Variance and luck in races and tournaments: some numbers.

I

ineedaspot

AzB Silver Member
Silver Member
Here are some numbers on the chance of winning races and tourneys based on the single-rack win percentage. To illustrate, I'm assuming one player is better than the field, and that this player has the same single-rack winning percentage over everyone else in the field. Obviously, this is simplified, because in reality not all opponents are exactly the same, but it's just to get an idea.

Here are the probabilities of winning a set, as well as the probabilities of winning a 64-man single elimination and double elimination tournament, based on the individual rack winning percentages, with different race lengths.

Code: 
[FONT="Courier New"]Race to 11
Rack    Set    TournSE  TournDE 
53%     61%    5%       6%      
55%     68%    10%      13%        
60%     83%    32%      45%  
       
Race to 17  
Rack    Set    TournSE  TournDE
53%     63%    7%       8%
55%     72%    14%      19%
60%     88%    46%      65% 

Race to 50  
Rack    Set    TournSE  TournDE 
53%     73%    15%      20%
55%     84%    35%      51%
60%     98%    88%      98%[/FONT]

IMO, it's hard to argue that any individual top player has a greater than 55% single rack winning percentage against many (or even any) of the other top 64 players in the world. A 55% winning percentage would mean spotting 10 racks in a race to 55 makes an even match. In fact, I would guess that there are 10-20 players among whom single rack winning percentage is at most something like 52% or 53% (Shane, Yu Lung, Jung Lin, Appleton, Orcollo, Niels, Mika, Wang, Ko, Biado, Wang, Ralf, Hohmann, Wu, and a few guys I missed or never heard of).

Problem is, 9-ball is a very time-inefficient way of determining who is a better pool player, because a lot of time is spent on routine shots. This is why there are so few repeat world champions. The best players have the best chance of winning, but there really is a lot of variance.

It's too bad, because it takes away the potential for domination, the way Federer or Nadal have done in tennis, which is one thing that makes sports great. In a race to 11, among top pros in the world, nobody is really scared or intimidated by anyone else in particular. And at the same time, everyone is scared of everyone else, because anyone can beat anyone. Probably, what players are most scared of is rolls, and getting the cue ball kicked in on the break, or making one or two careless mistakes.

I don't know what the answer is. Trying to invent a whole new pool game probably isn't going to fly. 10-ball isn't much better than 9-ball, and makes the game more of a breaking contest. Calling shots is pointless -- slop is a very minor factor at the pro level. Alternating versus winner breaks doesn't matter -- it changes the mental game a bit, but mathematically it comes out the same, all that changes is the order that the racks are played. Double elimination as a tournament format is a little better but still doesn't help too unless either we go to long races or the single rack win percentage gets over 55%, which is pretty high.

One thing that might work is nested round-robins the way the old IPT used to. Every day, say 8 guys all play each other and the 4 with the best record go through to the following day. At the end, the top 2 guys standing play a race to something like 30 to determine the champion.

BTW, I'm neither a Shane fanboy or a Shane hater. I think Shane is a great player and a class act. Is he the best in the world? I don't know and neither does anyone else. I'm just a pool fan who wishes that there were a tournament structure and more world-class tournaments that would be able to overcome the variance and determine who the best player in the world actually is. I don't know who would come out on top, but I'd like to see it.
 
Its not that easy to say...,

I think that the real problem with coming up with a best of the best is the lack of tournaments. If you had a high payout tournament every month, I mean 100K added, so that every body would show up with there game face on, then you might get a repeat winner or a dominate player.

You could at least see one guy win the lions share of the money maybe or win first place more than any one else, but with the tour in shambles its no way to tell, at least not in the USA.
 
By the way...,

Efren still dominates all of the One Pocket tournaments that he enters? He either wins them or finishes in the top, two or three? Maybe that's the game by which to measure whos the best?
 
King T said:
Efren still dominates all of the One Pocket tournaments that he enters? He either wins them or finishes in the top, two or three? Maybe that's the game by which to measure whos the best?
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Shane sure put the screws to him in their TAR match.
 
King T: both your points are good.

More tournaments would be great. It could me something like golf. For a while, Tiger was head and shoulders above everyone, but since then (and even while he was at his best, to some extent) there is a lot of variance in individual tournaments. But in golf, there are 4 majors a year, plus a huge number of smaller tournaments, so rankings actually mean something.

Re: one-pocket. A single rack of one pocket is much more of a test of skill than a single rack of 9-ball. A lot less routine shots, and a lot of shots where someone like Efren can do something amazing, as opposed to 9-ball where on most shots it's basically about not making a mistake. That's why Efren was even able to dominate for years, even in tournaments like the DCC race-to-3 format.

One-pocket is my personal favorite game to watch. But it's not too popular outside the US, and I can understand why some people might find it boring to watch.
 
____________________________________________________________
Great work! Statistics...you're speaking my language (mouth salivating)!

I think we might have to inject a bit of Factor Analysis into all of this as
there are many unseen variables that affect how a player performs—
these tend to affect the mental part of one's game, e.g. home life, health, general state of mind.

Your numbers seem really good.
Were they generated from the past Worlds Tournament in Doha?

All I can add—it's probably a reiteration—is that we just have to hope more
World tournaments take place so we can have a sufficient sample size that
will allow us to better determine who is the "best," if only for the short-term.

Thanks again, excellent work and perspectives!:p
 
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If I remember correctly Mika dominated for a year and a half to two years ,
a few years ago. That was when there were more tournaments, but they
were still short races. So if someone is playing good enough it can be done.
Seldom do you see any player play that good for that long. Before Mika's
streak the last one I remember was Nick Varner's streak.

There are shorter streaks of coarse more regularly such as Thorsten Homann"s
streak last year which lasted for a few tournaments. Now however with fewer
tournaments recently it's harder to keep a streak going simply for lack of opportunity
to compete regularly.

For these top players to get their games up to that point and then there's no
tournament for months it's like getting all dressed up with nowhere to go, and must be
very disheartening for the players.

At least there's a little stretch now with tournaments, that is if you are invited, of coarse.
It's sad that even when tournaments are held here in the U.S that there are more Asian
and Pinoy players invited to them than U.S. players.

This is unheard of in those places. They look out for their own.
 
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Re: boogeyman

boogeyman:

Good point about there being more factors in play. These numbers are just a simple baseline, just to get a ballpark idea of how different length races affect the overall chances of winning a tournament in SE or DE format. In reality it's a lot more complicated, there's not just one better player with everyone else being equal, etc. It does illustrate, though, that even if there is one player who is significantly better than the field (i.e. 55% single rack win percentage over the rest), the odds of that player coming first in a race-to-11 tourney just isn't very high.

The numbers are all theoretical calculations based on an assumed single rack winning percentage, so it's not specific to 9-ball or anything else. For example, in order to win a 64-man single elimination, you need to win 6 matches in a row, etc.
 
Nice job. This illustrates exactly what I've been saying on here for the last 3 years but sadly, most of these mental giants can't comprehend variance even if it's laid out on a platter.

This is why most of the top pros don't like the short race tourneys because they are a crapshoot at that level. The tourneys really mean nothing when you are trying to decipher who the better player is.
 
How about 15-ball? not what the pinoys grow up playing, but all 15 balls played like 10-ball, and the 15 ball has to be the last ball off the table.
 
Keith Jawahir said:
How about 15-ball? not what the pinoys grow up playing, but all 15 balls played like 10-ball, and the 15 ball has to be the last ball off the table.
Click to expand...

lol, it doesn't matter what the game is. This is just a statistical model that illustrates variance as it relates to race length and single and double elimination tourneys. You could play tiddly winks and the better player is is going to win the more you play. It's takes a special kind of stupid to not understand this relatively easy concept, but sadly there are a lot of special people on here.
 
how about a world cup-type format? Have 32 qualifying tournaments throughout the year, culminating a big shebang round robin to further eliminate half of that field, then a 16 player single elimination race to 30+, until a winner in crowned. I for one would feel that that title would be well-earned
 
ineedaspot said:
One thing that might work is nested round-robins the way the old IPT used to.
Click to expand...
This.

IMO, the IPT had the best tournament format in pool history. Nested round robins is what is required to determine a true champion. It is absolutely no surprise that Efren won two out of the three IPT tournaments (King of the Hill and the World Open), not to mention making it in the final round robin group in all three tournaments. Orcullo also made it to the final round robin group in the two tournaments in which he played.

I wonder if we'll ever see a pool tournament with a world class field use this format ever again.
 
This is great information. I did the same in the straight pool forum using a per shot make probably to see how likely it is to run an arbitrary number (50 is my personal goal). Stuff like this shows that just a small percentage advantage in ability is huge when it comes to actually winning a match, or running 50 instead of 30 balls in straight pool Or running a full rack of 9 balls vs missing at the 4 ball.
 
You can also use information like this working in reverse to find out how much better a player is than the rest. For example Efren won I think 5 straight years of the DCC 1 pocket, with roughly 300 players each year. What would be his corresponding "game winning probability" on a per game basis? Don't ask me to do the math:thumbup::thumbup:
 
corvette1340 said:
lol, it doesn't matter what the game is....It's takes a special kind of stupid to not understand this relatively easy concept, but sadly there are a lot of special people on here.
Click to expand...

YOU said it, I didn't!

:yes::yes::yes::yes::yes::yes::yes::yes::yes::yes:
 
it also shows how little chance anyone that isnt the best or close to it in the smaller tournaments people go to, have little chance to win unless it is a handicap tournament..

i see so many saying you need to play with the good players in the tournaments. but in reality it is just a transfer of money from the other players to the road and good players.
 
Bump this back up because it seems all of the eurotards just pass right over it and go directly to stupid.
 
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