1/ Musings about variance in trading, in sports, and in life.
A thread.
A thread.
2/ Why does poker get played for big $ but chess (mostly) doesn’t?
Because of variance.
In chess, if you’re rated 1800 ELO and you’re playing someone rated 2000, you pretty much know exactly your P(win) and P(tie). (It’s 15% and 19%, go check).
Because of variance.
In chess, if you’re rated 1800 ELO and you’re playing someone rated 2000, you pretty much know exactly your P(win) and P(tie). (It’s 15% and 19%, go check).
3/ There’s no sense in betting for two reasons:
- A wide spread of ability directly creates wide spread in outcome. A 2400 will NEVER lose to an 1800.
- All these probs are pretty much known. $ gets traded when people disagree about probs. No such thing exists in chess.
- A wide spread of ability directly creates wide spread in outcome. A 2400 will NEVER lose to an 1800.
- All these probs are pretty much known. $ gets traded when people disagree about probs. No such thing exists in chess.
4/ In poker, the variance is huge. Even if there’s a large spread in ability, the bad player still wins enough, on timescales that matter (days, weeks).
That’s what gambling is.
That’s what gambling is.
5/ Lots of people misunderstand what gambling is about.
Why aren’t there any coin-flipping tournaments for a million dollars? It’s plenty of variance right?
Why aren’t there any coin-flipping tournaments for a million dollars? It’s plenty of variance right?
6/ Because everyone knows P(heads) is 50%. That makes it boring.
When everyone agrees on probs, no one wants to gamble for real $.
People who know and understand the probs of slot machines don’t play them. People who don’t know or try to forget these probs do play slots.
When everyone agrees on probs, no one wants to gamble for real $.
People who know and understand the probs of slot machines don’t play them. People who don’t know or try to forget these probs do play slots.
7/ This is precisely what you see in trading.
Trading is the expression of disagreement about probabilities.
Trading is the expression of disagreement about probabilities.
8/ I decided to write this thread after seeing @LouStagner claim (correctly I’m quite sure) that match play doesn’t identify the best player that week nearly as well as stroke play.
9/ Yes that’s true.
But match play is more fun (as a rare event) because it has more outcomes and variance.
And in sports, high variance and disagreements about probabilities are very strongly connected (unlike with a coin flip).
But match play is more fun (as a rare event) because it has more outcomes and variance.
And in sports, high variance and disagreements about probabilities are very strongly connected (unlike with a coin flip).
10/ The thing that spectator sports are always optimizing for is having the right amount of variance.
11/ Too little var is boring. The same person/team winning every single time makes people turn away.
12/ Too much var is confusing.
If every baseball team had a .500 record, that would SUCK!
If the winningest player on the PGATour only won twice a year, that would be awful. People like *some* amount of predictability.
If every baseball team had a .500 record, that would SUCK!
If the winningest player on the PGATour only won twice a year, that would be awful. People like *some* amount of predictability.
13/ When Tiger Woods was dominating, a big part of the reason he drew people to the game is because his dominance pushed golf towards the optimal amount of variance.
Golf is a VERY high variance game. And his dominance (winning ~ half the time) was perfect for the casual fan.
Golf is a VERY high variance game. And his dominance (winning ~ half the time) was perfect for the casual fan.
14/ Why isn’t tennis scoring just one long game to 200 points or something? Because the better player will win basically 100% of the time.
Once the score gets to 120-90, the game just becomes an exercise in score management. Zzzz.
Games and sets are a way to increase var.
Once the score gets to 120-90, the game just becomes an exercise in score management. Zzzz.
Games and sets are a way to increase var.
15/ Remember Daytona 500 the video game?
When you were behind in a race, the game gave your car superpowers. So that you could catch up and make the race more exciting.
When you were behind in a race, the game gave your car superpowers. So that you could catch up and make the race more exciting.
16/ Back to poker. The forms of poker that persist over time are the ones that find the optimal amount of variance to make the game.
17/ If good players win all the time, the game dies. Fish lose money too fast.
If it’s too random, the game dies too. Pros don’t have an incentive to sit there and make the game during slow times.
It’s a balance. Optimal variance rules the world.
/END
If it’s too random, the game dies too. Pros don’t have an incentive to sit there and make the game during slow times.
It’s a balance. Optimal variance rules the world.
/END
18/ Following up on the tennis thing, I modeled the game assuming every point is the same (i.e. serving doesn't matter) and independent. 
19/ The x-axis is P(win point) and the curves are win probabilities for game, set, match and hypothetical 101pt and 201pt single-game matches.
Basically if you're 55% to win a point, then you're 95% to win a best-of-5 match.
Basically if you're 55% to win a point, then you're 95% to win a best-of-5 match.
20/ The best-of-5 curve is pretty similar to that 201pt hypothetical match.
But as @wait4thegoodlif and I were discussing yesterday, the multi-set match creates more inflection points, i.e. a subset of points which have a large effect on the match.
And hence more excitement.
But as @wait4thegoodlif and I were discussing yesterday, the multi-set match creates more inflection points, i.e. a subset of points which have a large effect on the match.
And hence more excitement.
21/ Just like match play does in golf. There is a higher variance in how much a random point or shot matters to the outcome, and that manufactures excitement.
Baseball's awesome at this. Most pitches don't matter, but bases loaded 3-2 counts are super exciting.
Baseball's awesome at this. Most pitches don't matter, but bases loaded 3-2 counts are super exciting.
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