Football Field Goal Probability Calculator
Estimate field goal success probability based on distance, weather, and kicker stats. Enter values for instant results with step-by-step formulas.
Calculator
Adjust values & calculateProbability by Distance
Formula
The base probability uses a logistic regression model where d is distance in yards, k is a steepness factor (0.115), and midpoint is the 50% probability distance (47 yards). Adjustments are made for kicker skill relative to league average, wind speed and direction, temperature, and indoor/outdoor venue.
Last reviewed: December 2025
Worked Examples
Example 1: Standard 40-Yard Attempt
Example 2: Long-Distance Indoor Attempt
Background & Theory
The Football Field Goal Probability Calculator applies the following established principles and formulas. Probability theory provides the mathematical foundation for analysing all games of chance. The fundamental measure assigns a probability between 0 and 1 to each outcome by dividing the count of favourable outcomes by the count of equally likely total outcomes. Rolling a standard six-sided die produces a 1/6 probability for each face; the probability that a fair coin lands heads exactly three times in five tosses follows the binomial distribution with parameters n=5 and p=0.5. Expected value (EV) is the probability-weighted average outcome of a random variable: EV equals the sum of each outcome multiplied by its probability. A fair coin flip paying $1 for heads and costing $1 for tails has EV of zero. Casino games are designed with negative expected value for the player; the house edge is the casino's average percentage profit per bet. European roulette with a single zero has a house edge of 2.7 percent, while American roulette's double zero raises it to 5.26 percent. Poker hand probabilities derive from combinatorics. From a 52-card deck, the number of distinct 5-card hands is C(52,5) = 2,598,960. A royal flush can occur in only 4 ways, giving it a probability of approximately 0.000154 percent. Blackjack basic strategy tables, derived from computer simulation of millions of hands, reduce the house edge from roughly 2 percent to below 0.5 percent by specifying the optimal hit, stand, double, or split decision for every player hand against every dealer up-card. Sports betting implied probability converts decimal odds to a probability estimate: implied probability equals 1 divided by decimal odds. Odds of 2.5 imply a 40 percent probability. The Kelly Criterion provides the theoretically optimal bet fraction: f equals (bp minus q) divided by b, where b is the net odds received, p is the probability of winning, and q is the probability of losing. This formula maximises the long-run geometric growth rate of a bankroll.
History
The history behind the Football Field Goal Probability Calculator traces back through the following developments. Physical evidence of dice play dates to around 2500 BCE at the Indus Valley city of Mohenjo-daro, where excavators found carved cubic astragali remarkably similar to modern dice. Ancient Egyptian, Greek, and Roman cultures all incorporated dice games into both leisure and religious ritual, suggesting gambling emerged independently across early civilisations as a universal human impulse. The first systematic attempt to mathematically analyse games of chance came from Gerolamo Cardano, the Italian polymath who wrote "Liber de Ludo Aleae" (Book on Games of Chance) around 1564. Cardano derived correct probabilities for dice combinations and introduced the concept of sample space, though his work remained unpublished until 1663. The field transformed into a rigorous discipline through correspondence in 1654 between Blaise Pascal and Pierre de Fermat prompted by a gambling problem posed by the Chevalier de Mere. Their exchange established the rules of probability, including the concept of expected value. Jacob Bernoulli's "Ars Conjectandi" (1713) formalised the law of large numbers, proving that sample frequencies converge to true probabilities as trials increase. The 20th century brought two pivotal developments. Stanislaw Ulam and John von Neumann devised Monte Carlo simulation methods in 1947 while working at Los Alamos, showing that complex probabilistic systems could be analysed by random sampling. Game theory and poker strategy developed in parallel, with John von Neumann's minimax theorem providing early foundations and later work by game theorists formalisingrational play under incomplete information. Online gambling launched in the mid-1990s following the passage of the Free Trade and Processing Act in Antigua in 1994, which issued the first online casino licences. The Unlawful Internet Gambling Enforcement Act of 2006 disrupted US online gambling markets. Esports betting and video game loot box mechanics brought probability and expected value calculations to younger audiences in the 2010s, prompting regulatory scrutiny of randomised virtual reward systems across multiple jurisdictions.
Frequently Asked Questions
Formula
P(success) = 100 / (1 + e^(k(d - midpoint))) x SkillFactor - WindPenalty + TempAdj + IndoorBonus
The base probability uses a logistic regression model where d is distance in yards, k is a steepness factor (0.115), and midpoint is the 50% probability distance (47 yards). Adjustments are made for kicker skill relative to league average, wind speed and direction, temperature, and indoor/outdoor venue.
Worked Examples
Example 1: Standard 40-Yard Attempt
Problem: An 85% career-accuracy kicker attempts a 40-yard field goal outdoors with 10 mph crosswind at 55 degrees Fahrenheit.
Solution: Base probability at 40 yards: 100 / (1 + e^(0.115 x (40-47))) = 69.2%\nSkill factor: 85/85 = 1.0x\nCrosswind penalty: 10 mph x 1.2 = 12.0 percentage points\nTemperature adjustment: 55F = no adjustment\nAdjusted probability: 69.2% x 1.0 - 12.0 = 57.2%\nExpected points: 0.572 x 3 = 1.72 points
Result: 57.2% success probability | 1.72 expected points | Decision: Attempt Field Goal
Example 2: Long-Distance Indoor Attempt
Problem: A 90% career-accuracy kicker attempts a 55-yard field goal in a dome (no wind, 72F).
Solution: Base probability at 55 yards: 100 / (1 + e^(0.115 x (55-47))) = 28.6%\nSkill factor: 90/85 = 1.059x\nNo wind penalty (indoor)\nNo temperature adjustment (72F)\nIndoor bonus: +5%\nAdjusted probability: 28.6% x 1.059 + 5 = 35.3%\nExpected points: 0.353 x 3 = 1.06 points
Result: 35.3% success probability | 1.06 expected points | Decision: Consider game situation carefully
Frequently Asked Questions
How is field goal probability calculated based on distance?
Field goal probability follows a logistic (sigmoid) curve that decreases as distance increases. NFL historical data shows that kickers make approximately 95 percent of attempts from 20 to 29 yards, 87 percent from 30 to 39 yards, 80 percent from 40 to 49 yards, and roughly 65 percent from 50 to 59 yards. Beyond 60 yards, the success rate drops below 30 percent. Football Field Goal Probability Calculator uses a logistic regression model fitted to these historical success rates, with the inflection point near 47 yards where probability crosses 50 percent for an average kicker. The sigmoid shape reflects the physical reality that each additional yard of distance requires exponentially more precise leg speed, angle, and timing.
How does wind affect field goal accuracy in the NFL?
Wind is one of the most significant environmental factors affecting field goal success. A headwind directly opposes the ball flight path, requiring the kicker to generate more power which often compromises accuracy, reducing success rates by approximately 1.5 to 2 percentage points per mile per hour of headwind. Crosswinds push the ball laterally, requiring the kicker to aim off-center and trust the wind to carry the ball back, reducing accuracy by roughly 1 to 1.5 percentage points per mph. Tailwinds provide a slight benefit of about 0.5 percentage points per mph by extending the ball carry distance. Wind gusts are especially problematic because inconsistent wind makes trajectory prediction nearly impossible for kickers adjusting their aim and power.
What is the longest field goal ever made in the NFL?
The NFL record for the longest field goal is 66 yards, kicked by Justin Tucker of the Baltimore Ravens in September 2021 against the Detroit Lions. The ball hit the crossbar and bounced through, making it one of the most dramatic plays in NFL history. Before Tucker, the record was 64 yards shared by Matt Prater (2013) and Tom Dempsey (1970). At 66 yards, statistical models estimate the success probability at roughly 5 to 10 percent for an elite kicker under favorable conditions. These extreme-distance kicks typically require ideal conditions including minimal wind, moderate temperature, and often high altitude like at Denver where the thinner air reduces air resistance and allows the ball to travel farther.
How do indoor stadiums affect field goal probability?
Indoor stadiums provide a controlled environment that eliminates wind and temperature as variables, resulting in measurably higher field goal success rates. NFL data consistently shows that kickers perform approximately 3 to 5 percentage points better in domed stadiums compared to outdoor venues, with the advantage increasing significantly for longer-distance attempts. The consistent footing, absence of wind gusts, and comfortable temperatures all contribute to more repeatable kicking mechanics. Retractable roof stadiums offer a hybrid advantage when the roof is closed. Teams that play in domes, such as the Atlanta Falcons and Indianapolis Colts, often see their kickers post higher season-long accuracy percentages compared to teams in outdoor cold-weather markets.
When should a coach attempt a field goal versus punting or going for it?
The decision to attempt a field goal involves expected points analysis that weighs the probability of making the kick against the cost of missing. A field goal attempt is worth 3 points times the success probability, but a miss surrenders possession at the spot of the kick (the line of scrimmage plus 7 yards for the snap). Advanced NFL analytics suggest that field goal attempts are generally advisable when the expected points from the kick exceed the expected points from punting or attempting a fourth-down conversion. As a rough guideline, kicks under 45 yards are almost always worth attempting, kicks from 45 to 52 yards depend on game situation and kicker ability, and kicks beyond 55 yards are rarely advisable unless the game situation demands it.
How does altitude affect field goal distance and accuracy?
Higher altitude significantly benefits field goal kicking because the thinner air reduces aerodynamic drag on the football. At Denver, Colorado (5,280 feet elevation), the air density is approximately 17 percent less than at sea level, allowing kicks to travel 3 to 5 yards farther with the same leg power. This is why several long-distance field goal records have been set at Mile High Stadium. The reduced air resistance also means the ball maintains its velocity longer during flight, making the trajectory flatter and more predictable. However, altitude does not significantly affect accuracy or direction control, so the benefit is primarily in extending maximum range. Kickers visiting Denver for away games also benefit from this effect, making it a venue-specific advantage rather than a home team advantage.
References
Reviewed by Sher, Sports Science & Nutrition Specialist · Editorial policy