You Play To Win The Game
– Herm Edwards
Let’s be honest, whether you’re participating in a contest to pick the outright winner or the team you think will cover the spread, if you don’t follow a consistent process you’re probably not doing very well.
I know because that was me.
After more than a few seasons of disappointing results in my leagues, I set out to find my edge and improve my chances of success. And it’s worked—if not for a ton of reading, hours upon hours of spreadsheet modeling, thought-provoking discussions with friends, and an accepting wife!
In this post, I will:
Introduce the basic concepts of probabilistic modeling,
Explain how to infer the win percentage from the point spread and vice versa,
Briefly discuss the various betting market differences, and,
Describe the common pick ‘em contest types.
Let’s get started.
Consider the following scenario in Week 6 of the 2019 NFL season:
New York Jets vs. Dallas Cowboys (-7).
Almost everyone picked the Cowboys to win the game (>95%). A strong majority (75%) even picked the Cowboys to cover the spread (in this case, to win by more than 7).
Ah ha! But it turns out the Jets not only covered the 7 points but also won outright! Let’s take this example to highlight the concept of win probability:
A line of 7 points implies the favorite has a roughly 72% chance of winning the game; conversely, the underdog has a 28% chance (ignoring, for purposes of this example, the minute probability of a tie). How did I come up with that probability? Here’s how:
The expected outcome of a matchup compares the relative strengths of each team per this equation,
E_a=1/(1+10^((R_b-R_a)/k))
where E_a is the expected win probability for team “a” and R is the pre-game rating assigned to team “a” and “b”, respectively. The expected probability loosely follows a logistic curve (as shown below) dependent on k, the shape factor. The shape factor determines the slope of the line; as k decreases, the slope becomes more pronounced.
For evenly rated teams, k has a small bearing on the implied win probability. However, as the inferred team disparity grows, the implied probability difference can be drastic and lead to overconfidence. That’s what happened to the DAL-NYJ game. The public was far too confident in DAL and that provided a value-taking opportunity on NYJ plus the points.
This method of inferring and comparing relative strengths is derived from the Elo Rating System. It’s proven to be a reliable rating system used by the United States Chess Federation, FiveThirtyEight’s popular sports prediction models, and even Oracle’s Universal Tennis Rating system that’s gaining popularity worldwide.
If you have a well-calibrated model, you can identify lines or prices that offer value relative to the market. It does not guarantee you will capitalize on the value presented, but if your model is true, you’ll be successful in the long run.
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So what are these markets available to us and how do they differ?
To get you into the right headspace, think of how the stock market works:
Shares are offered by a public company at an initial price (open) then buyers and sellers trade those shares at agreed-upon prices. If the purchase volume or buyer conviction outweighs that of the sellers, the price per share will rise until the market sentiment is satisfied or reverses. This is market-driven action.
Offshore sportsbooks tend to use this “marking-making” model to set lines for games. That is, they let the market participants decide what the line for a given game ought to be. This method of risk management prefers balanced money on either side of the line so that regardless of outcome the book gets their standard vig (i.e. a fee) without incurring losses.
There’s another market philosophy that I’d like to introduce by using the analogy of shopping for a new car. The price of a car is anchored on the MSRP (manufacturer’s suggested retail price) but most shoppers will attempt to negotiate with dealerships to get the best price possible. The lowest sales price a buyer can negotiate will be a function of a few factors: the public demand for the vehicle (higher demand means a higher price), the convenience of the dealership (more convenient location probably means the traffic through the showroom is sufficient to keep prices near the MSRP), and the price the buyer feels is “fair”. Different buyers will get varying levels of discount off the MSRP but all sales prices will be close. This is a “retail” market.
This retail model is the tactic most U.S.-based casinos use to set lines. While they, like the offshore books, are interested in enticing even action on either side of the line, they also must consider their price competitiveness relative to other properties and competing casinos. Since all sportsbooks take a cut of the profits (the vig), the higher volume they can drive to the betting window, the greater revenue for the casino. For this reason (and others outside the scope of this post), these casinos tend to match what the “consensus” line is for each game, with some minor shading, as needed. These sportsbooks are considered “retail” shops. (N.B. This is a cursory and coarse explanation of the different bookmaking philosophies. Please forgive the brevity. I’ll attempt to dive deeper into this concept and how to spot arbitrage opportunities in later posts.)
The key to finding value in the retail market is shopping around.
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Let’s shift gears to review the various types of popular pick ‘em contests. In addition to the full season prize, most contests offer prizes weekly or segment-based (e.g., weeks 1-4, etc.). Most of my modeling work has been to optimize the strategy for winning a season-long championship versus winning a weekly prize. With that in mind, let me describe the different types:
Straight-up - Pick winner for each game, most correct picks wins.
Straight-up with confidence points - Pick winner and assign points based on level of confidence, most points wins. Confidence points can either be continuous or discretized buckets. More on the implications of this in later posts.
Against the spread (ATS) - Pick the team to cover the spread, most correct picks or most points wins, depending on the contest rules.
My future posts will often refer to the SuperContest. This ATS contest, hosted by the Westgate Casino in Las Vegas, is the premier NFL pick ‘em contest in the world. In this contest, static lines (lines that do not change) are posted each week, on Wednesday, and contestants are obligated to select 5 teams to cover the spread. A team that covers the spread earns 1 point, a “push” ATS is 0.5 points, and a team that fails to cover doesn’t earn any points.
In the coming posts, I’ll describe how I use my probabilistic model to guide me to the best selections to remain competitive in my contests.