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Proper Best of 2 Matchup Pricing and Excel Formulas

๐Ÿ‘ค BVWAI Team ๐Ÿ“… October 6, 2025 โฑ๏ธ 10 min read

A case study in Fissure Universe 7 DOTA2 pricing: How to Calculate Fair Match Prices When Draws Pay Half

When betting markets offer odds on teams going 2-0 in a best-of-two series, but draws (1-1 results) are resolved by awarding each team half a win, how do we determine the fair price for each team to "win" the match? This article walks through the mathematical framework and provides practical Excel formulas.

The Problem Setup

Consider a best-of-two series between 1win (the underdog) and Avulus (the favorite) where:

  • 1win is +350 to go 2-0 (4.50 in decimal odds)
  • Avulus is +250 to go 2-0 (2.50 in decimal odds)
  • Draws (1-1 split) are resolved at 0.50 (each team receives half credit)

We need to find fair prices for assets that pay out $1 if that team wins, where the prices should sum to 1.

Understanding Best-of-Two Series

In a best-of-two series, there are three possible outcomes:

  1. Team A wins 2-0 (wins both games)
  2. Team B wins 2-0 (wins both games)
  3. Draw 1-1 (each team wins one game)

Unlike best-of-three series where one team must eventually win, best-of-two series naturally allow for ties.

Step 1: Convert Odds to Implied Probabilities

First, we extract the implied probabilities from the given odds. For decimal odds, the implied probability is simply:

Implied Probability = 1 / Decimal Odds

For our match:

  • P(1win goes 2-0) = 1/4.50 = 0.2222 (22.22%)
  • P(Avulus goes 2-0) = 1/2.50 = 0.4000 (40.00%)
  • P(Draw 1-1) = 1 - 0.2222 - 0.4000 = 0.3778 (37.78%)

These three probabilities sum to 100%, covering all possible outcomes in the best-of-two series.

Step 2: Calculate Expected Payouts

Since a 1-1 draw awards 0.5 to each team rather than 0, we need to calculate each team's expected payout across all scenarios.

1win's Expected Payout:

  • Win 2-0: Pays 1.0 with probability 0.2222 โ†’ 1.0 ร— 0.2222 = 0.2222
  • Draw 1-1: Pays 0.5 with probability 0.3778 โ†’ 0.5 ร— 0.3778 = 0.1889
  • Lose 0-2: Pays 0.0 with probability 0.4000 โ†’ 0.0 ร— 0.4000 = 0.0000
  • Total expected payout: 0.2222 + 0.1889 = 0.4111

Avulus's Expected Payout:

  • Win 2-0: Pays 1.0 with probability 0.4000 โ†’ 1.0 ร— 0.4000 = 0.4000
  • Draw 1-1: Pays 0.5 with probability 0.3778 โ†’ 0.5 ร— 0.3778 = 0.1889
  • Lose 0-2: Pays 0.0 with probability 0.2222 โ†’ 0.0 ร— 0.2222 = 0.0000
  • Total expected payout: 0.4000 + 0.1889 = 0.5889

Verification: 0.4111 + 0.5889 = 1.0000 โœ“

This is exactly what we need: prices that sum to 1, representing a complete probability distribution.

The General Formula

For any team X with given odds to go 2-0 in a best-of-two series, the fair price is:

Fair Price(X) = P(X wins 2-0) + (R ร— P(Draw 1-1))

Where:

  • P(X wins 2-0) = 1 / Odds_X (to go 2-0)
  • P(Draw 1-1) = 1 - 1/Odds_A - 1/Odds_B
  • R = Draw resolution value (0.5 in this case)

Expanding this formula:

Fair Price(X) = 1/Odds_X + 0.5 ร— (1 - 1/Odds_A - 1/Odds_B)

Excel Implementation

Here's how to implement this in Excel:

Setup:

  • A1: 1win decimal odds to go 2-0 (4.50 for +350 American)
  • B1: Avulus decimal odds to go 2-0 (2.50 for +250 American)
  • C1: Draw resolution value (0.5)

Formulas:

// 1win Fair Price
=1/A1 + C1*(1-1/A1-1/B1)

// Avulus Fair Price
=1/B1 + C1*(1-1/A1-1/B1)

Converting American Odds to Decimal (if needed):

// For positive American odds (e.g., +350)
=(American_Odds/100) + 1

// For negative American odds (e.g., -150)
=(100/ABS(American_Odds)) + 1

Final Results

Using our example:

Team Odds to go 2-0 American Fair Price
1win (Underdog) 4.50 +350 41.11ยข
Avulus (Favorite) 2.50 +250 58.89ยข
Total - - 100.00ยข

Interpretation

These fair prices tell us that:

  • An asset paying $1 if 1win wins the series should trade at $0.4111
  • An asset paying $1 if Avulus wins the series should trade at $0.5889
  • Despite being the underdog in the 2-0 market, 1win has a 41% chance of "winning" due to the 1-1 draw resolution favoring both teams equally

Key Insights

  1. Draw resolution matters: With 1-1 draws paying 0.5 to each team, both teams benefit from the draw probability (37.78%), which pulls their fair prices closer together than the outright 2-0 odds suggest.
  2. Prices sum to 1: This framework ensures a coherent probability distribution, essential for prediction markets and portfolio-based betting.
  3. Best-of-two structure: Unlike best-of-three or best-of-five series where someone must win, best-of-two series have substantial draw probability, making the resolution rule critically important.
  4. The formula generalizes: Change the draw resolution value (R) to any number between 0 and 1 to model different payout structures (e.g., R=0 means draws pay nothing, R=1 means draws count as full wins).

Practical Applications

This methodology is valuable for:

  • Prediction markets pricing binary outcomes with partial resolution
  • Esports betting where best-of-two formats are common
  • Portfolio optimization when allocating across correlated assets
  • Arbitrage detection by comparing market prices to fair values

This mathematically sound approach to price discovery can be applied to any market structure where intermediate outcomes have fractional payouts.