This may help some: 
Aaron Brown's NFL Sports Betting System.
- Thread starter TheBigShort
- Start date
Why aren't YOU betting sports? The kid could teach you.
good question - I never thought about it... prolly because at this point it won't make any difference in my lifestyle and I am never interested in basketball.
his parents were against in the beginning, but now he's teaching his dad lol.... and also a kid of similar age.
I'd still rather be the house when it comes to gambling. There are guys like this that can work it, but so many more that just love handing over their money. Long before trading I worked with a guy who was a bookie. He'd take me to lunch now and again and invariably it would involve picking up money from someone. Two different times I recognized the people handing over the envelope. One was a former big league ball player who was a real estate agent after retiring, and the other a musician of local note and a certain amount of national/international note.
The bookie friend, he retired at 38, he's 55 now, and is one of the better amateur golfers in the state. He also does his own investing, and has done very well on that end also. The former ball player, while not broke or anything is still plugging away at real estate, he's got to be 65-70 now. The musician is doing the get the band back together thing and hitting small venues and state fairs, I'm sure that's a blast. He is also 65-70 range.
I'll take the house.
The bookie friend, he retired at 38, he's 55 now, and is one of the better amateur golfers in the state. He also does his own investing, and has done very well on that end also. The former ball player, while not broke or anything is still plugging away at real estate, he's got to be 65-70 now. The musician is doing the get the band back together thing and hitting small venues and state fairs, I'm sure that's a blast. He is also 65-70 range.
I'll take the house.
I thought this post from cross validated pairs well with finding weak predictor variables. In it, whubber and others go in depth on patterns they see on a plot that looks like it has no relationship! I highly recommend you read it.
https://stats.stackexchange.com/que...ip-between-y-and-x-in-this-plot/114620#114620
https://stats.stackexchange.com/que...ip-between-y-and-x-in-this-plot/114620#114620
Here's a non-sports example of pure shrinkage.
A statistics professor instructs each student in the class to pick something that is unknown today, but will be known for sure next week, and to predict it. Students can pick anything--the high temperature in Central Park on Sunday, the closing Dow Jones Industrial Average on Friday, the number of parking tickets issued by campus police during the week, whatever.
The professor bets that whichever predicted number is the largest will be an overprediction, that is will be higher than the actual value; and that whichever predicted number is the smallest will be an underestimate, the actual value will be higher. She will win each bet more than 50% of the time. You can try this and see.
The reason is that each prediction will have an error, and the predictions with positive error (the overestimates) are more likely to be the highest number predicted, while the predictions with negative errors are more likely to be the lowest number predicted. Even though the range of predictions is very wide, and the predictions are independent of each other concerning independent events, this logic holds.
The mathematical version was first proved in a famous 1956 paper, Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution. If you are estimating the mean of three or more variables, you do better to shrink the estimates toward the mean of all variables--even if the variables are unrelated to each other.
In addition to the purely mathematical shrinkage effect, when you are predicting related things there is a causal reason to shrink. If the professor gives a test to the entire class, it's likely that the highest scoring student did better than her expectation on a repeat test, and the lowest scoring student did worse than her expectation. This is often confused with both regression to the mean and reversion to the mean (which are often confused with each other) but it is conceptually different.
As to specific questions, yes, it's possible for noise to be negative. Think of it this way. Suppose the true point spreads that would make each game a 50/50 proposition are uniformly distributed with one game at -7 for the home team, one at -6, and so up up to +7. Also assume that the bookmakers err by 1 for each game, equally likely to add or subtract 1. Half the time the lowest spread will be -8, an underestimate, because the -7 spread had a -1 error. One time in four the lowest spread will be -7, because the -7 game had a +1 error and the -6 game had a -1 error; again an underestimate. So 75% of the time, the lowest spread will be an underestimate. For the lowest spread to be an overestimate, the -7 and -6 games must both have +1 errors, which only happens 25% of the time.
Obviously this is oversimplified, but the same principle applies when you add symmetric noise to true values.
A statistics professor instructs each student in the class to pick something that is unknown today, but will be known for sure next week, and to predict it. Students can pick anything--the high temperature in Central Park on Sunday, the closing Dow Jones Industrial Average on Friday, the number of parking tickets issued by campus police during the week, whatever.
The professor bets that whichever predicted number is the largest will be an overprediction, that is will be higher than the actual value; and that whichever predicted number is the smallest will be an underestimate, the actual value will be higher. She will win each bet more than 50% of the time. You can try this and see.
The reason is that each prediction will have an error, and the predictions with positive error (the overestimates) are more likely to be the highest number predicted, while the predictions with negative errors are more likely to be the lowest number predicted. Even though the range of predictions is very wide, and the predictions are independent of each other concerning independent events, this logic holds.
The mathematical version was first proved in a famous 1956 paper, Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution. If you are estimating the mean of three or more variables, you do better to shrink the estimates toward the mean of all variables--even if the variables are unrelated to each other.
In addition to the purely mathematical shrinkage effect, when you are predicting related things there is a causal reason to shrink. If the professor gives a test to the entire class, it's likely that the highest scoring student did better than her expectation on a repeat test, and the lowest scoring student did worse than her expectation. This is often confused with both regression to the mean and reversion to the mean (which are often confused with each other) but it is conceptually different.
As to specific questions, yes, it's possible for noise to be negative. Think of it this way. Suppose the true point spreads that would make each game a 50/50 proposition are uniformly distributed with one game at -7 for the home team, one at -6, and so up up to +7. Also assume that the bookmakers err by 1 for each game, equally likely to add or subtract 1. Half the time the lowest spread will be -8, an underestimate, because the -7 spread had a -1 error. One time in four the lowest spread will be -7, because the -7 game had a +1 error and the -6 game had a -1 error; again an underestimate. So 75% of the time, the lowest spread will be an underestimate. For the lowest spread to be an overestimate, the -7 and -6 games must both have +1 errors, which only happens 25% of the time.
Obviously this is oversimplified, but the same principle applies when you add symmetric noise to true values.
Thanks for the response Aaron.
Unfortunately, your answers are so well explained that its hard to ask any follow up questions!
In your example it made sense to buy the lowest spread and sell the highest spread in the NFL. How would your strategy change if we traded in multiple sports games? For example, if the lowest NFL spread was -7 but the CFL lowest spreads were -8 and - 9, would you be more inclined to buy the two CFL spreads or the lowest spread from each league?
Here is a problem I face when selling vol around earnings. Let's say we break the market up into sectors. The consumer staples sector has an average earnings implied move of 2% with Walmart being the highest at a 4% implied move. The tech sector has and average implied move of 7% with NFLX and SHOP being the highest at an 11% implied move. Should I be more inclined to sell options on the over-all highest implied moves (SHOP, NFLX) or should I be selling options on the over-all highest implied move in each sector(WMT, NFLX)? I am looking at this problem from a multi-level/partial pooling perspective.
Thanks Aaron.
You touch on some of the subtleties of shrinkage. It is a mathematical curiosity that you can improve estimates using completely unrelated information. But the practical effect is small. It's related to Hempel's paradox.
If you want to investigate whether or not all ravens are black, you look for ravens and if they're black, you have a confirming instance. But logically your hypothesis is equivalent to, "All non-black things are not ravens." So you could more easily look around the room you're in--far from any ravens--and count all the non-black items that are not ravens as confirming instances. While this is logically correct, there are vastly more non-black things than ravens, so the method of investigation is impractically weak. Similarly, shrinking things with no possible connection at arbitrary scales does not lead to useful improvements in estimators.
In your case, CFL spreads might have enough relation to NFL spreads that you got some advantage from the method. A clear example is one of the early empirical demonstrations of shrinkage was estimating the batting averages of major league players in the second half of the season from their first-half batting averages. If you shrink all the first half averages toward the league average, you get better estimates. Then Ed George showed that if you instead shrink toward the average for each positions (all outfielders to the mean for all outfielders, all first basemen to the mean for all first basemen, and so on) you do even better. So the more related your measurements are, the more benefit from shrinkage.
In practical decisions like your earnings example, you have to both think through the issue and consult the data. There are many factors that can cause over-reaction or under-reaction. The over-reaction that I exploit in the NFL betting is not just the mathematical shrinkage effect. There are also psychological biases like recency that lead to over-reaction, both of bookmakers and the public bettors the bookmakers are trying to predict, and business reasons involved.
I look for over-reaction in the data, but if it's not there, I don't use it. But over-reaction is so common in so many similar situations, and there are theoretical reasons to expect it, so I will trust it on slimmer evidence than I would require for some random and inexplicable pattern.
The answer to your earnings question is ultimately empirical. You might find that it works best to sell the highest vol, or the highest vol per sector, or the highest vol relative to non-earnings vol, or the highest vol relative to average earnings vol for the same stock; or something else. Over-reaction could work on any or all of those levels. My guess, and it's only a guess, is that the most relevant would be high relative to average earnings vol for the same stock, as this is the factor I think is most likely to be adjusted by humans for market-clearing reasons, rather than by systematic algorithms for profit reasons.
If you want to investigate whether or not all ravens are black, you look for ravens and if they're black, you have a confirming instance. But logically your hypothesis is equivalent to, "All non-black things are not ravens." So you could more easily look around the room you're in--far from any ravens--and count all the non-black items that are not ravens as confirming instances. While this is logically correct, there are vastly more non-black things than ravens, so the method of investigation is impractically weak. Similarly, shrinking things with no possible connection at arbitrary scales does not lead to useful improvements in estimators.
In your case, CFL spreads might have enough relation to NFL spreads that you got some advantage from the method. A clear example is one of the early empirical demonstrations of shrinkage was estimating the batting averages of major league players in the second half of the season from their first-half batting averages. If you shrink all the first half averages toward the league average, you get better estimates. Then Ed George showed that if you instead shrink toward the average for each positions (all outfielders to the mean for all outfielders, all first basemen to the mean for all first basemen, and so on) you do even better. So the more related your measurements are, the more benefit from shrinkage.
In practical decisions like your earnings example, you have to both think through the issue and consult the data. There are many factors that can cause over-reaction or under-reaction. The over-reaction that I exploit in the NFL betting is not just the mathematical shrinkage effect. There are also psychological biases like recency that lead to over-reaction, both of bookmakers and the public bettors the bookmakers are trying to predict, and business reasons involved.
I look for over-reaction in the data, but if it's not there, I don't use it. But over-reaction is so common in so many similar situations, and there are theoretical reasons to expect it, so I will trust it on slimmer evidence than I would require for some random and inexplicable pattern.
The answer to your earnings question is ultimately empirical. You might find that it works best to sell the highest vol, or the highest vol per sector, or the highest vol relative to non-earnings vol, or the highest vol relative to average earnings vol for the same stock; or something else. Over-reaction could work on any or all of those levels. My guess, and it's only a guess, is that the most relevant would be high relative to average earnings vol for the same stock, as this is the factor I think is most likely to be adjusted by humans for market-clearing reasons, rather than by systematic algorithms for profit reasons.
SteveM said:
I respectfully disagree with both. There's more honesty and fair play among gamblers than among Wall Street dealers. And both Wall Street and the sports gambling business are highly evolved systems making it difficult for outsiders to pull money out. Setting accurate securities prices and betting spreads is only one of many defenses, and it's not done particularly well by either system. Simple quant methods without much domain knowledge can easily find more accurate prices and sporting event probabilities. But using that to extract value is like surviving in the jungle--getting enough food for yourself without becoming food for some other creature.
If a naive data person shows up on Wall Street with a winning system, she will find no one will take her bets. If she does manage to get someone to do it--probably by giving away a lot of her profits--she will find that she doesn't get paid as she should. If she does manage to get paid, she will find she has awakened other defenses.
Some people do manage to navigate all this to success, but the easier way is to figure out how to make your system help enough insider entities to make it worth their while to pay your winnings. In the case of sports betting, a common method is to place very early bets with bookies that give them information to refine their spreads before the big bets come in shortly before the match. Another method identifies imbalances such that bookies are happy to let you make positive expected value bets that reduce the bookies' risk.
In the case of Wall Street, the most common method is to raise enough money from investors to generate enough fees to cover your winnings. Of course, that means your investors do not get the benefit of your skill. Another common method is to identify market participants who are willing to write you checks consistently because you lower their risk or provide them some other benefit.