Compare go-for-it expected value with a field-goal or punt alternative, or solve the fourth-down conversion probability that makes the two modeled branches break even.

Required: conversion probability, net expected points after success and failure, plus the visible field-goal outcome inputs.

Use the current offense’s perspective and the same expected-points model for every branch.
A net value can be below 3 because the opponent receives the next possession.
Include expected landing position, touchbacks, returns, and the opponent’s ensuing possession in one offense-relative net value.

Fourth Down Expected-Points Formula

A fourth-down choice can be written as a small outcome tree. Going for it has one value when the offense converts and another when it is stopped. The conversion probability weights those two branches:

EP₍go) = p₍go)EP₍success) + (1 - p₍go))EP₍failure)

The expected-point values must use the same offense-relative scale. A negative value is allowed when the opponent’s resulting possession is expected to be worth more than the current team’s future scoring value.

Field-Goal Alternative

When field goal is selected, the calculator applies the same two-branch structure:

EP₍FG) = pₘₐₖₑEP₍made) + (1 - pₘₐₖₑ)EP₍missed)

The made-field-goal value does not have to equal exactly three net points. A complete offense-relative value can subtract the opponent’s expected value after the ensuing kickoff. The missed value can reflect the opponent’s field position after the miss.

Punt Alternative

Punt mode accepts one net expected-point value after averaging the likely punt outcomes. A well-formed input can account for net distance, touchbacks, returns, penalties, and the opponent’s ensuing possession. The calculator does not infer that value from punt distance alone.

Break-Even Conversion Probability

Set the go-for-it branch equal to the selected alternative and solve for the conversion probability:

p₍break - even) = (EPₐₗₜₑᵣₙₐₜᵢᵥₑ - EP₍failure)) / (EP₍success) - EP₍failure))

If the result falls between 0% and 100%, it is the entered scenario’s break-even conversion rate. A result below 0% means the go branch is at least as large even when conversion probability is zero under those branch values. A result above 100% means the alternative remains larger even at a perfect conversion rate.

Where the Inputs Come From

Public NFL models such as nflfastR and nfl4th estimate expected points, field-goal probability, fourth-down conversion probability, and win probability from play-by-play data. Their outputs depend on field position, yards to go, time, score, team strength, model version, and other features.

This calculator does not copy a partial lookup table or silently approximate a complete model. Instead, it lets an analyst enter internally consistent branch estimates from the model or scouting source they trust, then audits the arithmetic and solves the exact break-even threshold.

Example

Suppose conversion is estimated at 55%, net expected points are 3.0 after success and -1.0 after failure. Go-for-it expected points are 0.55 times 3.0 plus 0.45 times -1.0, or 1.20.

If a field goal is estimated at 80%, with net values of 2.2 when made and -1.5 when missed, field-goal expected points are 1.46. Under those illustrative inputs, the field-goal branch is higher by 0.26 expected points. The break-even conversion rate is 61.5%.

Expected Points vs. Win Probability

Expected points summarize average scoring value, but game decisions are often evaluated with win probability. Late in a game, a lower-EP option can sometimes fit the exact score and clock better, while a higher-EP option can sometimes create the needed upside. A complete decision model also accounts for remaining possessions, timeouts, overtime, opponent strength, weather, and uncertainty.

The output therefore describes which entered branch has the higher modeled expected value. It does not issue a play call or claim that one choice is universally correct.

Assumptions and Limitations

  • All branch values must come from the same expected-points definition and the current offense’s perspective.
  • The success and field-goal probabilities are treated as known estimates.
  • One average value represents each outcome branch; the full distribution of gains, returns, penalties, and subsequent plays is compressed.
  • The calculation does not model score, clock, timeouts, overtime, opponent, personnel, weather, or risk preference by itself.
  • Expected-point comparisons can disagree with a complete win-probability model.
  • The default numbers are illustrative worksheet values, not league benchmarks or recommendations.

Browse the complete Football calculator collection or return to the Sports & Fitness Calculators hub.

Sources

Romer D. Do Firms Maximize? Evidence from Professional Football. Journal of Political Economy, 2006.

nflverse. nfl4th package documentation and nflfastR expected-points model documentation. Accessed 2026.

National Football League Next Gen Stats. Introducing the Next Gen Stats Decision Guide: A New Analytics Tool for Fourth Down and Two-Point Conversions. 2021.