Chances of Winning a Tournament

[martinburley]

The RPSNZ data monkeys have been far from idle since finishing work on the infamous RPS Analyser. Their latest project involved calculating the odds of different types of players winning RPS knockout tournaments.

The spreadsheet they've developed is now up and running. Forms 48858-WUE4K-b and CL3495xq-ii have been submitted to and approved by the appropriate departments. We're pleased to share our findings with you.

For our model, we consider three types of players: RPS Pros, Average Joes, and Bozos. RPS Pros have an advantage over Average Joes, while RPS Pros and Average Joes both have an advantage over Bozos. We also took into account the fact that some players will be in form (red-hot) when the tournament begins, playing well and feeling confident, while others will be out of form (ice-cold), stuck in a losing streak. Red-hot players have an advantage over lukewarm players, and both have an advantage over ice-cold players.

To run our model, we take four factors into account:

Number of Players: Is it a 4-player tournament, a 64-player one, a 512-player one, etc.?
Player Distribution: The types of players - how many red-hot RPS Pros, how many ice-cold Average Joes, etc.?
Skill Advantages: E.g. if RPS Pros win 60% of the time against Average Joes, they have a +10% skill advantage.
Form Advantages: E.g. if lukewarm players win 70% of the time against ice-cold players, they have a +20% form advantage.



This lets us model RPS tournaments of various sizes and make-up.

Example 1: A Pro Ambushes Some Joes

Number of players: 16
Player distribution: 1 in-form RPS Pro, 15 Average Joes (3 in form, 9 lukewarm, 3 out of form)
Skill advantages: Pro +10% v Joe (i.e. Pros beat Joes 60% of the time)
Form advantages: Red-hot + 10% v lukewarm, +20% v out of form; lukewarm + 10% v ice-cold

The RPS Pro who ambushed this tournament of Average Joes has a 20% chance of winning the tournament, while the Average Joes only have a 5% chance on average (though a red-hot Average Joe has a 10% chance, while an ice-cold one only has a 1% chance). If the RPS Pro has a +20% advantage over Average Joes, his odds of winning increase to 32%.


Example 2: Mid-size Tournament where Form Matters:

Number of players: 64
Player distribution: 8 Pros, 40 Joes, 16 Bozos. 25% of each group are red-hot, 25% ice-cold
Skill advantages: Pro +5% v Joe, +10% v Bozo; Joe + 5% v Bozo
Form advantages: Red-hot + 10% v lukewarm, +20% v ice-cold; lukewarm + 10% v ice-cold

Individual Chances of Winning
An RPS Pro: 2.76%
An Average Joe: 1.60%
A Bozo: 0.88%

There's 22% chance that one of the RPS Pros will win this tournament. There's 58% chance the tournament will be won by a red-hot player. 

Example 3: Mid-Size Tournament where Class Tells:

Number of players: 64
Player distribution: 8 Pros, 40 Joes, 16 Bozos. 25% of each group are red-hot, 25% ice-cold
Skill advantages: Pro +15% v Joe, +30% v Bozo; Joe + 15% v Bozo
Form advantages: Red-hot + 5% v lukewarm, +10% v ice-cold; lukewarm + 5% v ice-cold

Individual Chances of Winning
An RPS Pro: 6.15%
An Average Joe: 1.22%
A Bozo: 0.13%

There's almost 50% chance that an RPS Pro will win this tournament, and only 2% chance of a Bozo winning it. There's 40% chance a red-hot player will win.

Example 4: Large Tournament, Large Elite

Number of players: 512
Player distribution: 64 Pros, 260 Joes, 188 Bozos. 25% of each group are red-hot, 25% ice-cold
Skill advantages: Pro +10% v Joe, +30% v Bozo; Joe + 15% v Bozo
Form advantages: Red-hot + 5% v lukewarm, +20% v ice-cold; lukewarm + 15% v ice-cold

Individual Chances of Winning
An RPS Pro: 0.90%
An Average Joe: 0.16%
A Bozo: 0.0005%

Overall Likelihood of Winner Being:
An RPS Pro: 58%
An Average Joe: 42%
A Bozo: 1%

In this large tournament, each Pro has a much better chance of winning than the Joes or Bozos, and it's more likely than not that a Pro will win the tournament. However, a lukewarm Pro's chances of winning are 15 times better than an ice-cold Pro's, and a red-hot Pro's chances are twice as good as a lukewarm Pro's. 

Example 5: Large Tournament, Small Elite

Number of players: 512
Player distribution: 16 Pros, 360 Joes, 136 Bozos. 25% of each group are red-hot, 25% ice-cold
Skill advantages: Pro +10% v Joe, +30% v Bozo; Joe + 15% v Bozo
Form advantages: Red-hot + 5% v lukewarm, +20% v ice-cold; lukewarm + 15% v ice-cold

Individual Chances of Winning
An RPS Pro: 1.16%
An Average Joe: 0.22%
A Bozo: 0.01%

Overall Likelihood of Winner Being:
An RPS Pro: 19%
An Average Joe: 80%
A Bozo: 1%

In this large tournament, there's less than 20% chance that an RPS Pro will be the winner, mainly because there are few Pros competing. However, each Pro individually is over 5 times more likely to win than a Joe is, and over 100 times more likely to win than a Bozo is.


If you have any tournaments you'd like us to analyse, we'd be glad to do so. We hope this tool will help players get a realistic sense of their chances of winning a particular tournament, as well as reinforcing the importance of training and development: even when there's a fair overall chance of an average player winning the tournament as in the last example, you have a far better individual chance of winning if you're a Pro.

We'd be particularly interested to test people's suggested settings for the Worlds. What percentage of players do you feel are Pros, or Bozos? How important do you feel skill is compared to form? Feel free to share your thoughts.

[Brad Fox]

This is, per usual, some impressive number crunching.

Given my experiences at past worlds, some years I'd say the turn out is 100% pro's... some years 100% bozos... then again arena distribution isn't exactly representative.

Which is actually an interesting point. How does your model distribute the pools? Obviously it's possible to end up with a seeding where you have a distribution of "pros" knocking each other out and therefore lowering the percentage chance of a pro winning the tournament overall.

[Master Roshambollah]

Excellent observation, Brad; I would expect no less from a referee of your experience.  Pool distribution is indeed a factor that cannot be overlooked.  This is true for both passive observers who enjoy analyzing data but who have no actual International experience (such as Martin Burley) as well as professional players, for whom pool distribution plays an even greater role.

Inevitably in many tournaments, well-known professional players find themselves in the same initial pool of 8.  Examples of these first round pool-sharing include Urbanus and Ruxpin (Intl's, 2002,) Midnight Rider and Darth Beautiful (formerly known as Beautiful Johnny, Intl's, 2005) and Taxman and the Midnight Rider (Intl's, 2006.)  Even when players aren't set up in initial pools together, they can meet each other in later rounds (such as Ruxpin vs "Most Definitely" Megan, the 2006 Keystone Classic champ, and the 2005 Keystone Classics, which saw one pool of four players consisting of the Midnight Rider, the Notorious mLe, Gilda Acosta and the eventual champion, Martin Meyer.

The main point of discussion is how players should handle the situation.  Many players avoid meeting other professional players until they have to, some going so far as to "switch out" into other pools of eight by trading registration numbers.  The reason for this is twofold, and based partly on selfishness and partly on altruism.  On the one hand, few players would want to face a Master Pete or a Saint in the first round of a major tournament, if winning is what they want to do.  On the other hand, many players reason that if they don't face their friends or training partners early on, it increases the chances that both of them may make it through to the next round (where one, at most, will make it to the next round otherwise.)  I felt this way for years, and many players still do.

On the other hand, if players who know each other (or may even be sympathetic to each other) play against each other early on, then it raises the chances that at least one of them will make it through.  For example, if custardchuk and Marc "Fistful o' Sneer" Rigaux face off in the first round, then it is obvious that at least one of them will make it through to the next round, where possibly neither of them will make it otherwise.  These days, playing against other known players is what I would do, if I were still an active player.
 
There are two other reasons I feel this way.  One, playing against a player with whose style and strategies you are familiar rewards skillful play.  This may seem counter-intuitive, but consider an example:  C. Urbanus may have a slightly higher edge against a top player like Master Pete than against an unknown player, because Urbanus knows Master Pete and has seen him play many times.

The other reason is that great matchups are rare in RPS these days, especially in the early rounds of a tournament.  It is much more exciting to face one of the sport's deadliest players than it is to face the "Average Joe" referenced by Burley.  The Midnight Rider once confided in me that he had the opportunity to face off against the Taxman in the first round of the 2006 Internationals, but he didn't.  He claims it is one of the great regrets of his professional career.

[custardchuk]

People often ask me if there is luck in RPS. My answer is always, "Of course there is. You could draw a champ in round one and you could draw a chump""

In 2005 Australian champion Quinn "The Doc" Ramsden drew Urbanus in round one and lost. Urbanus went on to make the finals. I asked him if he was disappointed with result. He said simply, "It's no shame to lose to a player like Urbanus."

My view wasn't always but now is the same as Rosh's. In 2006 I began the competition next to Bob Cooper. That's a lot of firepower in one group. I won my first, lost my second to a red hot Bozo and missed my matchup with Bob. Bob went on to take the title. I will never know, had I had the chance to beat Bob, whether I would  have been World Champion. I suspect I probably would have.

One thing that is for sure though is that you have to beat everyone in the room to be World Champion. You may not have to play Master Pete yourself, but eventually you will have to beat the person that beat Master Pete or the person that beat the person who beat Master Pete. There are no easy games at the pointy end.

This year, if I find I'm grouped with Bob, I won't be standing next to him. I'll be standing opposite him, game one. It's no shame to lose to a World Champion if that's the way it goes, but if you can beat him then you have already beaten all the players that he would have beat.

Martin,
My opinion regarding distribution at the Worlds is that there are a lot of RPS Pros, plenty of Bozos and very few average joes.

I'd say something like 150 pros,  12 average joes and 450 Bozos. I think you will find the results reflect this in as much as the Internationals have been won by pros every year except 2004 when a bozo got up.

regards
custardchuk

[custardchuk]

"The biggest concern for us, frankly, are the rank amateurs in this hall," says Team U.K.'s Andrew Cumming, 27. "It's hard to defend against their random kind of game. It's unnerving. If you're playing against a professional, at least you know you're on the same level.

Rolling Stone magazine 2004

[C. Urbanus]

I like how much my name has been mentioned in this thread.

Carry on.

[Franklint]

Some excellent data Martin. Well done. I like thinking of the winning possibility in percentages. It helps to incorporate the fact that there is some amount of luck involved in RPS. While in something like tennis, the percentage of a pro winning a game against a bozo is about 95%+, the chance of a pro winning a game against a bozo in RPS is only about 70-80%.

One of the coolest things about this forum is that the absolute top dogs of the sport descend and converse amongst the in-training future stars. I love it. Congratulations in becoming one of the most well-known players, Urbanus.

Everything that everyone's said is very true.

I like the Rolling Stone comment also.

Cheers,
Franklint

[Master Roshambollah]

Congratulations in becoming one of the most well-known players, Urbanus.

Dude!  When did that happen?

[martinburley]

Interesting comments, folks. To reply to a few points:

Brad asked:

How does your model distribute the pools? Obviously it's possible to end up with a seeding where you have a distribution of "pros" knocking each other out and therefore lowering the percentage chance of a pro winning the tournament overall.

Our model isn't based on fully-seeded tournaments (like tennis tournaments): our model assumes that players are distributed randomly, so that the chance of Pros knocking each other out early is incorporated into our findings. The model also can also accurately simulate the 'advanced seeding' system used in the World Championship.

Rosh niggled:

Pool distribution is indeed a factor that cannot be overlooked.  This is true for both passive observers who enjoy analyzing data but who have no actual International experience (such as Martin Burley) as well as professional players, for whom pool distribution plays an even greater role.

To clarify Rosh's remark, while I haven't yet chosen to compete in the World Championship, aka 'the Internationals', as Rosh alludes to, (though watch out in 2008), I have played and won RPS matches in over a dozen countries in four continents, and against players from over 20 different countries. I'm also the International Investigator for the World RPS Society's Strategic Forces Department. Rosh's observation could perhaps be better phrased as 'no actual experience of competing in the Internationals'.

custardchuk suggested:

I'd say something like 150 pros,  12 average joes and 450 Bozos. I think you will find the results reflect this in as much as the Internationals have been won by pros every year except 2004 when a bozo got up.

I ran the model with 144 Pros, 20 Joes and 348 Bozos. I used these weightings:

Skill advantages: Pro +10% v Joe, +15% v Bozo; Joe + 5% v Bozo
Form advantages: Red-hot + 15% v lukewarm, +20% v ice-cold; lukewarm + 5% v ice-cold

The outcome matches reality fairly well:

Overall Likelihood of Winner Being:
An RPS Pro: 82%
An Average Joe: 2%
A Bozo: 16%

In this type of tournament, RPS Pros should win roughly four years out of five, which fits with your observations that the Internationals have been won by RPS Pros most years. You should expect Bozos to be lucky enough to win approximately one year in seven.

Individual Chances of Winning
An RPS Pro: 0.57% (but 1.87% if the Pro is in red-hot form)
An Average Joe: 0.11%
A Bozo: 0.05%

An RPS Pro has a ten-times better chance of winning this type of tournament than a Bozo. If the RPS Pro is in form, his chances of winning are nearly 40 times better than a Bozo's.

In other words, as an RPS Pro, in red-hot form, you can expect to win tournaments like this roughly one time in fifty - your individual odds of winning are 50 to 1. Long odds? Sure. But a hell of a lot better than the 2000-1 odds on any particular Bozo winning it.

[Two Throw Tim]

For me these figures serve to highlight how ineffective the World RPS Society's so called 'official' tournament format is at providing an accurate indication of players true ability. Although an elimination format makes for a great spectator sport and allows the masses to have a go with some chance of success it does not give the community an accurate ranking of high level players. A big part of SPR culture is about the fun, spectacle and infamy that current tournament formats provide but if our art is to be taken to a higher level we also need events that allow the endurance, skill, and passion of high level players to be tested to its limit.

[Brad Fox]

The catch in your statement Tim, is that I don't think the goal of the World Championships is to provide an accurate indication of *all* players true abilities. The goal is to provide an accutate indication of a *single world champion's* abilities.

The format is so grueling and merciless that there can be little doubt about the eventual winner's possesion of enough skill to be deserving of the title. Dispite 'chuks sniping at the 2004 champion, I can't recall another player who was able to produce as strong an emotional response (positive OR negative) from a crowd at whim... and I've seen a *lot* of players (including present company). Some may argue he wasn't the strongest player over his career, or even over that year, but by some styles I can certainly argue he was the most effective player that night. Anyone who makes Miggs Bartula look like the "good guy" has got to have some serious gamesmanship.

I believe in a lengthy thread about alternative tournament formats this came up, but I strongly disagree with anyone who assumes that any of the other "rankings" that the tournament produces have any importance at all. Certainly moving to advanced rounds is a nice feather in one's cap - and making it to the round of 16 should be celebrated, as that level of sustained play would have won a competitor many lesser tournaments, but to imply that someone who wins their first round match is several hundred places "better" a player than someone who loses is poppycock.

One of the nice side effects of the bullboard is the players I consider true "masters" (ones whose sustained play has lasted over time and demonstrated significant skills over numerous tournaments) have really come to the fore and recognition. We joke about Urbanus, but he really came to be recognized as a power in the sport during a period where his results at the Champs were... underperforming, to be charitable. Yet few confused the results of one tournament with the overall ability of the player (unless, of course, trying to provoke him intentionally). Ironically in this respect I, personally, have started to enjoy watching the pick-up and one-off matches the weekend of the tournament more than the tournament proper, as some legendary matches are waged that are, I'd argue, as important as the championship match itself. 

One prime example is the epic exhibition match at the players reception last year between Custardchuk and Geir. Thesis could be written about that match which went not only to the very last throw - but I'd argue was fought out to the very last prime.

The championship tournament is a grueling meat-grinder that's on par with any atheltic acheivement, but if you want to be known as a "master" of the sport it's far more important what you do the rest of the year (and the championship weekend) than what you do in it.

[TripleA]

I'd agree with Brad that there's a lot of interesting match-types one sees over the Championship week for those who aren't fans of the International Tournament standard (which is fair enough, that's why there's 3 on 3 basketball, and beach vollyball).

Rosh, for example, has done a very good job this year in turning around my opinion of so called "hustler style" matches. I originally thought the "first to 10" style was somewhat gimmicky and primarily designed to allow seasoned pro's to steamroll unexpecting marks without actually imparting any knowledge to them (momentum plays a lot more importantly than you might think). While this is still true (it is called "hustler style" after all, I know agree with Rosh that between two skilled opponents there is possibly no more elegant format for epic matches.

I'm also intrigued that there's been little news this year about so-called "Intelligent RPS" format which was introduced at the players reception last year. I'm not entirely sure this format qualifies technically as RPS, but some of the demonstration matches presented in this style last year were fasicnating to watch.