Worked Examples

These examples walk through actual index calculations using the midprice-v1 methodology. Each example uses realistic numbers and can be replicated with a spreadsheet and public market data from Polymarket.

Every number below is computed using 8-decimal-place precision with round-half-up, matching the production system exactly. If you follow along in a spreadsheet, your results should match within rounding tolerance.

Example 1: Equal-Weighted Index with 5 Active Markets

A macro-themed series tracking 5 economic prediction markets, all actively trading with two-sided order books. Series Composition:

#	Market	Best Bid	Best Ask	Midprice	Raw Weight
1	Fed cuts by June	0.82	0.83	0.8250	0.20
2	CPI below 3% by Q2	0.71	0.72	0.7150	0.20
3	Unemployment above 4.5%	0.35	0.37	0.3600	0.20
4	10Y yield below 4%	0.44	0.46	0.4500	0.20
5	GDP growth above 2%	0.58	0.59	0.5850	0.20

Compute midprices

For each market, average the best bid and best ask:

Market 1: (0.82 + 0.83) / 2 = 0.82500000
Market 2: (0.71 + 0.72) / 2 = 0.71500000
Market 3: (0.35 + 0.37) / 2 = 0.36000000
Market 4: (0.44 + 0.46) / 2 = 0.45000000
Market 5: (0.58 + 0.59) / 2 = 0.58500000

Each midprice represents the market’s implied probability for that event occurring.

Normalize weights

Sum of raw weights = 5 x 0.20 = 1.00

Since the raw weights already sum to 1.00, normalized weights equal the raw weights:

w'_1 = w'_2 = w'_3 = w'_4 = w'_5 = 0.20000000

Compute the raw index value

Multiply each normalized weight by its market’s midprice and sum:

raw_nav = (0.20 x 0.82500000)
        + (0.20 x 0.71500000)
        + (0.20 x 0.36000000)
        + (0.20 x 0.45000000)
        + (0.20 x 0.58500000)

        = 0.16500000
        + 0.14300000
        + 0.07200000
        + 0.09000000
        + 0.11700000

        = 0.58700000

Compute Index Level

Assume the series launched with an inception raw index value of 0.55000000:

index_level = 100 x (0.58700000 / 0.55000000)
            = 100 x 1.06727273
            = 106.72727273

The index has gained approximately 6.7% from inception.

Interpretation: The weighted-average implied probability across all 5 markets is about 58.7%. The highest-confidence market is “Fed cuts by June” at 82.5%, while the lowest is “Unemployment above 4.5%” at 36%. The index is up ~6.7% from inception, meaning the aggregate probability of these events has increased since the series launched.

The markets in this example are illustrative, so live prices will differ. To verify a real published value, pick a live series, fetch the current best bid and best ask for each of its constituents, and follow the Independent Verification Guide – your result should match the published raw index value within the tolerances documented there.

Example 2: Index with Resolved Markets

A 4-market series where two markets have already settled – one won, one lost. Series Composition:

#	Market	Status	Tracked Outcome	Price Source	Price Used	Raw Weight
1	Fed cuts in January	Resolved	YES (Won)	Settlement	1.00	0.25
2	CPI below 2% in Q1	Resolved	YES (Lost)	Settlement	0.00	0.25
3	Recession by mid-year	Active	YES	Midprice	0.18	0.25
4	Core PCE below 2.5%	Active	YES	Midprice	0.62	0.25

Apply resolution prices

Market 1: The tracked outcome (YES) won – settlement price = $1.00
Market 2: The tracked outcome (YES) lost – settlement price = $0.00
Markets 3 and 4 remain active and use live midprices from the order book

Normalize weights

All four markets participate in the computation regardless of resolution status.

Sum of raw weights = 4 x 0.25 = 1.00
Normalized weight = 0.25 for each market

Compute the raw index value

raw_nav = (0.25 x 1.00)     Market 1: resolved winner
        + (0.25 x 0.00)     Market 2: resolved loser
        + (0.25 x 0.18)     Market 3: active
        + (0.25 x 0.62)     Market 4: active

        = 0.25000000
        + 0.00000000
        + 0.04500000
        + 0.15500000

        = 0.45000000

Interpret the result

The raw index value of 0.45 reflects the mix of settled outcomes and remaining active markets:

The winning market (#1) contributes its full weight (0.25) to the index value
The losing market (#2) contributes nothing (0.00)
The two active markets contribute based on their current implied probabilities

Resolved markets remain in the index with their settlement prices. They are not removed. This means a losing market at $0.00 permanently drags the index down by its weighted share, while a winning market at $1.00 permanently supports it. This is by design – the index tracks the full history of outcomes.

What if both resolved markets had won?

raw_nav = (0.25 x 1.00) + (0.25 x 1.00) + (0.25 x 0.18) + (0.25 x 0.62)
        = 0.25 + 0.25 + 0.045 + 0.155
        = 0.70

The index value would be 0.70 instead of 0.45 – a significant difference driven entirely by the resolution outcomes.

Example 3: Staleness – Missing Price Data

What happens when the system cannot fetch a current price for one of the underlying markets. Scenario: A 4-market series where Market #3’s price fetch fails after three retries.

#	Market	Current Price	Previous Price	Status
1	Market A	0.72 (live)	0.70	Fresh
2	Market B	0.55 (live)	0.53	Fresh
3	Market C	fetch failed	0.41	Stale (using fallback)
4	Market D	0.88 (live)	0.87	Fresh

All markets have equal weight (0.25 each).

Apply fallback for Market #3

The system attempted to fetch Market C’s order book three times with exponential backoff. All attempts failed (e.g., API timeout or network error).Fallback rule: Use the last successfully fetched price. Market C’s previous midprice was 0.41, so that value is used.

Compute the raw index value

raw_nav = (0.25 x 0.72)   Market A: fresh
        + (0.25 x 0.55)   Market B: fresh
        + (0.25 x 0.41)   Market C: stale (fallback)
        + (0.25 x 0.88)   Market D: fresh

        = 0.18000000
        + 0.13750000
        + 0.10250000
        + 0.22000000

        = 0.64000000

Flag the computation as stale

Because Market C used a fallback price, the entire computation is marked as stale. This flag is visible in the published data.If Market C’s actual price had moved (say, from 0.41 to 0.48), the true index value would be:

true_raw_nav = (0.25 x 0.72) + (0.25 x 0.55) + (0.25 x 0.48) + (0.25 x 0.88)
             = 0.65750000

The difference (0.6575 vs 0.6400) is 0.0175, or about 2.7% – entirely attributable to the stale data.

A stale index value should be interpreted with caution. The published value may be higher or lower than reality, depending on how the affected market’s price has moved since the last successful fetch. Once the price feed recovers, subsequent computations will use fresh data and the staleness flag will clear.

When does staleness trigger?

Condition	Result
API timeout or network failure	Stale – uses last known price
One-sided order book (only bids, no asks)	Stale – midprice cannot be computed
Market data unavailable for all markets	Computation fails entirely
Market is resolved	Never stale – settlement prices are definitive

Example 4: Tracking Index Level Over Time

How the Index Level tracks performance from inception to present, and how it relates to the raw index value. Scenario: A series launches with an inception raw index value of 0.4200. Over six weeks, market prices shift:

Date	Raw index value	Index Level Calculation	Index Level	Change
Week 0 (inception)	0.42000000	100 x (0.4200 / 0.4200)	100.00	–
Week 1	0.43500000	100 x (0.4350 / 0.4200)	103.57	+3.57%
Week 2	0.39800000	100 x (0.3980 / 0.4200)	94.76	-5.24%
Week 3	0.41000000	100 x (0.4100 / 0.4200)	97.62	-2.38%
Week 4	0.45000000	100 x (0.4500 / 0.4200)	107.14	+7.14%
Week 5	0.44200000	100 x (0.4420 / 0.4200)	105.24	+5.24%
Week 6	0.47600000	100 x (0.4760 / 0.4200)	113.33	+13.33%

Index Level at inception

At launch, the Index Level is always 100.00 – this is the base value.

index_level = 100 x (0.42000000 / 0.42000000) = 100.00000000

Index Level after a gain (Week 1)

The raw index value increased from 0.4200 to 0.4350 (underlying probabilities rose):

index_level = 100 x (0.43500000 / 0.42000000)
            = 100 x 1.03571429
            = 103.57142857

The index is up 3.57% from inception.

Index Level after a decline (Week 2)

The raw index value dropped to 0.3980 (some underlying probabilities fell):

index_level = 100 x (0.39800000 / 0.42000000)
            = 100 x 0.94761905
            = 94.76190476

The index is down 5.24% from inception. Note: the drawdown from Week 1 to Week 2 is even larger – from 103.57 to 94.76, a decline of 8.5% week-over-week.

Full recovery and beyond (Week 6)

By Week 6, the raw index value has risen to 0.4760:

index_level = 100 x (0.47600000 / 0.42000000)
            = 100 x 1.13333333
            = 113.33333333

The index is up 13.33% from inception. Over that span the index swung from 94.76 (Week 2 low) to 113.33 (Week 6).

Key properties of the Index Level:

Property	Explanation
Always starts at 100	The base value is set at inception
Proportional to the raw index value	A 10% increase in the raw index value = a 10% increase in Index Level
Inception value is fixed	The denominator never changes – it is locked at the first computation
Cannot go below 0	Because the raw index value is bounded between 0 and 1, and inception is positive
Cannot exceed ~238	Because the raw index value maxes out at 1.0 (in the inception_raw_nav = 0.42 example above)

The Index Level tracks theoretical index performance, gross of costs. It is a measurement of a basket, not a return anyone realized: no fund, product, or account tracks these indices.

Formula Reference

For quick reference, all formulas used in these examples:

Formula	Expression
Midprice	`(best_bid + best_ask) / 2`
Weight normalization	`w'_i = w_i / sum(w)`
Raw index value	`sum(w'_i x price_i)` for all markets
Index Level	`100 x (raw_nav / inception_raw_nav)`

Index Calculation Methodology

Full methodology specification with verification guide.

Perpetual Series

Reconstitution, chain-linking, and review cadence.

Getting Started

Understanding Indices

Belief Volatility

Transparency

Data Access

Risk & Legal

Reference

Example 1: Equal-Weighted Index with 5 Active Markets

Example 2: Index with Resolved Markets

Example 3: Staleness – Missing Price Data

Example 4: Tracking Index Level Over Time

Formula Reference

Index Calculation Methodology

Perpetual Series

​Example 1: Equal-Weighted Index with 5 Active Markets

​Example 2: Index with Resolved Markets

​Example 3: Staleness – Missing Price Data

​Example 4: Tracking Index Level Over Time

​Formula Reference

Index Calculation Methodology

Perpetual Series

Example 1: Equal-Weighted Index with 5 Active Markets

Example 2: Index with Resolved Markets

Example 3: Staleness – Missing Price Data

Example 4: Tracking Index Level Over Time

Formula Reference