Tuesday, January 20, 2009

A Primer on Two Coefficient-Based Sports Betting Strategies

This piece looks at whether or not it is beneficial to an individual sports bettor to use an exclusively extreme favorites or an exclusively extreme underdog system in betting.
Please note that I DO NOT BET on sports, and all information here is for entertainment purposes only, and comes with no warranty.

Here are some basics to ensure that everyone is starting off on the same page.
Why is sports betting interesting?
How does sports betting compare to other forms of gaming?
Odds systems
The two strategies defined
The data collection and the sample
Conclusion

Why is sports betting interesting?

I am not a sports fan, and I do not remember the last time I watched a game of any kind, to be honest. But since sports betting is a game of skill, I figured I’d take a look at a couple of basic strategies that a non-expert could use. You have to remember that the outcome of the event is not mathematically determined (despite the abundance of “statistics”) which means that there is no mathematically pre-defined house edge. If someone really thinks that buying a lottery ticket or going to a casino is a positive NPV transaction, this person should take a remedial math class and read up the information on “The Wizard of Odds”, a highly informative site. Just FYI, the house edge on most of the casino games listed there seems to be 1%-20%. Another FYI, the house edge on the NY State Lottery, per their site, is 40%+ (only 52.7% paid out). The only way to consistently make money at a place like this is to play against other people, and be better than them.

I was also interested in the fact that sports betting is not correlated to other financial transactions with uncertain outcomes, possibly providing a diversification benefit. In addition, after reading The Black Swan, in which Taleb discusses purchases of far out-of-the-money options, I began to view sports betting as a form of a short-dated option, just with a binary (in some cases) outcome. Keep in mind that since the basic wager is the same, betting on the sure thing will produce a miniscule payout if true, or, alternatively, result in an unlikely and large loss (so you are short a put on the favorite in a way).

Selling puts works fine most of the time: you just collect your premiums until one day you get a volatility surprise and you lose it all. I strongly recommend reading Andrew Lo’s piece on a fund called CDP, which was selling put options from the 1990’s to 2000 with spectacular success. CDP, by the way, stands for Capital Decimation Partners. The opposite side, betting on the highly unlikely underdog, means you are long some really out of the money option and you are bound to lose most of the time, and hope to hit it big time on enough occasions to make up the losses. Also, with options you lose 100% of the premium, just like you’d lose 100% of your bet.

So there it is: playing the favorites is selling volatility, betting on the underdog is going long volatility. I will be more precise in my definitions of favorite and underdog further below. I really should be saying “overwhelming favorites” but this is too long to type.

How does sports betting compare to other forms of gaming?

As I already mentioned above, with mathematical games, the average outcome is predetermined. You stand to lose over the long run. This is how casinos stay in business and state lotteries function. Mathematical games (this includes card games) should be played only against other people with very few exceptions where a player can have an edge (i.e. professional counters). Most other people should just look for other forms of entertainment. Or take their Vegas trip budget and buy lots of liquid OTM options.

The house does not determine the outcome of the sporting event. It only determines the odds. This means that an exceptionally skilled player, a true expert (think coaches, experienced players), can actually be ahead. The rest of us should probably stick to a simpler strategy. Just because some expert on ESPN tells you that Oklahoma has never won at Texas if the game is played in the 7 days after a full moon does not mean that the info is relevant.

Within sports betting, there are various ways to bet. I look at a very simple win or lose outcome. I do not think that point spreads or handicaps are even remotely possible for a non-expert to master. As you know, the spread is popular with high-scoring games (basketball, American football). My view is that a team plays for the win, not for the spread, and as such, I would prefer to bet on the overall outcome, rather than the spread. If basketball team is well-above the spread in the beginning of the 4th quarter, guess what, they won’t go for a blow-out. They will have an all-bench team whittle down some of the difference while the starters rest. What makes sense from a team perspective does not make sense from your perspective as a bettor for this team! This risk can be avoided if you bet on the outcome.

Odds Systems

There are two systems that I will touch upon. One is the standard US system, with a +/-, also known as a moneyline. It works like this: the - is the money you bet on the favorite to win 100, and the + is the money you get if you bet 100 on the underdog. So a -250/ +400 bet would be bet 250 to get 350 total back, or bet 100 to get 500 total back.
I personally do not like the moneyline system: I prefer seeing outcomes on a like-for-like basis. So, enter the coefficient system. The coefficient is simply a multiplier that is applied to your bet, if you win. So, in the example above, 350/250=1.40 and 500/100=5.00. I find 1.40/5.00 much easier to compare.

There are a couple of other pertinent points.
In Europe, the home team is listed first.
A home team win is designated as “1”, a draw as “X” and a visitor win is a “2”. What this means is that in games like soccer, betting for the underdog means buying both the X and the 2 option: this requires twice the capital.
American sports rarely end is a draw: culturally unacceptable probably. Someone remarked once “a draw is like kissing your sister: you really do not feel ahead”.

The Strategies Defined

I tracked two separate strategies. One is bet on the extreme favorites. I define “extreme” by betting on teams with coefficients of 1.10 or lower. These are the highly likely outcomes.
The second strategy is the mirror image of the first: short the favorite, be long volatility, or whatever you want to call it.
Now keep in mind that the outcomes are not mirror images from the player’s perspective because the house sets the odds.
I wanted to see if “slow and steady” wins the race, or may be the Black Swan does, or may be neither. But there has to be either sufficient payouts from those black swans or enough periods of low volatility to help you earn more than you’d almost certainly lose sooner or later betting on the favorites.

Also, the way I see the bet on favorites is in terms of safety of your principal. A successful strategy would mean that you can safely double your initial capital, set aside your original principal, and play from then on only with the winnings. This is hard to do. If you keep all of your money in (meaning you do not set anything aside), at a coefficient of 1.03, you’d need to win 24 consecutive games. At 1.01, it is a dreadful 70 games and at 1.05, it is 15 games. Behold the power of exponents. The goal really is capital preservation.

There are two ways to bet: keep our winnings in the game, and bet consecutive games, or start with a ton of 1-units, and bet on single games, with no compounding.
In this "study", I use the latter: simply bet 1 on the particular outcome without re-betting the "new" amount. This is the more practical approach, as there might be several suitable (extreme favorites/extreme underdogs) games at the same time.

The Data Collection and the Sample

I used data from Interwetten, one of the major houses in Europe, and every week or so, I went through their entire book (all sports), and wrote down the games and the odds that fit the criteria. I later checked the site for the results. Since I did all of this manually (I doubt they’d provide the data to anyone), so there might be errors. I also abbreviated some team names, and may not always be consistent in my abbreviations.

There is something else worth noting: the vast majority of the games are not soccer. I think this is because the national leagues and the international tournaments have been gradually changing the rules, and making the weaker teams eliminate each other for the most part early on in the tournaments, with the best teams coming in later on. THIS DECREASES THE LIKELHOOD OF HAVING EXTREME FAVORITES. The national championships all have a relegation system, ensuring that complete outsiders never play against the elite 16-20 teams. This also decreases the likelihood of having extreme favorites.

At the current stage in the tournament set-ups, the only ways to have a “good”- in my view- game is either having some lucky 3rd division team advance in a direct-elimination cup tournament, or bet on world cup qualifiers, in which the world powers (Germany, Italy, England, France) play against some non-team (Andorra, San Marino, etc.).

On the other hand, random sports, such as handball or volleyball, provide plenty of such “good” games as there might well be only one professional league in the country and a newly promoted team is still largely at the amateur level of play.

Also worth noting is that a 1.01 coefficient in soccer is rarely the equivalent of 1.01 in, say, volleyball. The 1.01 in soccer is Germany vs. Lichtenstein, something most people would not bet against (ex-last minute heavy snowfall or something). The x2 coefficients on a 1.01 could be 15.00 and 30.00.
On the other hand, in volleyball, the 1/2 coefficients are 1.01/10.00.

Technical specs:
Sample size 166 games, 147 non-soccer, 19 soccer.
Time frame: September 06, 2008, to November 05, 2008
Descriptive: mostly European, sports include soccer, handball, volleyball, basketball, Australian rules football, rugby, water polo, tennis, table tennis.

Conclusion

As you would expect, both strategies lose money. The “favorites” strategy would have required 166 units of betting but resulted in 144.21 in payouts. The “short the favorites” strategy required 262 units (remember that to short the favorite, you need to bet on the the X if needed), and resulted in a paltry 184.00 in payouts.
This means a loss of 15.5% for the “favorites” strategy over the time period, and a loss of 29.8% for the “underdog” strategy. Since the observation took place over 2 month, the annualized rates of these losses (1+result to the sixth-1) are negative 63.7% and negative 88.0% for the two strategies.

These are truly dreadful results that imply that risk (=coefficients) is substantially mispriced when you bet against the house, even when the outcomes are not mathematically controlled. On one particular soccer game, I checked a peer-to-peer site, and the underdog was at 70x, versus only 22x for the house. This evidences that the house is actively reducing tail risk by simply setting its high coefficients much lower than a true market would imply. The favorite numbers were very close b/n the house and the p2p site. The house also limits max payouts, max bets, and similar.

My conclusion is that a better venue for testing these strategies would be a true marketplace with numerous participants who price out the risk independently. I know of only one site that does just this: their operating model is similar to InTrade but I am not otherwise familiar with them. BTW InTrade is a good idea but liquidity is questionable and transaction costs are extraordinarily burdensome.

Update on Shorting the Government

When I wrote the post, TBT had closed at $35.85 (12/30). It shot up to $42 and change in a few short days. Not bad annualized. Somehow, intuitively, I think it might be too early to jump in. The S&P has some ways to go down which theoretically should bring TBT lower in price again as risk aversion reappears.