TWL White Paper: Options, the Greeks and Sports Betting.

 

How to Navigate the Structure of a Probability Priced Sports Betting Exchange Platform by Using Options Theory/Application and Greek Risk Variables

A probability based sports betting exchange is predicated on the buying and selling of probabilities (just like it sounds) of pre-game/contracts and in-game/contracts. A "sports bet" is the same as an options contract and is composed of underlying price (the score of the game), the strike price of the option (the point spread or total of the game depending on the bet), the time remaining in the contract (time left in the game, half, etc.) and implied volatility (the total expected scoring remaining in the contract). From this point forward, the contracts will be referred to as "the game" (obviously there are also bets to be made on halves of games, quarters of games, etc. just as there are weekly, monthly, quarterly and LEAPs options and the same adjustments would be applied).

It is very important to understand that the probability/Delta structured "sports betting exchanges" are NOT structured as "trade sports like stocks", as you might have heard advertised. They ARE structured as "trade sports like options". Stocks only have a price component. They DO NOT have the components of probability, volatility and time. Options contracts have all the components of price, probability, volatility and time. Sports "betting" contracts also have all the components of price, probability, volatility and time.

A probability based sports betting exchange operates under the same principles as the "Delta" Greek risk variable in options trading. There are 3 definitions for Delta in options trading. 

1) Hedge Ratio 

2) Percent change in the price of the option relative to price change in the underlying instrument 

3) Percent chance of the option finishing "In the Money" (That means that "the bet" wins if the option was bought and the bet loses if the option was sold. It is opposite if the option finishes "Out of the Money". That means that "the bet" loses if the option was bought and the bet wins if the option was sold). The Delta definition that is relevant for the probability based sports betting exchange is #3.

As the game goes on, there are 3 variables that can affect the Delta/probability of the bet winning/losing/finishing In The Money/finishing Out of the Money. Those variables are 1) the changes in the score (represented by the options Greek risk variable "Gamma"), 2) the passage of time in the game (represented by the options Greek risk variable "Theta") and 3) changes in the expected scoring to take place for the ret of the game (also known as "implied volatility" represented by the options Greek risk variable "Vega")

The Binary Markets
There are two binary markets in sports betting. The spread market and the totals market. They both have an established barrier number that adjusts based on supply and demand. if the transaction costs/juice/vig/bid-ask spread, etc is taken out, then these pre-game probabilities will be basically 50% for both sides. This is called the "At the Money" strike price. It is important to understand that all options will expire at either 100% or 0% at the end of the contract/game. So here, we can use a very tight market example of Team A being a 3.5 point favorite in an NFL football game. The pre-game market for Team A would be 49 X 51 (-3.5 points). If you buy Team A (bet on Team A -3.5 points) at the offering price of 51%/51 Delta, your profit would be 49%/49 Delta if Team A covered/expired at 100%/100 Delta (100 - 51 = 49). If you sold Team A (bet on Team B +3.5 points) at the bid price of 49%/49 Delta, your profit would also be 49%/49 Delta if Team A did not cover/expired at 0%/0 Delta. This is the parity of the market. The Delta/probability "fair value" will always be the "mid-market" or the median number between the bid (here 49) and the ask (here 51) so that would be 50%/50 Delta. The At the Money strike price. As the 3 conditions mentioned above change during the course of the game, the Delta/probability % for these bets will vacillate between 0 and 100 but NOT AT 0 or 100 until the game is completed. Just like in traditional options markets. In the exchange, as long as there is an appropriately sized bid/ask on the other side of your order, then you can exit your position/bet at any time before or during the game. Again, this is just like an American options contract where open positions can be closed or exercised early with the Delta of the contract being between 0 and 100.

In both the spread market and the totals market, the exchange will offer alternate "strike prices" (just like a traditional options chain). Very simply, if you "buy" points, runs, goals, etc, you are buying probability and buying an "In the Money" option. The more points, et al that you buy, the more probability you are gaining, the more In the Money your bet/position becomes and the more expensive it will be. Conversely, if you "sell" points, runs, goals, etc. you are selling probability and buying an "Out of the Money" option. The more points that you sell, the more probability you are losing, the more Out of the Money your bet/position becomes and the cheaper it will be. This same concept applies to the other side of the market. So in our Team A (-3.5 points) example, if you buy Team A at (-7) then that will be a cheaper bet with lower probability/increased ROI and if you sell Team A at (-7)...(Bet on Team B + 7) then that will be a more expensive bet with higher probability and decreased ROI. As your bet/trade becomes more In the Money (more probable to win), the fair value/market will move towards 100. As your bet/trade becomes more Out of the Money (more probable to lose), the fair value/market will move towards 0.

The Moneyline Market
The Moneyline market is a probability market that is only concerned with the winner and loser of the game. So when a buy side trader/"bettor" is searching for inefficiencies, they will not be found in the barrier numbers/strike prices like in the binary markets of spread and totals. Instead, the inefficiencies of the market will be found in the probability that the market assigns. The Moneyline market implies the % of the time (Delta) that the favorite and underdog would be expected to win (lose) the game if that same fundamental game were to be played an infinite number of times. In a traditional "bookmaker"/"broker-dealer" model, that would be calculated by finding the "mid-market"/"fair value" price and then solving for the %. So if a game closes at -160/+140 (a standard 3.5 point spread scenario) then the implication of the market is that if this exact fundamental game were to be played an infinite number of times, then the favorite would win 60% of the time...150 times out of every 250 played (150 divided by 250 = 60%) and the underdog would win 40% of the time...100 times out of every 250 played (100 divided by 250 = 40%). These "Delta percentages" would be reflected in the exchange as "the prices" and presumably would have tight bid/offer numbers around them. The "transaction cost" being charged in the bookmaker/broker-dealer model is approximately 13% of fair value/mid-market. Hopefully the exchange would be tighter than that. This metric of the margin to mid-market % is different from the "hold %". The margin to mid market % gives a trader an idea of how much "juice/transaction cost" they are paying relative to the market. Just as in options trading, again, that % will increase as the "bets" move away from parity/even money/50 Delta and volume will of course decrease. That is why the majority of volume is nearly always so significantly on the spread/At the Money strike price as opposed to the wide margins away from the spread/At the Money strike price. So very simply with Moneyline and its correlation to options Delta, an underdog would be an "Out of the Money" call (an "In the Money" put) and a favorite would be an "In the Money call (an "Out of the Money" put). At the expiration of the contract (end of the game, half, quarter, etc) the Delta of all contracts will be 100 or 0. Within the confines of the contract, etc. (Live/In-game) the Delta probability prices will be somewhere between 0 and 100 and will vacillate based on supply and demand of the market, changes in score, changes in implied volatility and the passage of time.

It should be addressed here that 

1) The sports securities markets are chronically inefficient in all 3 markets. This is because of the Behavioral Economics of the market. We know this because the closing prices are made up of "The Efficient Market Hypothesis", which posits that all publicly known fundamental information is "baked into the market", thus an irrelevant absolute, "Transaction costs" which are also absolute, and Behavioral Economics which is the "unknown" aspect of the market. If the binary markets were truly efficient, then every football game where the favorite was (-10) and the total was 50, market implying a final score of the favorite winning 30-20, would have that score realized 100% of the time and of course we know that is not the case. 

2) Just as in traditional options markets (the 100% correlations continue), after the "juice, vig, transaction cost, brokerage fee, bid-ask spread, or anything else you want to call it" is taken out, then the two sides of the relationship/market will always have absolute value probabilities that add up to 100. Just as in traditional options with the Delta probability price of any particular strike price always having a sum of 100 when the call is added to its corresponding put. I discuss this concept at further length here,,, https://www.thewolfline.com/page/optioncomponents

Using Options Greeks in a Sports Betting Exchange
Gamma - This is probably the simplest Greek to understand in the context of the Live/In-game Delta/Probability based Exchange. If the team that you bet on is scoring enough to beat the point spread/strike price (or in the case of Moneyline, scoring enough to win the game) then that will positively affect the Delta price of your position/bet and it will move closer to 100. Conversely, if the opposite is happening and the scoring is going against your position/bet then that will negatively affect your Delta price and it will move towards zero. It should be made clear that Gamma is most sensitive when the game score is closest to the point spread/strike price and closer to the end of the contract. For example, if the favorite in a basketball game is -3.5 points and they are wining the game by 3 with .1 second on the clock and one more free throw to shoot (we have all seen this) then Gamma would basically be infinite because the prospect of the contract/game finishing at 100 or 0, regardless of what side, is completely contingent on this final play. If the same scenario is happening with 10 minutes left in the first quarter, then the Gamma would be very low because the affect on the Delta price would be minimal. When a total (implied volatility) is lower, then gamma would be higher (points, etc. "mean more" to the Delta price). When a total (implied volatility) is higher, then gamma would be lower (points, etc. "mean less" to the Delta price).

Theta - Theta is the effect that the passage of time in the contract has on the Delta price of the position/bet. If the position is "winning/covering" (In the Money) then the passage of time helps and will push the Delta price towards 100 (not taking change in score or implied volatility/expected scoring into consideration). If the position is "losing/not covering" (Out of the Money) then the passage of time hurts and will push the Delta price towards 0. Like Gamma, Theta is the most sensitive when the score is closest to the point spread and closest to the end of the contract. So using our previous example of the favorite in a basketball game being -3.5 and winning by 3 with 5 seconds left and somehow there is no foul, then that 5 seconds has much greater effect on the Delta price then it would if the same thing happened in the first quarter. Theta also applies to a "totals/volatility" bet. If you bet the under (selling volatility) then the passage of time helps the position (known as "long theta"). If you bet the over (buying volatility) then the passage of time hurts the position (known as "short theta") Vega - In traditional options, Vega is a measure of how much changes in implied volatility will affect the price of an option. Because "price" in the sports betting exchange is represented by Delta probability, we will discuss what the changes in implied volatility (expected scoring) will have on that (as we did with Gamma and Theta). "Implied volatility" correlates to the total amount of scoring expected during the term of the contract in the sports exchange. "Realized volatility" correlates with how much scoring actually occurs during the term of the contract. If a position is "long volatility", then that is like "betting the over" and the presumption is that realized volatility will be greater than implied volatility. If a position is "short volatility", then that is like "betting the under" and the presumption is that realized volatility will be less than implied volatility. In terms of the effect that Implied Volatility changes have on the Delta price (Vega), if the implied volatility goes down, then "winning/covering/In the Money" bets will mover closer to 100 and "losing/not covering/Out of the Money" bets will move closer to 0. If the implied volatility goes up, then the Delta price of all positions/bets will move closer to 50.

What Does This Mean for Regulation?
We now know that very esoteric options risk and mechanics concepts can be 100% correlated to the sports betting exchange platforms as they are structured and now legalized and regulated. As a former Registered Investment Adviser with the US Securities and Exchange Commission (SEC) and the Financial Industry Regulatory Authority (FINRA). I have always firmly believed, and been very vocal, that the "sports bets" are "securities" as defined by Supreme Court case SEC vs WJ Howey 1946 as well as much more Federal and State statutes and case law. There is also multiple cause for "means and instrumentalities of interstate commerce" in the "sports betting markets". Because of this, I think that the 2 Federal commissions mentioned above must take control over this marketplace and the associated issuers, broker-dealers, market makers, etc. immediately and the States should be relegated to a supportive role as per Uniform Securities Act of 1956. In addition, when it is established that there is "an option" listed, regardless of the underlying instrument, then that option has been established to be a "security". I believe that I have made that quite clear here and it is time that the correct Federal regulations are applied. "Gamification Economics" is the novel sub-discipline of economics that is concerned with the transference economics/financial market theories, practical applications, products, platforms and regulations to the context of "games", especially sports securities markets. TheWolfLine.com has been the only home for Gamification Economics (including Technical Analysis, Behavioral Economics, options, stocks, forex, ETFs, pairs trading, etc) since 2010. After centuries of being called "the stale, dead, stodgy, dismal, insular science", Gamification Economics applications to the extremely exciting and wide reaching scope of sports betting/fantasy sports, those derogatory labels will no longer be applicable.

K. Gregory (Greg) Wolfe
Co-Founder/CEO
Icarus Hegel Analytics, LLC