Should a larger sample size significantly change these results? If so, why?

I'd like to amend my question since it doesn't ask what I want to know. (too late to edit)

Instead of one year, take 10 years of WSOP performance. I don't see any reason why the results of that much larger sample size, and the ones in this chart should be markedly different.

Sure, if you include specialists playing only their specialties, results will be "better", but that is a biased sample.

This chart seems to be a totally random, average sampling and although it is small, it could accurately reflect average results obtained by an average group of very skilled MMT players.

1500 tournaments is a small sample size? How many tournaments would you expect a player to enter over the course of their entire career?

I would be interested in seeing the confidence interval around the win rate presented here if all of these individual entries were treated as being played by a single player (particularly if the entries paid and buy-ins won were normalized to # of buy-ins....i.e. rather than saying Mizrachi won $1.45 M in the $50k, say he won 29 buy-ins).

i doubt any player plays enough live tournies over thier lifetime to see thier true ROI.

Calculating ROI by gross cashes for players that play $1k buyins and $50k buyins in the same year really skews results towards the big buyins.

You should use relative ROI, I.e. # of buyins cashed for.

Or just calculate two ROIs avg and overall.

Just from this data, you can get a reasonable level of confidence as to "true" cash %. There were 2069 events entered and 304 cashes (if I didn't make any typos replicating the numbers), for an overall cash % of 14.7%.

Assuming each entry is an independent trial with a constant cash %, using the sqrt((p(1-p)/n)) formula, I get a 95% confidence interval of [13.2%, 16.2%].

does that mean this pool cashes with 95% probability between 13-16%?


God I love this stuff.

seems like you don't understand what "sample size" actually means


This, as well.



Yes, but still you need to keep what "cashing" in the series means in context. Whatever the true cash # is, it's still lower than the cash % for players of equal caliber who are playing in such a way to maximize ROI.

During the series, the opportunity cost of playing many of these events is quite high, so a lot of people play a -EV style in 1ks and stuff to either try and run well and build a big stack or bust early to play other events, and also sit out of events or punt small stacks to go reg other stuff, etc.

I think I see what you're saying..
There is the reality of how players actually play, and then there is the theoretical maximal ROI way to play.

but i don't understand why the latter should be considered as part of the calculations, since it doesn't happen..

ofc not, but that doesn't mean it's not still statistically significant. There's a reason you can sometimes call the results of an election with only 10% of the vote reporting. If you want to get some of the real stat geeks from the probability forum to chime in here, we may get a more informed take.

Well also as some people pointed out, a few bricks in big buy ins, and a few cashes in small buy ins yields a massively -ROI, when that is not really an accurate way of assessing it.

Right because none of the people who lost had other winnings to deduct from...

In the sense of RIO of every dollar spent, yes it is.

Who cares about ROI?

It's all about the bracelets baby.

I think OP got Tom Dwan Sr

Yes, that's exactly what it means. This is not a statistically significant sample size. It's not even close.

Also, you do realize that "only 10% of the vote" is like a sample size of 20 million, right? Not that that's even the most relevant reason why that analogy doesn't mean anything.

1500 tournaments is a laughably small sample size for large field MTTs.


I'm saying that as well, but your post isn't in reference to that.

One Drop should be included, or at least it would be nice to see the distorting effects of it in a separate chart. Of course the entrants generally had small pieces, but it would be interesting to see overall results/ROI

Taking off about 30% for taxes and let's say - and I think this is pretty conservative - about $5K in expenses, you're left with about $20K in 6 weeks. While that's not terrible, if the world series happened year round that would mean the very best tournament players would be earning $140K a year (from tournaments), which isn't bad, but certainly doesn't justify the $1K / hr coaching or w/e that many claim is necessary to make it "worth their time"

when i play next for the first time when im 21, all records will be broken

It seems pretty silly to be deducting for expenses in this situation. A sizeable number of these players live in Las Vegas. And if you are just talking about general food and rent and stuff like that, everyone has to pay this...you dont usually deduct this beforehand when estimating your income. Everyone has to pay taxes too.

What has bonomo ever won with more than 25% of himself?

As a recreational player who has occassionally fantasized about quitting my day job to join the MTT circuit, this is pretty eyeopening/depressing data.

Sure, it's a pretty small sample size, and certain quirks in the methodology might skew the results a little bit, but I think it does show a few things...

- tournament poker variance is so severe that even massively ev+ players can lose a lot of money in a short period of time.
- the constaints of a human lifespan probably make it impossible for any player to know his or her true roi with any real certainty, and, even if you did know your expected roi, you might never get to play enough tournaments to actually realize that ROI
- assuming basic tournament competency, one's ability to actually make a living at tournament poker depends very heavily on the ability to negotiate good staking deals/swaps...

I'd love to see this data from only NLHE and a list of the top 100-200 players for 2011/2012.

Fair enough, I suppose if the series did run all year round then most tournaments players would live in Vegas. In any case though I was just pointing out that these guys really don't make money that is all that extraordinary despite being the best at what they do.