ROI vs Number of Players

[Avicenna]

In a recent thread, are the 20/180s worth it?, players started to discuss ROI vs Number of Players. I thought that it deserved its own thread.
Doing various searches on the forums, I found that most agree that the ROI, says for $11 Sit'n'Go with one table, may reach 20%. That a two-table SnG could double the ROI to 40%. The "doubling law" won't extend easily to MTT's though: a decent MTT player will make 100%. Actual figures do not matter; the question is:

a) Is ROI somehow proportional with the number of players?
b) Or is ROI invariant whatever the field size?

One may advocate (a), and say that ROI increase non-linearly with the number of players. That is, a big increase in players means a small increase in expected ROI. That is, an exponential law . I discarded the linear relationship from experience at one-, two-, five-tables SNG's and MTT's.

Or, one may believe in (b) for a big number of players. This would be an asymptotic law : ROI increasing til a maximum. This would also mean that there exists a player bound . Past this bound, ROI would cease to increase. ITM would, however, certainly dimish, and it would make sense not to play in overly large tournaments.

What's your opinion?

[Dr1Gonzo]

The theory is that for big MTTs you win about 1 in 100 of these and ITM about 10 in 100.
This seems reasonable for tournaments of 500-1000 people and it would make sense that the more people that enter, the more you win, and therefore the higher the ROI.
However, I suspect that once you go beyond a certain number of players (like the World Series), the 1 in 100 stats are not be applicable.
Conversely, the less people, the more you should ITM but this just doesn't seem to happen from my experience.

?

[AceLuby]

[ QUOTE ]
This seems reasonable for tournaments of 500-1000 people and it would make sense that the more people that enter, the more you win, and therefore the higher the ROI.

[/ QUOTE ]

This would be true if you are winning the 500-1000 person tournaments as often as a 180 person tournament. In a 180 it has been said that you need to win at least 5 60/40 'flips' (which is no easy feat). For a 500-1000 person tournament you will need to take at LEAST 3x as many, which means higher variance, and less chance to take first. So if you win 1/100 180's you would win somewhere around 1/200-1/300 in bigger fields, which means you have a very similar ROI because you are investing more (variance) for a slightly higher return. It all comes out in the wash. That's why ROI is used across buy-ins, because it doesn't matter which levels you're playing or the number of players, it is the way to see how well you are doing in tournaments for a reason.

[guaranteedBluff]

I think these are a few important points to consider:

1) If every player is equal, then everyone's roi is 0%, exactly (minus rake i suppose - assume no rake), regardless of field size.

2) there exists an "edge factor", which tells how much better than the remaining field hero is.

If this edge remains constant throughout the course of a tournament, then ROI should be the same for small and large tourneys. Another way of saying this is that if your chance of winning a 180-man is 1/100, then your chance of winning a 360-man is 1/200, exactly half.

3)Is the "edge factor" a static or dynamic thing? If it is dynamic, this has important implications for ROI vs field size.

Case 1) Edge decreases over the course of a tournament. This is certainly plausible because perhaps only the best players are left at the end of the tournament. If this is true, there are more players to get through at less of an edge, which implies lower ROI with increasing field size.

Case 2) Edge increases over the course of the tournament. Perhaps the disparity between experience and skill becomes wider as you go deep, and hence in larger tourneys you have more opportunity to assert this edge. In this case, ROI increases with Field size.

Please comment and critique this analysis, I'm not sure if I believe it myself.

[durkahdurkah]

I'm leaning toward thinking this is closer to an asymptotic law than anything else, but since the reality is is that no one individual has enough tournaments to hit the "long long long" term (and likely never will), I have a hard time believing this could be proven.

Thus, IMO, a graph of feasible ROIs that could be attained by any given player would look something like:



with the worst players at the left side and the best on the right. As mentioned, I'm not sure this can be proven, but it makes intuitive sense to me.

[mornelth]

[ QUOTE ]
The theory is that for big MTTs you win about 1 in 100 of these and ITM about 10 in 100.
This seems reasonable for tournaments of 500-1000 people and it would make sense that the more people that enter, the more you win, and therefore the higher the ROI.
However, I suspect that once you go beyond a certain number of players (like the World Series), the 1 in 100 stats are not be applicable.
Conversely, the less people, the more you should ITM but this just doesn't seem to happen from my experience.

?

[/ QUOTE ]

Maybe it's time to re-evaluate your game? Or take a look at stats and realize that 100 tournaments' worth of data is statistically irrelevant? (Small sample size).

[mornelth]

Besides edge factor there's also a volatility factor. You will need to risk chips to accumulate chips, you will need to get lucky EVEN if you have a tremendous edge and always get your money in as a 60/40 favorite. The longer the tournament - the more chances you will have to bust out, decreasing your ROI.

The funny part is is that the NUMBER of people matters as much as the speed/structure of the tournament. The "faster" the structure - the more chances you will need to take to survive/accumulate, and so you'll need to make more speculative moves with less-than-premium holdings (increase risk).

I do not know how to take all of these factors into account to calculate and compare ROI's... [img]/images/graemlins/confused.gif[/img]

[aplunk]

sorry to be a geek but when you say exponential i'm sure you mean logarithmic - that's what get's my vote

i've got a maths degree (1st class hons - oxford uni), i win big tournaments, i'm sure ROI isn't bounded

i do agree that life is too short for this to ever matter, either intellectually or practically

[AceLuby]

[ QUOTE ]
sorry to be a geek but when you say exponential i'm sure you mean logarithmic - that's what get's my vote

i've got a maths degree (1st class hons - oxford uni), i win big tournaments, i'm sure ROI isn't bounded

i do agree that life is too short for this to ever matter, either intellectually or practically

[/ QUOTE ]

If you don't think it's bounded (I'm a maths major too) then show me someone w/ a significant # of tourneys played w/ an ROI over 400%... 300%... 250%... maybe, but it'll be rare. If it wasn't bounded there would be people w/ that kind of ROI. It's just not possible w/ variance, luck, & bad plays.

[mornelth]

[ QUOTE ]
[ QUOTE ]
sorry to be a geek but when you say exponential i'm sure you mean logarithmic - that's what get's my vote

i've got a maths degree (1st class hons - oxford uni), i win big tournaments, i'm sure ROI isn't bounded

i do agree that life is too short for this to ever matter, either intellectually or practically

[/ QUOTE ]

If you don't think it's bounded (I'm a maths major too) then show me someone w/ a significant # of tourneys played w/ an ROI over 400%... 300%... 250%... maybe, but it'll be rare. If it wasn't bounded there would be people w/ that kind of ROI. It's just not possible w/ variance, luck, & bad plays.

[/ QUOTE ]

It's GOT to be bounded beciuse the opposite is clearly not true (math/CS major here too, wtf).

to the OP - Should we try and cross-post this in Probability forum that's densely populated with major math geeks?...