Multiple short races is a great format!

Jaden said:

There are more variables than the statistics of probability for this to be valid.

You're allowing for better player, but that's just not the case.

You are only allowing for a one dimensional analysis here. It's multidimensional.

Jaden

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These other "variables" go both ways. Why would they adversely affect the stronger player more than the weaker player? And if they do, then would the stronger player really lay claim on being the "stronger" player?

poolscholar said:

11 races to 5 is a max of 99 games while a race to 55 is a max of 109 games. Seems like the long race would favor the better player with more games.

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That was my initial intuition as well. But the math says otherwise.

But I just want to add that the differences in probabilities are pretty minute. It's not like the sets are significantly more advantageous than the single race.

For example, given that the stronger player wins 51% of the games, then he'll win the 11 sets race to 5 match 59.029% of the time, whereas he'll win the single race to 55 match 58.290% of the time. Not very significant, but as far as I can tell the former is always greater than the latter.

poolscholar said:

If someone could post the math that would be appreciated

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I'm not sure ineedaspot did it, but I simply plugged in numbers into a binomial distribution calculator, such as this one here. You want to look at the cumulative probability P(x >= # of successes), which is the bottom window.

Races to five are too short. It definitely doesn't determine the best player.

ineedaspot said:

Race to 11 races to 5 is actually a max of 189 games. This happens if every set goes to the hill (9 games per set) and the whole match goes to the hill also (21 sets total).

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Aha, that is precisely where my intuition failed! So the 11 races to 5 actually does require more games. That makes sense now, since the winner will most likely win more than 55 total games. Thanks for pointing that out.

Nevermind my initial post. So for a given number of max possible games (which is the appropriate comparison), it does favor the single race. The more appropriate comparison should be a single race to 95 (max 189 games). Using the numbers in my previous post, the probability of the stronger player (0.51) winning is 60.847%, which is greater than 59.029%.

best event on the planet, euros are better by far, have 5 guys all on elite level
shane only won who close to them..
3 of US team are not real considered pro's,

format not the issue, US need to move with the times. all the bar box tournaments on bad equiopment creates bad habits i mean you seen multiple times US players off centered stance, jump up on shots etc
euros are playing all over world every top event used to the top conditions and tough atmosphere, sorry but the smokin aces bar box tourny in a smoke filled room with ac/dc on the background doesnt help your game

punter said:

Races to five are too short. It definitely doesn't determine the best player.

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Yes

Less and longer matches. Or have the competition last longer.

Deep six the the noise. It would be nice is the players could mute it.

A major distraction.

I watched Chinese 8 ball championships with Gareth Potts, a snooker player winning.
Outstanding pool, skill, and a quite presentation. Run out 8 ball on a snooker table.

Outstanding.

I think these races don't necessarily favor the better player. When you get to level of these Mosconi Cup guys it can be tough to determine a "better" player. The shorter races favor the hotter player, not necessarily the better player.

ineedaspot said:

Race to 11 races to 5 is actually a max of 189 games. This happens if every set goes to the hill (9 games per set) and the whole match goes to the hill also (21 sets total).

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The post I replied to said 11 races to 5 which is 9x11 = 99 which is less than a race to 55 in which 109 games are possible

Race to 11 set wins with races to 5 is as you described


Anyway, the premise which I don't believe is that the same number of games divided into sets vs straight race favors the better player. Clearly, if there are a lot more total games it favors the better player.

I agree it's a fine format.

I did the math in another thread. If anyone is not tracking ineedaspot's logic, try this link -->

http://forums.azbilliards.com/showpost.php?p=4418347&postcount=1

The math isn't hard but it can be lengthy.
Let's say you feel strongly that one player has an edge on the other, by 2%.
So he should win 51% of the time vs. the other guy winning 49%.

If you wanna calculate the underdog's odds are of winning a race, you just add up
his odds of winning exactly 1 game in the set,
plus his odds of winning exactly 2 games in the set,
plus his odds of winning exactly 3 games in the set,
and so on until you have every possible outcome added up.

So for a single game, the underdog's odds are 49%. But a race, even a short one, worsens his odds.
The likelihood of the underdog winning a race to 5 is about 47.5%.

Now do multiple races, and the odds keep stacking against them.
They should only win the short race 47.5% of the time,
so what are the odds that out of 21 short races, they win 11 of them? About 41%.

A race to 65 (aka a best-of-129) also comes up with about 41% for the underdog, so that's where ineedaspot's figure came from.

That math only works if there is exactly a 2% gap in skill between the players.
But of course you can't measure a skill gap that exactly, and the mosconi cup is multiple players,
some of whom are better and some are worse.
Shane's odds vs. appleton in 9 ball are probably not identical to justin bergman's odds.
And there's lucky rolls, bad ref calls, someone forgot to clean the 3 ball, darren's in a good mood, etc. etc.

If you consider the luck factor in 9 ball to be strong enough that every game is truly a 50/50 proposition, despite the slight skill gap between players, then it doesn't matter how you break it up... race to 65 or 21 races to 5 or whatever... the final probability is still 50/50 for winning the whole thing.

A few people seem to cling to the idea that the format is "stupid" and "a joke" and it's a "carnival game" and so on.
That's the same thing as saying it's all down to luck. That's the same thing as saying it's 50/50 for either team to win.

If that's true, then Europe has pulled off a statistical miracle... in 8 'coin flips' it has come up heads for them 7 times.

The odds of that are about 3%.

Does anyone really believe that this is an all-luck format and Europe just pulled off another 3% miracle?
Or can they finally admit that this is a fair contest and we just have a weaker team?

US chances would improve if they switched to a race to four.

In the marathon that is the Mosconi, the best team has a big edge.