Beyond the Odds: Master Sports Betting

A market is efficient if prices reflect all available information, and the cost of trading is significantly less than the expected return.

Some sports betting markets are fairly efficient:

• USA professional sports

• Popular USA college sports (basketball/football)

• Spreads, totals, and moneylines

Others are not:

• Player props

• International sports

Pricing derivatives involves calculating the price (odds) of a bet based on full-game spreads and totals (which are efficient) as a baseline.

Being able to do this better than sportsbooks gives you valuable intellectual property (IP).

Specializing in smaller, less mainstream markets (like first-half NFL totals) can provide a higher return on risk than larger, more efficient markets.

Key points:

Any derivative market price must consider the full game spread and total, usually from market-making sportsbooks like Pinnacle, Bookmaker, BetOnline, and Circa (as of 2025).

Avoid using recreational books to price the parent lines as it introduces errors into your models.

Ensure the sportsbook you’re using as a base is sharp in the sport/league you're pricing (e.g., Pinnacle for tennis, ISN for soccer).

The Answer Key is an automated solution to pricing.

First step: Build a dataset including the following indexed information:

• Pregame spread

• Pregame total

• Final home/away scores

Second step: Expand the data for analysis (not indexing):

• Alternative spreads and totals

• Scoring by quarter

You can add additional data as needed, though acquiring it may be difficult.

1. Program your analysis:

   1. Identify parent spread/total, including vigorish (house cut for offering the market)

   2. Index every game in your dataset to reflect how well the game matches up to the parent line

   3. Sort your dataset with the most relevant data at the top

2. Choose a sample size (Elihu starts with 500)

3. Curate your sample dataset

4. Validate your sample using mean spread and total

   1. If the total or spread is too low, increase the target by the difference

   2. Validate your sample’s median compared to the parent line

5. Refine your sample

   1. Remove a game from the sample that will improve it (start from the bottom of your list)

   2. Add a game from outside the sample that will improve it (start from game 501 on your list)

When is your data good enough to use?

Your dataset is usable when it is within ±1 datapoint (0.2%) of your target cover rate on both spreads and totals. If your sample never becomes good enough, reduce your sample size. The tradeoff is increased noise in your final answer.

Build your Answer Key in a performant coding language:

• Pascal

• C#

• Python

Push Rate Definition: A push rate is how often your bet pushes or hits the index exactly. For example, if a spread is Bears -7 and they win by exactly 7, your bet pushes.

As an advanced player, you need to understand:

1. How to calculate push rates

2. How to use push rates

3. How operators use push rates

1. Use your Answer Key to target a whole-point spread and total.

2. Once your sample is refined, count the number of times the spread or total hits exactly. For instance, 27/500 = 5.4%.

3. Push rate charts must account for rule changes in the game. For example, when the NFL lengthened the distance for PATs, the PAT conversion rate dropped. Using data from before and after that rule change in the same set negatively impacts the data.

Push charts allow bettors to compare two prices and determine which is better, such as whether -7.5 at -110 or -6.5 at -130 offers more value. Steps include:

1. Convert each moneyline into a win percentage.

2. Adjust the line by a point using the push rate (or half the push rate for half-point moves).

Push-rate analysis enables you to make plays while consistently obtaining the best price.

Sportsbooks actively try to profile players using statistics:

Win/Loss Records

These are very noisy and random in small sample sizes.

Closing Line Value (CLV)

This is calculated by:

1. Comparing your bet to a sharp closing line.

2. Converting the index if different.

3. Measuring the difference in implied win-rate.

In smaller markets, push charts often don’t exist, particularly for markets without published lines and in-play bets, which lack a closing price.

Unskilled players usually don’t achieve CLV, while most skilled players do.

Recreational sportsbooks (as opposed to sharp books) have their closing prices “contaminated” by optimizing for public opinion rather than accuracy. To circumvent this, one should use closing prices from books perceived as sharp.

A teaser is a parlay with two key changes:

1. The player adjusts the spread or total by a fixed number of points (e.g., Cowboys +1.5 to Cowboys +7.5).

2. The payoff is reduced based on the number of points the line is adjusted.

To evaluate teaser potential, consider:

Breakeven Rate for Each Leg

How often must you win each leg to show a profit? This is the breakeven rate for each leg.

If you played a 2-team teaser at -110, the teaser breaks even at .524%. The breakeven rate for a 2 team teaser is the square root of .524, or about .724 -> 72.4%.

Capture Rate

This is the difference between 50% and your breakeven rate (e.g., 27.5% in the above example).

A teaser is favorable if you beat both the breakeven and capture rates. If you meet the breakeven rate but not the capture rate, straight betting the line is better.

The closing line in efficient markets (e.g., NFL sides) is a near-absolute statement of truth.

For example, If a game closes at +3.5 -110 / -110 at a market-testing sportsbook like Pinnacle, it indicates exhaustive analysis by top models and experts, accounting for factors such as:

• Weather conditions

• Player injuries

• Coaching tendencies and errors

• Homefield advantage

• The officiating crew

Once the game starts, CLV can no longer be evaluated. Even if an underdog wins by 20 points, the pre-game line remains “correct” because the actual game score is often lower-quality information compared to CLV.

Metrics can either be valuable and predictive (signal) or random and nonpredictive (noise):

Noise:

• Average points scored/allowed in an NFL game

• Yardage totals during games

Signal:

• Player injury considerations

• Strength of schedule

• Weighting the recency of games

Maximizing the signal-to-noise ratio is crucial for informed betting decisions.

How Do You Tell Which Model Is Better?

Three major tools:

1. Log Loss Error Ratings

   • De-vig markets by removing the sportsbook’s margin (vig).

   • Log loss measures how far off a projection is from the actual outcome.

2. CLV

   • Indicates how much you beat the closing price of a market.

3. Observed Win/Loss

   • Assesses model accuracy over time.

De-vigging involves converting odds into implied probabilities, then adjusting to remove the vig. Divide the probability by the sum of the probabilities to get de-vig’d odds.

When you convert odds for/against a market to implied probabilities, they will always sum to over 100%. The extra is the vigorish, or the sportsbook's cut.

Log loss measures errors:

• A minor error occurs if a 10% projected win rate loses.

• A large error occurs if a 90% projected win rate loses.

An ideal model would have bets expected to win 90% of the time win exactly 90% of the time

Accurate models align projected probabilities with observed outcomes, allowing for profitable betting strategies. Most of the time, the error rate is "tiny", but too much to overcome the vig from a sportsbook price.

CLV measures how much you outperform the closing price of a market. Long-term winners consistently accumulate CLV, but its predictive value varies depending on market efficiency:

Efficient Markets: CLV is highly predictive of accurate pricing.

Inefficient Markets: Examples include player props or exclusive offerings by a single book. In such cases, CLV may be meaningless.

Self-Induced CLV: Betting close to the closing time may produce CLV that doesn’t reflect true market efficiency.

CLV does not apply to in-play wagers, or markets with high vigorish and low limits. While accumulating CLV benefits your bankroll, it also signals sharp behavior to sportsbooks, potentially leading to account restrictions.

This is easy to measure - compare the price you bet at to the closing price after converting both to implied probabilities.

E.g. If you bet at -130 and the market closed at -138

• -130 is a probability of .565

• -138 is a probability of .58

• You beat the closing price by 0.015, or +1.5%

If you bet at a worse price than the close, your CLV will be negative.

These are wagers with an index, like spreads and totals.

A simple approach to calculating these is to use the same index throughout - this works the same as moneyline.

If you want to calculate CLV of different lines, you will need to account for the push rate for each point the index moves.

Many player props fit this mold:

• NBA rebounds

• MLB strikeouts

• NFL rushing yards

For these, you have two options:

• Discard the data

• Estimate the push rate using tools like Poisson or binomial distributions, based on the variables involved (sample size, etc.)

Sports betting is asymmetric warfare between sportsbook operators and players.

Operators

• Use price discovery and skilled trading.

• Market to unskilled players and limit sharps.

Players

• Most are unskilled.

• Fewer than 2% are skilled enough to threaten sportsbook profitability.

There are two types of sportsbook operators:

Market Testers (e.g., Pinnacle, BetOnline):

• Aim to identify accurate market prices.

• Rely on automove algorithms for pricing adjustments.

  
  

Recreational Sportsbooks (e.g., DraftKings, ESPNBet):

• Focus on short-term profitability.

• Limit and ban winning players.

Market testers have two goals:

• Figure out the correct price of a market as cheaply as possible.

• Take as much betting volume as possible at the correct price.

They generally do not limit players.

They rely heavily on automove. Automove is a per-player rating that will move the price of a market via formulaic amount after accepting a bet from the player.

They allow a player to rebet the same market after adjusting the price.

They adjust prices based on sharp information, not per-market financial exposure.

They use sophisticated player profiling. CLV may be done granularly by league or market.

They spend millions of dollars on good math, and model and account for factors like rule changes (NFL XP line moved) and statistical trends (NBA 3-pointers).

Recreational sportsbooks’ goal is to maximize short-term profitability as cheaply as possible.

They will limit and kick out winning players they think are smart. The greatest risk to their business is kicking out a winning dumb player, so they need to be careful with who they kick out.

They assume players are morons, and that 98% can't win without promotions.

They reward large betting players that are flagged as squares.

They have bad or no player profiling.

They have no math, and copy market testers.

They are heavily focused on marketing to new players.

They deliberately offer off-market prices to the public to fleece players if action is lopsided.

They are more forgiving of players who win through parlays instead of straight bets.

There are four "classes" of bettors.

Beginner:

You are either down money or win less than $1,000/year.

You may get lucky, but are not going to win in the long run.

98% of bettors are beginners.

Your wins are short-term loans from the sportsbook that you will pay back with interest.

Either level up or quit betting to save your money.

Intermediate:

You win $1,000-$25,000 / year

You understand Expected Value (EV) and risk management but have not mastered it.

You limit your bets to where you think you have an edge.

You are developing price shopping skills.

Nearly 2% of bettors are intermediate.

Advanced:

You win $50,000+ per year.

You have mastered +EV and risk management where it matters.

You are looking to bet as much as you can to maximize your edges.

You only place +EV bets unless you are grooming accounts.

Fewer than 1 in 400 are advanced bettors.

Syndicate:

You win $250,000+ per year.

You often bet at a dozen sportsbooks in under 2 mins.

Your biggest challenge is getting and keeping accounts.

You have industrialized your analysis, pricing, and betting so that much of it is automated.

You may manipulate markets to get better prices.

You have no doubt that your betting approach wins.

The biggest difference between bettors as you move up the food chain is the quality and precision of +EV edge estimation. Edges should be consistent with push rates if your analysis is correct.

A data-driven approach with precise analysis is more sustainable than a subjective approach - analyzing data using push rates is more sustainable than quickly betting after injury news.

Betting derivative lines is one of the most lucrative markets for quants.

Sportsbooks accept players who win as long as they don't demonstrate a long-term edge.

When a book identifies you as a long-term winner, they take several actions:

They will remove your access to marketing promotions.

Recreational sportsbooks collar (or limit) your bets so that instead of betting $1000s per bet, you can only bet $100 or less.

Market tester sportsbooks use automove instead of collaring your bets. The purpose of automove is not to find the correct price, but to account for risk until determining the correct price. Market testers will also often remove parlays from known sharps. Sharps can use parlays to gain additional edge and handle, and market testers are aware of this.

After your first account is collared beyond usability, a risky approach is to obtain a new account in someone else's name. All books view this as fraud. It is important to understand the risks before proceeding.

There are two categories of risk when pursuing this approach:

Grey market sportsbooks

Grey market means the sportsbook is legal in its operating country but not in the USA. Examples include Bookmaker and BetOnline.

Their recourse DOES NOT include physical violence - the consequences would be too catastrophic for their businesses, and Elihu has never witnessed or heard of this in 25+ years.

Their optimal response is to do nothing until a payout is requested, then seize the balance.

Black market sportsbooks

Black market refers to local bookies who only take cash bets and are not registered or licensed.

White market sportsbooks are legal and regulated, like FanDuel or DraftKings.

These sportsbooks experience a much higher percentage of fraudulent accounts than offshore books

Syndicates have been creating new accounts and winning 6-figure payouts over single weekends, with yearly profits well into the millions. These fraud rings can pose an existential threat to recreational sportsbooks.

Based on Elihu's 1000+ fraud investigations for sportsbooks, these forensic factors link proxy accounts:

Money trail

Can large ($100k+) sums of money be traced between accounts?

User identity

• Device

• IP address

• Internet service provider

• Physical location

MO (betting patterns)

Are the suspected linked accounts betting similarly, using the same winning strategy?

Connecting proxy accounts is straightforward for sportsbooks:

1. Identify the accounts

2. Measure the harm

3. Seize the funds

Eventually, the financial losses from proxy betting will become too significant, forcing sportsbooks to take more drastic action.

Their options include civil lawsuits and criminal prosecutions for identity fraud.

Consider an unsophisticated fraud operation:

The leader opens 10 accounts using friends' IDs. Money is transferred via PayPal, cash, crypto, etc. All accounts are forensically linked by IP address, physical location, and betting strategy. A subpoena reveals phone/texts between participants and money flow.

Risk of detection increases nonlinearly based on the number of accounts involved and their degree of linkage. 10 accounts betting from the same location and IP is more suspicious than 3.

Risk of legal action also increases based on the amount of money - books are more likely to pursue a $1m+ winner than a $10k winner.

Most USA sportsbook have a rule in their T&Cs: no one but you may use this account

A classic case of fraud has 3 elements

• misrepresentation

• a party relying on misrepresentation

• a party suffering loss due to misrepresentation

For example:

• your own account is restricted

• you use your girlfriend's ID to open a new account

  • this is misrepresentation

• you use a signup bonus profitably

  • access to the signup bonus relies on misrepresentation - it is for new players, not restricted ones

  • profit from the signup bonus is loss for the sportsbook

• so all 3 criteria are met

A safer alternative is to use partnerships:

• the account owner is placing their own bets

• the account is funded with their own money

• there is no foul in advising your partner which bets to place and splitting the profits

The biggest risk for professional bettors is overbetting - determining how much to wager on a given bet with a given edge is a critical skill for +EV bettors.

Underbetting is sub-optimal but lacks the risk of overbetting - you will not bust out underbetting if you have an edge.

Properly sizing your bets leads to optimal nonlinear bankroll growth until you hit the limits at a sportsbook, at which point your bet sizing becomes simple: bet the limit.

The goal is not to maximize EV on a given bet but to achieve the highest long-term bankroll growth.

F = P - (1 - P) / B

or

F = P - (Q / B)

Where:

F = the fraction of your bankroll to wager on this bet

P = decimal odds of winning bet

B = decimal odds price of your bet

Q = (1 - P) = probability of loss

This is the most straightforward way to size a single bet. If you bet double what you should based on this formula, you will bust with 100% certainty in the long run.

Evaluating risk across a series of bets is more complex, as correlated bets concentrate risk. Optimizing overall bankroll growth across many bets, including parlays, introduces complexity beyond the scope of this course.

In practice, Elihu uses 1/3 sized bets from Kelly Criterion when bet sizing is important.

While there are a few effective parlay strategies, they represent a tiny minority compared to most parlays.

Parlays are generally worse than straight bets for bankroll growth. Sportsbooks understand this and profile players accordingly.

Four exceptions when parlays are beneficial:

Correlated parlays

These are covered in-depth later.

"Key leg" principle

This is when you want to bet as much as possible on a key play, and parlays provide more exposure.

Huge bankroll

When your bankroll is huge, you want more exposure on your bets.

Account grooming

Sharp players rarely play 3+ leg multi-team parlays. You can use this to profile an account as square. Adding volatility in this way increases account longevity.

Correlated parlays offer recognized +EV due to their all-or-nothing nature:

• Ohio State -40 parlayed with Over 48

• App State +40 with Under 48

  
  

These benefit account grooming by checking desired boxes:

• Parlays

• No CLV

• High volatility (wins appear lucky)

• No red flags

  
  

A 2x2 matrix of outcomes typically shows two more likely and two less likely results. For example, consider O/U 165 lbs and O/U 5'9" height for a person. Both unders or both overs are intuitively more likely than one under and one over.

These aren't automatically profitable - examine individual leg prices carefully.

Betting on full-game moneyline and half-game moneyline are correlated in every sport - a team that wins the first half is more likely to win the whole game, in a vacuum.

The ideal bankroll management strategy accounts for correlation and reduces bet size due to increased exposure. Over-betting is the cardinal sin, and correlated bets often conceal this risk.

The safe-and-easy way to play correlated bets is to assume 100% correlation and bet half as much. While not optimal for bankroll growth, this approach prevents busting out and is simple to implement.

If overbetting is a sin, betting negatively correlated plays is a virtue.

Lowering volatility without sacrificing much EV is phenomenal for bankroll growth. Arbitrage is a great example - volatility approaches 0, though you sacrifice more EV than necessary.

Betting a 0 EV negatively correlated play (aka hedge) can increase long-term bankroll growth by reducing volatility, despite not being a winning play by itself.

Kelly Criterion correctly balances EV with variance to produce bet sizes, but this scenario falls into its blind spot. It also doesn't work well for markets with more than 2 possible outcomes.

When your bankroll is large enough that you're betting the limits for everything, this approach loses much of its value and may not justify the time/effort.

An underappreciated +EV CP structure for MLB involves pairing a home underdog with the under.

Data suggests several reasons for this value:

1. When the home team leads in the middle of the 9th, they skip their final at-bat, reducing total runs.

2. Home underdogs typically win because favorites underperform offensively, not because underdogs win shootouts.

NFL and college full-game parlays generally lack +EV, and more profitable edges exist elsewhere.

First half spreads offer greater value due to:

• More challenging analysis

• Greater price variations

• Favorite/over and underdog/under remain the preferred CP combinations

Betting opposite, favorable parlays reduces variance - lower variance typically accelerates bankroll growth.

When you have the advantage, press your attack before the books can adapt. Round robins are perfect for this.

A round robin parlay by twos is a wager where you have at least 3 plays, and every combination of two teams is played:

• For 3 +EV plays: A, B, C

  • This creates 3 parlays: AB, AC, BC

• For 8 plays, you end up with 28 two-team parlays

  • AB, AC, ... AH, BC, ... GH

• 8 plays by 3s results in 56 3-leg parlays

  • ABC, ABD, ... FGH

There are two main benefits:

1. You can wager beyond normal limits

2. Each dollar wagered is leveraged multiple times

For most players, round robin parlays are unnecessary and inadvisable. Straight bets below the limit are preferable. Variance from parlays increases, so the amount you should risk decreases. Only when your bankroll becomes truly huge do round robin parlays become superior to straight bets.

Two main advantages of round robin parlays:

1. Parlays are worse than straight bets, and sportsbooks know this. They will likely let you play longer as a winner if you use parlays.

2. You can bypass straight bet limits using parlays.

Do not bet your entire bankroll on uncorrelated plays via round robin. This introduces the risk of busting your bankroll if all picks lose. It’s unlikely but possible.

Opening an account with a large deposit and then getting CLV on a large round robin will likely get your account restricted immediately.

Consider what happens if you hit all legs and your balance balloons - will the sportsbook pay you? Legal US ones will; offshore books may create difficulties.

In 2021, DraftKings introduced no-limit 20-team round robin parlays.

DraftKings offers a bonus based on total handle ("DK Dollars"): $500 risked earns you $1. This is significant when deploying a large bankroll regularly, providing an extra 0.2% return.

Betting 20 plays by 3s is superior to straight bets at DK. Early losses due to variance can earn large bonuses. Eventually, when you win, you will likely be limited.

Caesars offers an even more favorable rewards program and allows 25-pick round robins.

Generally, the more selections allowed and the higher number of legs accommodated, the better it is to bet big. This provides both lower volatility and more leverage.

All sportsbooks profile accounts. It's advantageous for them to think you're a recreational bettor or "degen". They have formulas to distinguish sharp from recreational betting patterns. The ideal strategy is to camouflage your bets to appear recreational.

Your first bets at a book are crucial. Showing signs of sophisticated betting leads to:

• Lower limits

• Bet delays

• Trader reviews

This is a noisy metric that draws overreactions from recreational books. Too much randomness exists for this to be useful over a small sample size.

To exploit this, use a high volatility strategy: Lose big and win big, so wins are attributed to luck. The best methods include parlays and big underdog/favorite moneylines.

Your first 10 or so bets at a sportsbook are most crucial.

Certain behaviors will almost certainly get you limited/banned if exhibited too soon:

• Betting steam

• Taking a shot

• Consistently getting CLV

• Betting and winning player props

• Taking a payout

• Price sensitivity

• Organized betting / circumventing limits

• Using optimal bonus strategy

Betting steam occurs when you bet into a line shortly before it moves. For example, responding immediately to Twitter injury news is betting steam.

Betting steam too early sacrifices long-term account EV for short-term bet EV, and is generally not worth it.

This involves betting on something that has already happened when the sportsbook mistakenly leaves the line up too long. For example, if an NFL team returns the opening kickoff for a TD and you can still bet pre-game lines, betting the pre-game line would be taking a shot.

Unlike betting steam, this could be considered fraudulent activity and isn't worth the risk.

Another example is when sportsbooks post obvious mistakes. Instead of Ohio State -30 points, someone types Ohio State +30, and you place a max bet.

Most instances will be caught by the sportsbook and flag your account.

Recreational bettors don't consistently beat CLV. Doing this within your first 10 bets is a clear signal you are a sharp bettor.

Less data is available on props, leaving sportsbooks to rely primarily on win/loss analysis for props.

The strategic approach is to avoid props outside of parlays for your first 10 bets.

Delay payouts as long as possible. Your first payout triggers account examination, making sharp plays more noticeable. Busting out is preferable, as books offer deposit bonuses to accounts profiled as recreational.

When traders review your bet in real-time, they compare their price to other sportsbooks. If your bet is NOT at the best price, they'll mark you as recreational (desired). These notes carry significant weight during later account reviews.

Consistently betting at the best price flags you as price-sensitive.

Avoid using multiple accounts to place identical bets simultaneously, especially from the same device or IP address.

Expect problems when using this approach to place multiple max bets before a sportsbook adjusts lines.

Betting big underdog moneylines optimizes large bonuses. Combining this with your remaining balance on the same bet to minimize rollover signals sophisticated betting.

Accounts showing large losses are valuable. During reviews, significant losses without other warning signs often end the analysis. Once your account shows big losses, you can accumulate CLV consistently with less scrutiny.

Betting large amounts before line movements will trigger limits after one bet at most sportsbooks.

Market Manipulation

Betting against yourself at the same book is easily detected by the sportsbook.

Betting the wrong way at a market-testing book can move lines enough to create +EV opportunities at recreational sportsbooks. This works if done at different sportsbooks, hedging some exposure with the initial bet.

Line mistakes

This is the cardinal sin of betting. Expect voided bets and account penalties. For example, when the Ohio State spread is typed as +30 instead of -30 and you bet into the mistake.

Fixed matches

This area contains significant grey zones. Some examples:

1. A tennis player who just won a final and has plane tickets booked after the first round of the next tournament

2. A player with contract incentives to play through an injury at less than 100%

The common approach for these "key plays" is using them as anchor legs in parlays with heavy favorites as the other legs. Multiple occurrences become suspicious.

When your bankroll grows massive, finding +EV bets becomes less challenging than deploying capital daily. Good news: The USA market currently offers opportunities for those who know how to groom accounts.

Optimal strategy for first 10-12 bets: correlated parlays

This avoids:

• Steam chasing

• Shot taking

• CLV

• Props

• Payouts

• Taking best prices

A trader reviewing your account sees a recreational bettor placing $100 or $1000 same-game parlays.

Benefits:

• Large deposit bonuses after losses

• Higher limits

• Ongoing bonuses that can create +EV plays while appearing -EV to books

This approach can sustain winning for extended periods. Eventually, books will recognize your success even without understanding the method and act accordingly.

Advantage play (AP) at casinos complements EV sports betting. Casino losses extend your viability in sports betting, which remains +EV overall.

A $100k sportsbook winner who loses $50k at the casino is preferable to a $40k sports-only winner.