What is more impressive?

[sirio11]

I posted the following in P5s; to generate some discussion about how this apply to the rankings, and to help vanish a misconception about impressive performances. What is your take on it?

______________


Scenario #1:

Player A played 500 $100 tournaments with 100 entries each, and won 5 times.

Player B played 500 $100 tournaments with 500 entries each and won 1 time.


Scenario #2:

Player A played 500 $100 tournaments with 100 entries each and won 10 times.

Player B played 500 $100 tournaments with 500 entries each and won 2 times.

Scenario #3:

Player A played 500 $100 tournaments with 100 entries each and won 10 times.

Player B played 100 $100 tournaments with 500 entries each and won 2 times.

Scenario #4:

Player A played 250 $100 tournaments with 100 entries each and won 5 times.

Player B played 50 $200 tournaments with 500 entries each and won 2 times.

Scenario #5:

Player A played 250 $100 tournaments with 100 entries each and won 10 times.

Player B played 25 $200 tournaments with 500 entries each and won 2 times.

_________

[Exitonly]

1) player A

2) Player A

3) Player A

4) Player A

5) Player A

A,A,A,B,B

[the_main]

[ QUOTE ]
A,A,A,B,B

[/ QUOTE ]

aaabb

[curtains]

I dunno. Do they actually use a really objective criteria for those rankings?? I just assumed it was more of a popularity contest. I mean how do they actually determine who is number 1 and who is number 15.

[Exitonly]

i switch.. #4 to B

[justT]

1) equally impressive
2) equally impressive
3) B
4) B
5) B

[TheJackal]

Ok are we looking at how much better we are than the rest of the field?
Scenario 1 - Player A 100:1 would be average player to win. Player A win's 500:5 or 100:1, which is average.
Player B 500:1 would be average player to win.
Player B win's 500:1, which average. Neither is more impressive than the other. They are both average players and given the buy-in, the fields should be equal in skill level.
Scenario 2
Average player 100:1 to win. Player A wins 500:10, or 50:1, he is twice as good as the average player.
Average player 500:1 to win. Player B wins 500:2 or 250:1, he is twice as good as the average player.
Maybe I'm missing something here but neither are more impressive to me, although Player B's odds of winning are 5x harder than Player A's. As far as skill level, they are the same.
Scenario 3
100:1 average, we win 50:1, twice as good as the field.
500:1 average, we win 100:2 or 50:1, we are ten times as good as the field. Player B feat is much better.
Buy in same, skill level the same.
Scenario 4
100:1, we win 250:5, or 50:1. we are twice as good as the field.
500:1, we win 500:2 or 250:1. We are twice as good as the field, although our buyin is twice as much. If we believe skill level is higher at the higher levels, Player B's feat is more impressive.
Scenario 5
100:1 average, we win 250:10, or 25:1, we are 4 times better than the field.
500:1 average, we win 500:2 or 250:1, out of 25 tries, we are 10:1 better than the field, variance has been kind to us. Also we are playing in a higher buyin than player A, Player B's feat is much better.

Yes it is more impressive to win through bigger fields than smaller fields.
1. Same
2. Same
3. B
4. B
5. B

A A B B B

The third one is close, but having to go through a larger field is more challenging so i chose B.

In 4 and 5 player B could just be hot and not be better than player A, but its still more impressive.

[Exitonly]

[ QUOTE ]
Ok are we looking at how much better we are than the rest of the field?
Scenario 1 - Player A 100:1 would be average player to win. Player A win's 500:5 or 100:1, which is average.
Player B 500:1 would be average player to win.
Player B win's 500:1, which average. Neither is more impressive than the other. They are both average players and given the buy-in, the fields should be equal in skill level.
Scenario 2
Average player 100:1 to win. Player A wins 500:10, or 50:1, he is twice as good as the average player.
Average player 500:1 to win. Player B wins 500:2 or 250:1, he is twice as good as the average player.
Maybe I'm missing something here but neither are more impressive to me, although Player B's odds of winning are 5x harder than Player A's. As far as skill level, they are the same.
Scenario 3
100:1 average, we win 50:1, twice as good as the field.
500:1 average, we win 100:2 or 50:1, we are ten times as good as the field. Player B feat is much better.
Buy in same, skill level the same.
Scenario 4
100:1, we win 250:5, or 50:1. we are twice as good as the field.
500:1, we win 500:2 or 250:1. We are twice as good as the field, although our buyin is twice as much. If we believe skill level is higher at the higher levels, Player B's feat is more impressive.
Scenario 5
100:1 average, we win 250:10, or 25:1, we are 4 times better than the field.
500:1 average, we win 500:2 or 250:1, out of 25 tries, we are 10:1 better than the field, variance has been kind to us. Also we are playing in a higher buyin than player A, Player B's feat is much better.

Yes it is more impressive to win through bigger fields than smaller fields.
1. Same
2. Same
3. B
4. B
5. B

[/ QUOTE ]


Include variancec... any schmuck can win in short term.. therefore more wins = better.

[TheJackal]

[ QUOTE ]
Include variancec... any schmuck can win in short term.

[/ QUOTE ]

Yeah and he seemed to win twice out of a field of 500 playing in 10% of the amount of events as Player A. Player A won more times, but he also played in 10x the events as Player B. The buyin was also lower as well. Player B's feat is much better.

[Exitonly]

[ QUOTE ]

Scenario #1:

Player A played 500 $100 tournaments with 100 entries each, and won 5 times.

Player B played 500 $100 tournaments with 500 entries each and won 1 time.


Scenario #2:

Player A played 500 $100 tournaments with 100 entries each and won 10 times.

Player B played 500 $100 tournaments with 500 entries each and won 2 times.

Scenario #3:

Player A played 500 $100 tournaments with 100 entries each and won 10 times.

Player B played 100 $100 tournaments with 500 entries each and won 2 times.

[/ QUOTE ]


First two they played the same, so the more wins = more impressive to me. ... and the 3rd one they won the same ratio, so the one that occured over a longer stretch is more impressive to me.

--

And the other two are more opinion i guess.

[sirio11]

[ QUOTE ]
First two they played the same, so the more wins = more impressive to me. ...

[/ QUOTE ]

So you think is equally impressive to win a tournament no matter the entries?

[locutus2002]

the question is designed to weight 3 factors in order of impressiveness:

Consistency - proxied by the number of 1st place/ field size
Size of win - proxied by field size
Strength of field - proxied by buy in amount


The proxies are only proxies so the multiple questions will only give you a relative weighting of the proxies.

Qualitatively, Consisency needs to be the most important quaility for a good player. If you can't consistently post winning numbers then you are just playing the lottery looking for a string of winning hands.

The size of the win is the least important as it only represents variation in the expected outcome: which is only a few times your buyin at most. This is the aspect of the game that makes the game appealing to average/below average players, and the gambler in most of us.

That means strength of field is the second most important aspect. As we move up in buyin categories, the strength of the field does go up, but at the highest level: a WSOP event, there are still plenty of amateurs. Once you pass $100 buyin there are less recreational players, and hence less errors that are being made: of course the qualifier has dispersed many players through all levels of the game.

[justT]

How about this one?

Scenario #6:

Player A played 10,000 $100 tournaments with 100 entries each and won 100 times.

Player B played 100 $100 tournaments with 100 entries each and won 1 times.

[AlphaWice]

No, the type of reasoning expressed by most posters has a fatal flaw.

Suppose in a coinflipping tournament of 8 players, you are 60% to win each coinflip. Then your likelyhood of winning the tournament is .216 instead of .125. Notice that you are 1.728 times more likely to win the tournament, as opposed to what you may think (1.2 or maybe 1.5 more)

Essentially, the more players there are, the more your edge "compounds", and this should be taken into account.

Therefore, we conclude: An above average player has a _stronger edge_ in a _larger_ tournament. Thus, with two scenarios that admit equal chances given the play of an average player, the scenario where the above-average player's ability is less "amplified" (ie. the scenario where there are less entries) should be given more points, since it would take more raw edge to attain the same result.

[locutus2002]

Incidently, I am in awe over Sirio's continued outstanding results. This is MOST impressive.

[Exitonly]

[ QUOTE ]
[ QUOTE ]
First two they played the same, so the more wins = more impressive to me. ...

[/ QUOTE ]

So you think is equally impressive to win a tournament no matter the entries?

[/ QUOTE ]


Not no matter the entries, but 100 person field isn't too shabby, and you have to get luckier to win the bigger ones. Not that theres not more skill too.. but eh..

more wins is generally more impressive, with exceptions for drastically bigger field size, or buyin.

[burningyen]

[ QUOTE ]
[ QUOTE ]
First two they played the same, so the more wins = more impressive to me. ...

[/ QUOTE ]
So you think is equally impressive to win a tournament no matter the entries?

[/ QUOTE ]
It's clear he only meant that if A & B are otherwise equivalent, the number of wins acts as a tiebreaker.

[sirio11]

[ QUOTE ]
It's clear he only meant that if A & B are otherwise equivalent, the number of wins acts as a tiebreaker.


[/ QUOTE ]

But why?. If B plays 500 tourneys with 500 people, he's expected to win one time in average. If A plays 500 tourneys with 100 people each, he's expected to win 5 times in average. Both are just doing what is expected by mere probability; why the 5 wins are more impressive?

[Exitonly]

Maybe this isn't the right thinking... but theres more variance in a 500 person field than a 100 person field right? Therefor one win in the 500 field doesn't show as much as 5 wins in the 100.

[burningyen]

Well, more wins = more validation of a player's skill short-handed and heads-up.

[adanthar]

Variance is right. Anybody can win a tournament once; it means very little as to your overall skill level. 5 wins in 500 tries is closer to a statistically significant event (even though it still isn't) so you are likelier to be at least average.

[sirio11]

[ QUOTE ]
Well, more wins = more validation of a player's skill short-handed and heads-up.

[/ QUOTE ]


Mmmmmm, you're aware that he played 500 tourneys, win 5 and lost 495 right?

Most probably he finished 5 times in 2nd place, 5 in 3rd, 5 in 4th, ..........., 5 in 100th place.

How this exactly imply more skill short-handed?

[sirio11]

Frankly I didn't understand your point. Are you trying to say that a person winning just 1 tournament out of 500 tourneys with 500 entrants is not likely to be average /images/graemlins/confused.gif?

[sirio11]

[ QUOTE ]
Maybe this isn't the right thinking... but theres more variance in a 500 person field than a 100 person field right? Therefor one win in the 500 field doesn't show as much as 5 wins in the 100.

[/ QUOTE ]

You're like saying,

The person with the 5 wins in the 500/100 is more likely to be average than the person with the 1 win in the 500/500 because of the variance; so, this more likeness to be average is more impressive /images/graemlins/confused.gif

[burningyen]

[ QUOTE ]
[ QUOTE ]
Well, more wins = more validation of a player's skill short-handed and heads-up.

[/ QUOTE ]
Mmmmmm, you're aware that he played 500 tourneys, win 5 and lost 495 right?

Most probably he finished 5 times in 2nd place, 5 in 3rd, 5 in 4th, ..........., 5 in 100th place.

How this exactly imply more skill short-handed?

[/ QUOTE ]
Again, I think we all agree the two are basically equivalent mathematically, but if indeed player A made it to the final table 50 times and finished 1st 5 times and player B made it to the final table 10 times and finished 1st once, that gives us more confidence that player A is at least average when it comes to final table play (see the variance comments above).

[Exitonly]

[ QUOTE ]
[ QUOTE ]
Maybe this isn't the right thinking... but theres more variance in a 500 person field than a 100 person field right? Therefor one win in the 500 field doesn't show as much as 5 wins in the 100.

[/ QUOTE ]

You're like saying,

The person with the 5 wins in the 500/100 is more likely to be average than the person with the 1 win in the 500/500 because of the variance; so, this more likeness to be average is more impressive /images/graemlins/confused.gif

[/ QUOTE ]


Yes.. player A is more likely to be atleast average than player B, who's success is more likely to be a fluke.

[adanthar]

[ QUOTE ]
Frankly I didn't understand your point. Are you trying to say that a person winning just 1 tournament out of 500 tourneys with 500 entrants is not likely to be average /images/graemlins/confused.gif?

[/ QUOTE ]

No, I'm saying it's really impossible to tell because he could be way above average or way below it and the sample size is simply not there. The data is 1 set of 500 vs. 5 sets of 100 - neither is important but the latter is slightly more significant.

[AlphaWice]

[ QUOTE ]

Again, I think we all agree the two are basically equivalent mathematically,

[/ QUOTE ]

Actually, I don't. Please read my post. This also goes for the other posters that happened to reply and glossed over my point.

Edit: I am sorry, upon re-reading your post, I seem to have taken your post out of context. However, my initial point still stands that people should scroll up to read my first post as it gives another idea.

[Blindcurve]

Quick response before I read on:

#1: A
#2: A
#3: A
#4: A
#5: A

I am assuming that the size of the wins hasn't changed the life of the player in question. I found that the more tournies played, the more impressive the number of wins because I tend to believe that larger numbers indicate greater consistency.

[sirio11]

Hey Alpha, I read your post, but I'm having a hard time accepting your example.

[TheJackal]

[ QUOTE ]
Hey Alpha, I read your post, but I'm having a hard time accepting your example.


[/ QUOTE ]

I agree Sirio. Winning a tournament with 5x the amount of entrants meaning accumulating 5x the amount of chips to win. I don't see how a pros edge is higher in this instance. His EV might be higher if he plays better than the rest of the field, but his chances of winning are much harder. Where the [censored] is Paul Phillips when you need him? I think he officially gave up on twoplustwo.

[locutus2002]

I think this requires alot more statistics than most players are capable of.

You are comparing extreme values for random variables that are unlikely to have a uniform underlying distribution. It's a bold assumption to even say that the average tournament result is normally distributed around the 1/2 way point.

If you assumed that the average player was IID then
1/500 is about 3 s.d. away from the mean if normally distributed.
1/100 eyeballs at about 2.7 s.d. away from the mean.

You could test confidence intervals to see which player was less likely to be normal if you could show they were both positive.

[justT]

[ QUOTE ]
that gives us more confidence that player A is at least average when it comes to final table play (see the variance comments above)

[/ QUOTE ]

minor point, but more data actually gives you better confidence in your win rate. Variance works both ways such that "at least" is just as correct or incorrect as "at most".

The big problem here is really in defining impressive. Instead of poker players, look at cars. Consumer reports doesn't use just one performance measure, they use many. Handling, acceleration, fuel economey, price tag etc. For poker players, it's should probably be a mix of ROI, consistency, total $ won, # of tourney's played, # of types of games played, etc.

[AtticusFinch]

1: Neither
2: Neither
3: B
4: B
5: B

Simple math, really. The first two had equal multiples of the average expected number of wins for an even field. In the last three, player B exceeded his EV by far more than player A did.

#1 -- Player A
#2 -- Either or.
#3 -- Player B
#4 -- Player B
#5 -- Player B

----

Most people went with AABBB, i'll explain my reasoning.

In A both with 500 appearances, 5 #1's vs 1 with 5x the ppl, I think repeating versus a smaller crowd is a tad more impressive then 1 big win. Though they do add up the same, Winning is winning. How many World series did the Yankees win before there were 30 teams in the league? You dont discount the small wins when you talk about achievments.

In #2, in the prior scenario i said discount the small wins vs the big wins, but if you factor in another win vs a large crowd, my perspective changes slightly, 10 Wins is astounding none the less but 2 very big wins adds some prestige. This is a toss up, depends if you are a person who tells alot of stories.

New scenario #3/4/5, Less time is invested, in each scenario we are talking about 5x the amount tournies minimum, thats alot of time... /images/graemlins/grin.gif

[mmbapmashida]

AABBB