Derivative Props

Derivative props are event-based wagers that depend on specific occurrences during a game. Unlike volume-based player props (which accumulate stats), derivative props are binary: the event either happens or it doesn't.

Warning

Derivative props carry significantly higher variance and typically have higher vig than standard Over/Under props. They should be treated as situational bets, not core strategy.

What Makes Derivative Props Different

Characteristic	Volume Props (Yards, Points)	Derivative Props (TD, HR, First Basket)
Outcome Type	Continuous accumulation	Binary (yes/no)
Variance	Moderate	High
Market Structure	Two-way (O/U)	Often one-way
Typical Vig	4-7%	15-40%+
Modeling Approach	Normal or Negative Binomial	Poisson or direct probability
Edge Required	~3-5% to profit	~10-15%+ to overcome vig

Types of Derivative Props

1. Anytime Scorer Props

Examples:

Anytime Touchdown Scorer (NFL)
Anytime Goal Scorer (NHL, Soccer)
Home Run (Yes) (MLB)

These are the most common derivative props. You're betting whether a player will achieve at least one scoring event during the game.

NFL Anytime Touchdown Scorecard:

Prop Type	Softness	Stability	Modelability	Execution	Tag
RB Anytime TD	Medium	Medium	Medium	Medium	Situational
WR/TE Anytime TD	Medium	Low	Low	Medium	Situational
QB Anytime TD (Rushing)	High	Low	Low	Medium	Situational

Key Insight

Anytime TD props are often structured as one-way markets (Yes only, no "No" option). This hides the true vig. Without a "No" price to compare against, you can't calculate the exact hold—but assume it's 20-40% or higher.

2. First Scorer Props

Examples:

First Touchdown Scorer (NFL)
First Basket Scorer (NBA)
First Goal Scorer (NHL, Soccer)

These combine two levels of uncertainty: will the player score at all, AND will they score first?

First Scorer Scorecard:

Prop Type	Softness	Stability	Modelability	Execution	Tag
First TD Scorer	High	Very Low	Low	Low	Avoid (except promos)
First Basket	Medium	Low	Medium	Medium	Situational
First Goal Scorer	High	Very Low	Low	Low	Avoid (except promos)

Warning

First Scorer props have extreme variance. Even with a 15% edge, you could easily go 1-10 before regressing toward your true win rate. These should only be bet with promotional boosts or overwhelming evidence of mispricing.

3. Scoring Method Props

Examples:

First TD by Pass/Rush/Return
First Basket by Dunk/3-Pointer/Layup
Exact Number of Touchdowns Scored

These add another layer of specificity and uncertainty.

Prop Type	Tag	Notes
TD Scoring Method	Avoid (except promos)	Compounds uncertainty
Exact TD Count	Avoid	Very high vig, lottery-ticket style

The Hidden Vig Problem

In a standard two-way market like Over/Under 26.5 (-110/-110), you can calculate the vig:

Implied Over: 52.38%
Implied Under: 52.38%
Total: 104.76%
Vig: 4.76%

But in a one-way market like "Derrick Henry Anytime TD (Yes +150)," there's no "No" to compare against.

How Books Hide the Vig:

Let's say the true probability of Henry scoring a TD is 45%.

Fair odds at 45%: +122 (100/0.45 - 100)
Book offers: +150

Wait, that looks like good value! But here's the trick: the true probability might actually be closer to 50%, making fair odds +100. The +150 still looks appealing, but the book has built in 15-20% margin by underestimating the true probability in their pricing.

Implied Probability (Positive Odds)

Implied Probability = 100 ÷ (Odds + 100)

Excel: =100/(A1+100)

Example Calculation:

Anytime TD at +150
Implied probability: 100 ÷ (150 + 100) = 100 ÷ 250 = 40%
If true probability is 50%, book has 10% edge
If true probability is 45%, book has 5% edge

Calculate the implied probability and vig on any derivative prop

When Derivative Props Make Sense

Despite the structural disadvantages, there are specific situations where derivative props become viable:

1. Promotional Boosts

Sportsbooks frequently offer profit boosts (20%, 50%, 100%) on derivative props. A +150 boosted to +200 can flip a -EV bet to +EV.

Example:

Anytime TD at +150 (implied 40%)
Your projection: 42% probability
At +150: EV = (0.42 × 1.50) - (0.58 × 1) = 0.63 - 0.58 = +0.05 (+5% edge)
With 50% boost to +225: EV = (0.42 × 2.25) - (0.58 × 1) = 0.945 - 0.58 = +0.365 (+36.5% edge)

Tip

Promotional boosts can transform derivative props from -EV to strongly +EV. Always calculate the boosted expected value before assuming a promo is good.

2. Extreme Role Changes

When a player's role dramatically changes and the market hasn't adjusted, derivative props can offer edge:

Backup RB becomes starter (TD probability doubles)
Star WR ruled out, slot receiver becomes primary red zone target
Goalie injury creates goal-scoring opportunity for offense

3. Specific Matchup Exploitation

Sometimes you can identify a matchup that dramatically increases scoring probability:

Goal-line back vs. worst red zone defense
Shootout game script (high total, close spread)
Opponent allows most first baskets to opposing center

MLB Home Run Props: A Special Case

MLB "Home Run (Yes)" props are derivative but more modelable than most:

Input	Impact
Batter power metrics (ISO, barrel rate)	High
Pitcher HR/FB rate	High
Ballpark factors	High
Weather (wind, temperature)	Medium
L/R matchup splits	Medium

Key Insight

MLB home run props are one of the few derivative markets where systematic modeling can generate consistent edge—but only if you account for all the relevant factors. The variance is still high; you need a large sample to realize your edge.

📝 Exercise

Instructions

Test your understanding of derivative props and their unique characteristics.

Why do one-way derivative props (like Anytime TD with no 'No' option) have 'hidden vig'?

A sportsbook offers 'First TD Scorer: Travis Kelce +650'. What is the implied probability?

Which scenario represents the BEST opportunity to bet an Anytime TD prop?

First Scorer props are categorized as 'Avoid (except promos)' primarily because:

Vig Calculator

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