cause i didnt feel it would be fair and didnt want to over skew the results. in my players picked i have 4 final tables in 955 main events played. the average field size was about 6500-7k over that time i believe, so the players i chose final table about 3x as likely as the average player, which seems about right given how many weak players are in it who final table like 1/10 as often as average. i think i chose a pretty fair list of players overall.

but CLEARLY im not perfect and i probably chose a few too many players who ended up being great that got their careers started with a pretty good main event score, or became well known after a 25th place and started doing well. im not positive, but i had to choose guys who played a bunch of main events (and i knew how many they likely played),and i consider big winners over the years they played.

however there are 3 main issues with trying to estimate ROI empirically:

1. not every player is the same. some of these guys are probably 130% ROI guys, others are 300%.
2. the games have gotten tougher since 2005. i needed a larger sample so i extended it to 05, but the tournament was bigger and softer in 05/06/07
3. the sample size is still way too small. likely need about 200k main events to get a pretty good idea, not 1k.

i think the cash rate is likely pretty accurate which gives us a likely floor of 68%. and then i think good players are a bit more likely to move up in spots: i.e. i think im more likely to finish 9th than 10th, more likely to finish 12th than 15th, etc. id guess my cash rate is likely around 15% and with the boost from the bubbles and some good spots to accumulate later on against weaker players im probably in the 75-100 range. but there are guys who will probably cash more than me and will play tougher than me late.

cloutier oopz

On May 30 2014 00:48 Skoal wrote: cloutier oopz

hes not great now (still a winner though given how amateurs play against famous pros), but in 05-07 he was likely one of the biggest ROIs in the field.

wow that is a sick sick list of 0 itms

I randomly looked it up and found that Annette ITM'd last year though?

http://pokerdb.thehendonmob.com/player.php?a=r&n=74867

On May 30 2014 01:29 player999 wrote: I randomly looked it up and found that Annette ITM'd last year though? http://pokerdb.thehendonmob.com/player.php?a=r&n=74867

i assume others did as well. i made this list sometime in june of 2013 before last year's main event and took the scores from 05-12. timex was shorting people in the main event and i wanted to get a better idea of good player ROIs.

also for dudes that went 0 for 8 there are guys like sorel who went 4/6 with 196k in cashes or ben lamb who went 3/7 with a 3rd place and a 12th place or allen cunningham who is 4/8. i think it evened out pretty fairly from the players i chose, but again, i probably did overchoose a little bit because im human

ok, thought it included 2013

On May 29 2014 19:20 Smuft wrote: Daut: How much does including a ME winner change the ROI? Also seems you excluded not just ME winners but some other big wins to "not skew the data" Doesn't that also skew the data though? brief explanation for us math noobs pls

including one ME winner, assuming ME payout is $9mil, turns that 196% roi in Daut's sample into 273%.

Deciding who is and isn't in the sample definitely skews the data. Daut realised this and tried to "curate" the data as he explains later in this thread, but even this method is full of problems (high sensitivity of result to small changes in sample, selection bias is impossible to avoid)

For a hypothetical big winning 214% roi player with the probability distribution of payouts given in spoiler (from point 3 of orig post):

+ Show Spoiler +

Expected return per tournament (mu) is $31,364 (214% roi)
Standard deviation of payouts (sigma) is $333,457

Over a sample of 955 MEs, this player will return an average amount per ME played that is normally distributed with mean of mu and variance of sigma^2/955 (Central Limit Theorem)

95% Confidence Interval:
payout = $31,364 +/- 2.575 * sqrt($333,457^2 / 955)
= [$20573 , $42154]

So we are 95% confident that over 955 tournies an imaginary player with true expected roi 214% will net an roi of something in between 106% and 322%.

This is a pretty huge range of uncertainty for a sample of 955 (as we could all have guessed).

Following the same method as above, for a hypothetical 68% true expected roi player (from point 2 of op), we are 95% confident that over 955 MEs the imaginary player will net an roi of something in between 4.5% and 131%

That's an interesting result - based on that, and on a very important (and likely false) assumption that Daut's basket of good players isn't subject to any kind of selection bias (which skews results massively), we can reject the hypothesis that the players in Daut's basket had a true roi as low as 68% and were running good over the sample.

Now what do we do about the damn selection problem. If we can get over that, we can at least come up with a pessimistic estimate of good player roi (towards the lower part of confidence interval) given some observed result. Based on what I've done so far, I wouldn't be surprised if Daut's 75%-100% guess for a good player is actually quite reasonable.

On May 29 2014 21:28 Smuft wrote: http://www.nsdpoker.com/2011/01/mtt-pros/ MTT variance article seems like a sample of 1000 is approaching significance but not quite there yet?

the main event has the best structure of the year. noahSD's article touches on large fields with generally not-great structures. essentially pressing a smaller ROI a greater number of times. live 10k+ tournaments are the opposite. fewer numbers of them, but better structure.

so basically a sample of 1000 is closer to approaching significance in something like the main event, BUT field strength is very relevant. i played the main from 08 to 12 and the field got wayyy better in my limited experience. that itself could be variance just from my vantage.

what about taxes?

I always (possibly naively?) thought that's something US players can take care of when they file for taxes, declare that they had x% of their own action and the rest of the cash was paid to xyz people who should be responsible for paying tax on their share?

I remember if a non-US national cashed in WSOP, they'd have to apply for some ITIN number (they have the forms at the rio) so that they can pay out that person's cash without any tax withheld.

Perhaps when the US player is collecting his/her cash, a foreign backer can accompany him/her and show their own ITIN number so the backer's share of the cash does not get tax-withheld?

Good point though, that's not something I would want to get involved bothering with if I can help it.

I have no idea, I hear the it is possible to get it back and stuff, doesn't seem clear as to how

but I was wondering how it would change the mark up math assuming you COULDN'T get a refund