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Model Confidence Intervals for Over/Under Lines: How Wide Should You Trust a Prediction?

ttotals

2026-01-30

11 min read

Learn to read confidence intervals around totals projections, convert them to probabilities, and decide when to fade or follow with smart bet sizing.

Stop Treating a Totals Projection Like Gospel — Read the Interval

If you've ever stared at a model's totals projection and wondered how wide a margin of error to trust, you're not alone. Bettors and fantasy managers get burned when a model gives a single number and nothing about uncertainty. That gap costs money and poor lineup choices. This guide explains how to read confidence intervals around a totals projection, how to convert them into actionable probabilities, and exactly when to fade the model or follow it — with practical bet-sizing and risk-management rules you can apply in 2026.

Top takeaways (most important first)

Always use the predictive distribution — not just the projected mean. The predictive distribution combines inherent game randomness with model uncertainty.
If the market total lies outside your model's 95% confidence interval, you almost always have a strong edge worth investigating — but not always a bet.
Convert the model's distribution to an implied probability and compare to the market after removing vig; this tells you if there is positive expected value (EV).
Use a fractional Kelly approach to size bets and dial down exposure when model uncertainty (interval width) is large.
In 2026, live lines and rapidly updated ensemble models make timing and calibration essential — update predictions as new info arrives and track calibration regularly.

Why a single totals projection misleads — the two types of uncertainty

Most models spit out a single totals projection (e.g., O/U 48.5). That number is the model's best estimate of the expected total — but it hides two sources of uncertainty:

Aleatoric uncertainty — the inherent randomness in any sporting contest (weather, turnovers, bounces). This is irreducible at the game level and shows up as spread in final scores even if you knew the "true" game mean.
Epistemic uncertainty — model error from limited data, parameter uncertainty, injuries not accounted for, or new tactics. This shrinks as you get better data or model ensembles.

Good predictive work reports a confidence (or credible) interval that reflects both components. In modern practice (late 2025 into 2026), serious totals models deliver a predictive standard deviation and thus a 68%/95% interval for the final total.

What a confidence interval tells you — and what it doesn't

A 95% confidence interval of [44.0, 52.0] around a projected mean of 48.0 means the model's predictive distribution expects the true final total to land in that range approximately 95% of the time, considering both game randomness and model uncertainty.

What it doesn't mean: it isn't a guarantee for one game. It expresses long-run frequency from the model's perspective. But for decision-making that single-game projection is exactly what you need — if you translate it into a probability for the over and under.

Convert an interval into a probability for Over/Under

Most models provide the mean (μ) and predictive standard deviation (σ). Assuming the predictive distribution is approximately normal (a reasonable first-order assumption for totals), you can compute P(total > market_total) quickly with a z-score.

Step-by-step formula

Get your model's predictive mean μ and predictive standard deviation σ (σ accounts for game variance + model uncertainty).
Compute z = (market_total - μ) / σ.
Lookup P(total > market_total) = 1 - Phi(z), where Phi is the standard normal CDF.

Worked example (NBA style)

Model projects μ = 47.5 points with a predictive σ = 6.0 (reflecting typical NBA game variance plus model uncertainty). The sportsbook posts O/U = 50.5.

z = (50.5 - 47.5) / 6.0 = 0.5
P(total > 50.5) = 1 - Phi(0.5) ≈ 0.31 (31%)

This tells you the model thinks the under is ~69% likely. If market odds (after vig) imply less than 69% for the under, you might have an edge.

Account for juice — convert odds to vig-free probabilities

Totals lines usually have symmetric juice like -110 on both sides. For -110, the sportsbook's implied probability per side is ~52.38% before removing vig. You must remove vig to compare the model's probability to the market fair probability.

Quick vig removal for two-outcome market

Convert American to decimal odds (e.g., -110 → 1.909 decimal).
Compute implied probabilities for both sides (p1 and p2). Sum = S > 1 due to vig.
Fair probability for side 1 = p1 / S.

Example: both sides -110 → p1 = p2 = 0.5238, S = 1.0476, fair probability for over = 0.5238 / 1.0476 = 0.5. So at -110 symmetry, fair price is 50/50, but many totals markets move and vig structures differ — always normalize.

Decision rules: when to fade the model vs. follow it

Use a structured decision framework rather than gut feel. These rules assume you have μ and σ and have computed the market's fair probability q for your side (e.g., under).

Rule A — Strong follow (high conviction)

Market total lies outside your model's 95% predictive interval.
Model probability p for chosen side > market fair probability q by ≥ 5 percentage points (p - q ≥ 0.05).
No late-breaking injury or weather news contradicting model inputs.

Action: place a calculated-sized bet (fractional Kelly, see sizing section) and monitor line movement.

Rule B — Conditional follow (moderate conviction)

Market total is outside the 68% but inside the 95% interval.
p - q between 2–5 percentage points.
Line liquidity is reasonable and limits allow your target size.

Action: small bet, use smaller Kelly fraction (e.g., 10–20% of full Kelly), prefer mid-market or sharp books.

Rule C — Lean but don't bet (low conviction)

Market lies inside the 68% interval.
p - q < 2 percentage points.

Action: no bet, but track line for movement after news. Consider live or micro-bets if lines move outside interval.

Rule D — Fade the model

Market is strongly inside the opposite tail of the interval (market total near model median but odds imply the other side much more likely).
Historical calibration shows your model underestimates a known factor (e.g., pace or new coach adjustments).
Or you detect a clear market inefficiency: public overreaction to recent low-sample events.

Action: proceed cautiously. Unlike following, fading exposes you to model misspecification risk. Use small, conservative sizing, and require additional evidence (team news, line moves) before expanding exposure.

Confidence intervals tell you the size of your uncertainty. Let that size drive how much capital you risk.

Bet sizing: translate probability edge into stake size

Once you have a model probability p and a market fair probability q, compute expected value and then apply a staking plan. We recommend a fractional Kelly due to non-stationarity in sports markets and model misspecification risk.

Quick formulas

Decimal odds d (e.g., -110 → 1.909). Edge EV per $1 = d*p - 1.
Full Kelly fraction f* = (bp - (1 - p)) / b, where b = d - 1.
Use fractional Kelly: 20–33% of f* is a common conservative choice.

Example with numbers

Model gives p = 0.60 (60% chance under). Book's fair probability q = 0.52 at -110 (decimal d = 1.909). b = 0.909.

Full Kelly f* = (0.909*0.60 - 0.40) / 0.909 = (0.5454 - 0.40)/0.909 = 0.1599 ≈ 16.0%
Fractional Kelly at 25% → stake = 0.25 * 16.0% = 4.0% of bankroll.

Because sports models often have overconfidence, many pros use 5–10% of full Kelly (i.e., 0.8–1.6% of bankroll in the example) for conservative long-term growth.

Calibration checks — the secret to trusting your intervals

Intervals are only useful if calibrated. In 2026, best-in-class modelers run routine calibration diagnostics:

Reliability diagrams: compare predicted quantiles to actual outcomes across thousands of games.
Backtesting by market conditions: separate calibration for high-pace vs. low-pace games, inclement weather, or playoffs.
Bootstrapped confidence intervals: estimate uncertainty of your interval width itself.

If your 95% intervals only capture ~80% of outcomes historically, widen them or retrain until well calibrated. If they're too wide, you're being overly conservative and leaving EV on the table.

Live betting and 2026 trends that change how you use intervals

Late 2025 and early 2026 brought several market shifts you must account for:

Faster line updates via AI and wider API access: books now update in-play lines faster, shrinking reaction windows. Your model must ingest real-time inputs to keep intervals meaningful for live bets.
Model ensembles are standard: Many professional groups average multiple architectures (XGBoost, neural nets, Bayesian models) to better quantify epistemic uncertainty and produce more reliable intervals.
Public availability of line-movement data: New datasets let you model market microstructure and detect when the sharp money is driving a move — useful to avoid following overcrowded edges.
Regulatory pressure on limits: sharper bettors may face limits sooner; build sizing plans that consider reduced liquidity.

Practical workflow you can implement tonight

Calculate μ and predictive σ for the game using your model (or get them from a trusted provider).
Compute the market fair probability q after removing vig.
Compute model probability p for the side you prefer using the z-score method.
Check calibration history for similar game types (home/away, playoff, weather). If calibration is poor, shrink stake.
Apply fractional Kelly based on p and d; if the market is outside 95% CI, you can be more aggressive, but still use fractional Kelly.
Track line movement. If sharp books move against you, reassess; if public books move but sharps hold, be cautious.

Case study: When a wide interval says "do not bet"

Scenario: early-season NHL game between two teams with a new coaching staff. Model projects μ = 5.2 goals, with a wide predictive σ = 1.8 because of limited data. Book posts O/U = 6.0.

z = (6.0 - 5.2) / 1.8 = 0.444 → P(over) ≈ 0.33
Model says under ~67% likely, but σ is large due to epistemic uncertainty.
Decision: because interval is wide and calibration on new-coach games is poor, you either decline to bet or use tiny stake (e.g., 1% of what you'd risk on a well-calibrated scenario).

Why? Even though the model favors the under, the wide interval signals low confidence. Fading the model here would be foolish because the model acknowledges high uncertainty.

When to fade the model — specific red flags

Your model's interval is narrow but historically miscalibrated for this matchup type (e.g., after a mid-week schedule for NFL).
Market makers with known sharp activity consistently disagree and move the line in pre-game minutes — this often signals information your model lacks.
There is asymmetric information your model can't incorporate quickly (sudden injury morning of game, lineup scratch, travel issues).

Putting it all together: an actionable checklist

Get μ and σ. If your tool doesn't report σ, don't trust the single-number projection.
Translate σ into 68%/95% intervals and human-readable probabilities for over/under.
Remove vig and compute market fair probabilities.
Apply decision rules A–D and verify calibration for similar games.
Size with fractional Kelly and adjust down when interval width is large.
Monitor line flow and sharp moves; be ready to cancel or hedge if new credible info arrives. For observability and incident learnings, study recent failures and how they affected feeds (postmortems on outages).

Final thoughts — what smart bettors do differently in 2026

In 2026, the winners will be the bettors who treat projections as distributions, not certainties. That means paying attention to interval width, routinely checking calibration, and sizing bets to reflect model confidence. Ensemble models, live updates, and better market data mean you can act faster — but that speed increases the penalty for ignoring uncertainty.

Start small, think statistically, and let interval width dictate risk. The single best behavioral change you can make is to reduce stake when uncertainty grows and only increase it when both your probability edge and your historical calibration justify a larger bet.

Call to action

Want intervals, calibrated probabilities, and a built-in staking calculator for every totals projection? Try our totals.us model overlay that shows μ, σ, 68%/95% intervals, and a suggested fractional Kelly stake in real time. Sign up for alerts and get notified the moment a market moves outside model confidence bounds — so you can act with conviction, not guesswork.

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