Prop Bet Calculator
Calculate implied probabilities and expected value for over/under and prop bets. Enter values for instant results with step-by-step formulas.
Calculator
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Formula
For each side of a prop bet, calculate the implied probability (1/odds), remove the overround to find true probabilities, then compare against your estimated probability. Expected value is your estimated probability times the profit minus the loss probability times the stake. Positive EV indicates a value bet.
Last reviewed: December 2025
Worked Examples
Example 1: Player Passing Yards Prop Analysis
Example 2: Game Total Over/Under Analysis
Background & Theory
The Prop Bet Calculator applies the following established principles and formulas. Sports statistics and performance metrics represent one of the most data-rich domains of applied mathematics available to the general public. Baseball, in particular, has developed an exceptionally dense vocabulary of calculated metrics. Earned run average (ERA) quantifies a pitcher's effectiveness as (earned runs × 9) / innings pitched, normalising performance to a nine-inning standard regardless of how many complete games were pitched. WHIP, or walks and hits per inning pitched, is computed as (walks + hits) / innings pitched and provides a complementary measure of how frequently a pitcher allows baserunners. Batting average, one of the oldest statistics in the sport, is simply hits / at-bats, though more modern metrics such as on-base percentage and slugging percentage have largely supplanted it as primary performance indicators. The NFL passer rating formula is considerably more complex, combining completion percentage, yards per attempt, touchdown rate, and interception rate into a composite score scaled to a 0–158.3 range. Golf handicap calculation, now governed by the World Handicap System introduced in 2020, uses a Handicap Differential formula applied to the best 8 of a player's most recent 20 score differentials, with adjustments for course rating and slope. The Elo rating system, originally developed by physicist Arpad Elo for chess ranking in the 1960s, has become a widely adopted framework for competitive ranking in sports ranging from football to table tennis. It updates each player's rating after every match based on the margin of expected versus actual result. In endurance sports, pace calculation converts total time to a per-mile or per-kilometre rate, informing training intensity and race strategy. In cycling, power-to-weight ratio (watts per kilogram) is the primary determinant of climbing performance and is central to both professional race analysis and amateur fitness tracking. Fantasy sports scoring systems synthesise multiple individual statistics into aggregate point totals, requiring participants to understand the relative value of different performance categories across sports.
History
The history behind the Prop Bet Calculator traces back through the following developments. Organised athletic competition has roots extending to ancient Greece, where the Olympic Games were held at Olympia beginning around 776 BCE. These early games were embedded in religious observance and civic identity, featuring events such as sprinting, wrestling, and the pentathlon. The codification of modern sport rules accelerated dramatically in 19th century Britain, where industrialisation created both the leisure time and the institutional infrastructure for organised competition. The Football Association formalised the rules of association football in 1863, and similar governing bodies for cricket, rugby, tennis, and athletics followed in subsequent decades. Pierre de Coubertin, a French educator inspired by the English model of sport as character-building, campaigned to revive the Olympic Games as a modern international institution. The first modern Summer Olympics were held in Athens in 1896, establishing the template for international multi-sport competition that has continued to the present. FIFA, the international governing body for association football, was founded in Paris in 1904 with seven member nations. The serious statistical analysis of baseball, later termed sabermetrics, was pioneered by writers and analysts including Bill James beginning in the late 1970s. James self-published his Baseball Abstract annuals starting in 1977, introducing rigorous empirical methods to a domain previously dominated by traditional counting statistics and subjective scouting. His work influenced a generation of analysts and front-office executives. The publication of Michael Lewis's Moneyball in 2003, documenting the Oakland Athletics' 2002 season and their use of on-base percentage and other undervalued metrics, brought sports analytics to mainstream attention. The subsequent analytics revolution reshaped hiring practices and game strategy across professional sports leagues. Fantasy sports, which require participants to engage directly with statistical outputs, grew from a hobby practised by a few thousand enthusiasts in the 1980s into a multi-billion dollar industry by the 2010s, with tens of millions of participants across football, baseball, basketball, and other sports.
Frequently Asked Questions
Formula
EV = (Prob x Profit) - ((1 - Prob) x Stake)
For each side of a prop bet, calculate the implied probability (1/odds), remove the overround to find true probabilities, then compare against your estimated probability. Expected value is your estimated probability times the profit minus the loss probability times the stake. Positive EV indicates a value bet.
Worked Examples
Example 1: Player Passing Yards Prop Analysis
Problem: A QB passing yards over/under is set at 275.5. Over odds: 1.87, Under odds: 1.95. You estimate 58% chance of going over. $100 stake. Is the over a value bet?
Solution: Implied over = 1/1.87 = 53.5%\nImplied under = 1/1.95 = 51.3%\nTotal = 104.8%, Overround = 4.8%\nTrue prob over = 53.5/104.8 = 51.0%\nYour estimate: 58% (7% edge over true implied)\nEV over = (0.58 x $87) - (0.42 x $100) = $50.46 - $42.00 = $8.46\nEV% = 8.46%\nKelly = (0.58 x 0.87 - 0.42) / 0.87 = 9.7%
Result: Over is +EV: +$8.46/bet (8.46%) | Edge: 7% | Kelly: 9.7%
Example 2: Game Total Over/Under Analysis
Problem: Game total is set at 220.5. Over 1.91, Under 1.91. You estimate 47% over probability. Should you bet the under?
Solution: Implied each side = 1/1.91 = 52.4%\nTotal = 104.8%, Overround = 4.8%\nTrue prob each = 50%\nYour estimate under = 53%\nEV under = (0.53 x $91) - (0.47 x $100) = $48.23 - $47.00 = $1.23\nEV% = 1.23%\nSmall edge, borderline value\nKelly = (0.53 x 0.91 - 0.47) / 0.91 = 1.3%
Result: Under is marginally +EV: +$1.23/bet (1.23%) | Kelly: 1.3% (small bet)
Frequently Asked Questions
What is a prop bet and how does it differ from traditional bets?
A proposition bet, or prop bet, is a wager on a specific occurrence or non-occurrence within an event rather than on the final outcome itself. While traditional bets focus on who wins or loses, prop bets can cover anything from individual player statistics like passing yards or points scored, to game events like the first team to score, or even non-athletic events during major games. Props can be player props, team props, or game props. They are especially popular during major events like the Super Bowl where hundreds of prop markets are available. Props give bettors opportunities to exploit specialized knowledge about specific players or situations.
How are over/under lines set for prop bets?
Sportsbooks set over/under lines using a combination of historical data, statistical models, and market demand. For a player passing yards prop, the book analyzes the quarterback average performance, the opposing defense ranking against the pass, weather conditions, game pace projections, and other contextual factors. The line is initially set by odds compilers and then adjusted based on where the betting action flows. If heavy money comes in on the over, the book will move the line up to balance their liability. Sharp bettors who bet early often move the lines significantly. Understanding how lines are set helps identify potential value when your analysis disagrees with the market.
What does implied probability tell me about a prop bet?
Implied probability converts the decimal odds into a percentage that represents how likely the sportsbook believes the outcome is, including their built-in margin. For a prop with over odds of 1.91 and under odds of 1.91, each side has an implied probability of 52.4 percent, totaling 104.8 percent. The extra 4.8 percent is the bookmaker overround. By removing the margin, you find the true implied probabilities are roughly 50/50. If your own analysis suggests the over probability is actually 58 percent, you have found significant value. Always compare your estimated probability against the implied probability after removing the margin to identify genuine betting opportunities.
How do I find value in player prop bets?
Finding value in player props requires developing a systematic approach. Start by building a database of player performance metrics and identifying trends related to opponent matchups, home versus away splits, rest days, and weather conditions. Compare your projected stat lines against the posted lines to find discrepancies. Look for situational edges like a receiver facing a weak secondary, or a running back facing a team that allows high rushing yards. Track line movement across multiple sportsbooks to identify where the market may be mispricing a prop. Using a projection model that accounts for pace of play and game script is particularly effective for identifying over/under value.
What is the correlation between prop bets and how can I exploit it?
Correlation in props refers to the relationship between different prop outcomes. For example, if a quarterback throws for many yards, his receivers are also likely to have high receiving yardage, and the game total is likely to be high. Same-game parlays often allow you to combine correlated props, which sportsbooks try to price correctly but sometimes fail to adjust fully. You can exploit correlation by pairing logically connected props, such as a quarterback over on passing yards with his top receiver over on receiving yards. Negative correlation can also be valuable, like pairing one team dominant with the other team under on their props. Identifying mispriced correlations is one of the most profitable prop betting strategies.
What are alternate lines in prop bets and when should I use them?
Alternate lines are prop bet options at different thresholds than the primary posted line, offered at adjusted odds. For example, if the main line for a player rushing yards is 65.5 at -110 each side, alternate lines might offer over 55.5 at -200 or over 75.5 at +150. Alternate lines are useful when your model strongly suggests a player will significantly over-perform or under-perform the main line. If you project a player for 85 rushing yards, the over 75.5 at +150 might offer better expected value than the main over 65.5 at -110, even though the odds are longer. Always calculate the implied probability and compare it to your projection before selecting an alternate line.
References
Reviewed by Sher, Sports Science & Nutrition Specialist · Editorial policy