Methods and sources: the rebate cut on low-priced combos

How Splitrule calculated the proposed rebate change for low-priced combos: formulas, rounding, eligibility, scope, sources and open questions.

Splitrule September 30, 2026

This note explains how Splitrule calculated the figures in The rebate cut that could pay makers more on low-priced combos. It gives the rules, formulas, rounding treatment, scope limits, sources and open questions behind that article.

Every fill in the calculations is invented. The fills are scenarios for the published rules. They are not observations of trading, and they describe no account.

The public sources were read up to September 30, 2026 at 01:15 UTC. The fee page and the politics combo amendment were read again later that day. The October terms remain a proposal. Splitrule did not contact the exchange.

The finding and its limits

The finding connects two published rules. The current fee page pays combo makers the standard maker formula. The September 22 proposal replaces that standard formula with a share of the taker fee charged on the maker's fills, before taker rebates. Combo takers pay a surcharge. If the fee share covers combo fills, part of that surcharge reaches the maker.

At the proposed top maker rate of 15%, the combo reward exceeds today's formula below about 29.8 cents per contract, before rounding. At the same rate, the comparison that uses the 0.0695 standard taker coefficient pays 83.4% of today's reward at every price. That is a 16.6% decrease before rounding. The 5% and 10% rates never exceed today's formula on a combo.

The one-fill example keeps its direction under ordinary cent rounding. For 1,000 contracts at 10 cents, today's maker rebate is $1.12 on either product. The gross taker fees are $6.26 for the standard contract and $8.88 for the combo. At 15%, the maker entitlements are $0.939 and $1.332. If each credit rounds once to cents, they become $0.94 and $1.33. Those rounded amounts illustrate one possible credit rule, not actual account credits.

This analysis does not claim any of the following:

The proposal cuts every maker reward.
The top-rate combo result applies to makers in every tier.
A lower-priced combo necessarily has more legs.
29.8 cents is an exact cutoff on an account statement.
Tying maker rewards to fees is a new exchange design.
A larger maker reward proves tighter quotes or better execution.
The remaining share of the fee measures exchange profit.

Scope

The article covers the published standard schedule and the combo executions that the standard schedule governs. It excludes crypto combos, cross-category combos and block trades.

The current fee page, labeled effective September 25, states that combo makers use the standard maker formula. The September 22 proposal replaces that standard formula. Neither document names a combo family in connection with the October replacement. The combo result is therefore conditional: it holds only if the replacement covers the relevant combo fills.

Family or execution	Documentary evidence	Treatment
Sports combos (CAOC)	The September 22 product terms define athletic constituent contracts. Current combo guidance uses CAOC identifiers and the standard maker baseline.	In scope, conditionally. This note does not assert that every CAOC fill moves to the new tiers.
Political combos (CPOC)	The public September 22 amendment defines Combination Outcome Contracts: Politics. It intends amended listing no earlier than October 6. It states no fee rule.	In scope under the same condition. The listing does not prove availability or fee coverage.
Crypto combos (CCRYOC)	The product terms place the family in the cryptocurrency category. The fee proposal keeps a separate 35% crypto maker rebate.	Excluded. The inspected text does not decide which rate applies to a whole crypto combo fee.
Cross-category combos (CROSS)	The product terms label the category Custom and allow constituents from several categories, including cryptocurrency.	Excluded until the applicable classification is stated, including a CROSS combo without a crypto leg.
Block executions	The proposal leaves block fees and rebates outside the change. A June 24 filing sets a separate per-contract block schedule.	Excluded for every product.

The fee page's September 25 date is later than the September 22 filing but earlier than the intended October 6 start. The two documents can describe different periods. The newer date therefore does not settle the October scope.

The natural reading applies the proposed share to the whole taker fee on a covered combo fill. The filing's fee-revenue rationale supports that reading. Current combo documentation also bases taker rebates on the actual combo fee. Neither point expressly assigns the future maker rule.

The main competing reading keeps combo makers on the 0.0125 formula. The fee page states that coefficient explicitly, and no underlying filing for the 0.04 combo term was found. Under that reading, the combo gain disappears. No inspected source supports a share of only part of the combo fee, or the removal of combo maker rebates.

The open question is: does the proposed standard maker fee share replace the 0.0125 maker formula on the relevant non-crypto combo executions, with no product-specific exception? An effective fee schedule, a filed amendment or a dated official implementation notice that answers it for those executions can settle it. A generic promise of lower fees, a product listing, an archive timestamp or the absence of an exclusion cannot.

Inputs and units

Current rules: the fee page as read on September 30 at 01:13:25 UTC. The standard taker coefficient is 0.0695, effective September 17. The maker coefficient is 0.0125.
Combo taker coefficient: 0.0695 + 0.04 × (1 − p)³, after the common factor C × p × (1 − p). Combo makers currently use 0.0125.
Proposal: the September 22 amendment, with an intended start on October 6. Maker rates of 0%, 5%, 10% and 15% are assigned scenario inputs, not anyone's actual tier.
Table Tennis: the announced 0.10 taker coefficient from September 30 at 11:59 p.m. ET, compared with today's 0.0125 maker formula. The comparison assumes that the proposed share applies.
C is the number of contracts. The price p is in dollars per contract. Fees and rebates are in dollars.
Prices cover every cent from $0.01 to $0.99. Combo terms permit a tick as small as $0.0001, so the chart's one-cent start is not a price floor.
Quantities run from 0.01 to 10,000 contracts. The fractional quantities test arithmetic edges. They do not assert that every product accepts them.
All money arithmetic uses exact decimal values. Maker and taker roles stay separate. The calculation assumes no common owner and estimates no profit.

The algebra

Let X = C × p × (1 − p), and let r be the assigned maker rate.

Today's unrounded maker reward is 0.0125X. The proposed standard reward is r × 0.0695X before fee rounding. Their ratio is r × 0.0695 / 0.0125.

At r = 5%, 10% and 15%, the ratios are 0.278, 0.556 and 0.834. The reward decreases are 72.2%, 44.4% and 16.6%. These are percentage changes in the reward, not percentage-point changes in a rate.

For a combo, the ratio is r × [0.0695 + 0.04 × (1 − p)³] / 0.0125. For any positive rate, it falls as the price rises. At r = 15%, the two formulas are equal where:

(1 − p)³ = (0.0125 / 0.15 − 0.0695) / 0.04
p ≈ 0.29807784530180044855

Exact decimal bisection brackets this root. No floating-point cubic solver is used.

At 10 cents, the continuous top-rate combo change is +18.392%. At 50 cents, it is −10.6%. These figures compare exact formulas, not rounded account credits.

As the price approaches zero, the combo ratio approaches 1.314 at 15%, 0.876 at 10% and 0.438 at 5%. The lower two limits stay below 1. So neither lower rate can beat today's formula at any price, including prices below one cent. The 1.314 limit is not a payout at a zero price.

The surcharge relative to the standard fee is 0.04 × (1 − p)³ / 0.0695. It is 41.96% at 10 cents and 7.19% at 50 cents, before rounding. The article rounds these values to 42% and 7%.

For Table Tennis, 0.15 × 0.10 / 0.0125 = 1.20. That is a 20% increase at every price before rounding, on the condition that the proposed share applies there.

The algebra carries the finding. The rounding examples below show where cents change it.

Rounding and fill splitting

Current single-fill taker fees and maker rebates round to the nearest cent, with exact halves to the even cent. In the calculation, the gross taker fee rounds first. The proposed entitlement is r times that rounded fee.

The proposal does not state how its percentage credits round or aggregate. The calculation therefore reports two hypothetical credit rules: round each fill's credit, or round the total once. Across 6,336 equal-total split-fill scenarios, they classify gain, loss or tie differently in 1,304. That count describes the scenario grid, not real trading.

For a multi-fill order, current documentation caps cumulative taker charges at the rounded cumulative exact fee. A fill's adjustment can only lower its individually rounded charge. The calculation uses one allocation that obeys these limits. It is not the exchange's verified allocation method.

These examples show the limits of the continuous result:

At 1 cent, 100 one-contract standard fills each round to a zero taker fee. The 7-cent rounded cumulative total is only an upper cap. It cannot create a charge.
At 50 cents today, 1,000 contracts in one fill earn a $3.12 maker rebate. As 500 two-contract fills, they earn $5.00, because each $0.00625 rounds up to $0.01. As 1,000 one-contract fills, they earn nothing. These are counterexamples, not a suggestion to split orders.
At 30 cents, the exact combo reward for 1,000 contracts at 15% is $2.621745, below today's exact $2.625. When the gross fee rounds first, the entitlement is $2.622, above today's paid $2.62. With one cent-rounded credit, both amounts are $2.62.
The 10-cent example keeps its direction under both credit rules: $0.939 and $1.332 exact, or $0.94 and $1.33 rounded, against $1.12 today.

The 30-cent case shows why the statement "all combo fills below 29.8 cents gain and all above lose" is false.

For one standard fill, a decrease after both rounding stages is certain when 0.002075 × C × p × (1 − p) > 0.01075. The right side allows $0.005 of error in today's rounded rebate, $0.00075 from 15% of the fee's rounding error and $0.005 of credit rounding error. For every price from 1 to 99 cents, 524 or more contracts satisfy this condition. It is sufficient, not necessary. Smaller fills need their own calculation.

Eligibility and fee flows

Today's standard maker formula has no volume floor, although small fills can round to zero. Under the proposal, a maker who qualifies for no standard tier loses that rebate.

The ordinary maker tiers use the previous calendar month's maker volume. The rate is 5% from $10 million, 10% from $50 million and 15% from $200 million. The tier sets the rate for the next period. It does not pay only on the volume above a threshold. With the next period's taker fees on a maker's fills held at $10,000, each five-point step adds $500 of calculated rebate. That example isolates the rate effect and predicts no activity.

Accepted external volume can qualify a maker for a different tier, and that route continues after the first month. In the first effective month, the tier uses the greatest of three inputs:

The previous calendar month's local volume.
Accepted external volume over the trailing 30 days.
The immediately preceding seven days of local volume, divided by seven and multiplied by thirty.

For example, with $1 million of prior local volume, $3 million of accepted external volume and $1.4 million over the preceding seven days, the scaled seven-day input of $6 million is the largest. Maker and taker volumes count separately. The proposal does not state exact normalization rules for maker or external volume.

The assigned maker rate applies to the taker fees charged on that maker's fills, before taker rebates. Let F be the collected taker fee, r the maker rate and b the taker rebate rate. Then the maker receives rF, the taker rebate is bF and the remainder is (1 − r − b)F.

The maker's amount does not depend on b. An $8.88 combo fee gives the maker $1.332 at 15% whether b is 0% or 50%. A fee-free fill gives no percentage maker rebate, but separate liquidity programs still apply. At the proposed maximum rates, the remainder is 35% of F before credit rounding and other programs. It is not an estimate of exchange profit.

The whole combo fee applies to a combo execution as a unit, not to each leg separately. The proposal does not change that gross fee. It changes the maker's share and the taker rebates.

The four previously rebated ordinary taker bands change as follows:

Prior-month taker volume	Current rebate rate	Proposed rebate rate
$250,000 to below $1 million	10%	0%
$1 million to below $10 million	25%	10%
$10 million to below $25 million	50%	15%
$25 million to below $50 million	50%	30%

The band below $250,000 stays at zero, and the band from $50 million stays at 50%. Placement exceptions can change a participant's rates. The current page says "over $250,000" in its text while its table starts at $250,000. The exact boundary treatment is therefore unresolved, and no article example depends on it.

With the gross fee held fixed, the taker's net fee rises by 0%, 11.1%, 20%, 70%, 40% and 0% across the six ordinary bands. The largest proportional increase is in the band from $10 million to below $25 million. Price and quantity change the dollar amounts but not these ratios, before credit rounding.

Claim audit

The table separates documentary statements from derived results and open points. Source labels refer to the list in the next section.

Claim in the article	Basis	Where this note shows it
October 6 is the intended start, subject to review	Documentary: S2, p. 1	Scope
The current baseline is a 0.0695 taker coefficient and a 0.0125 maker coefficient	Documentary: S1, with S3 for the September 17 date	Inputs and units
Current documentation pays combo makers the 0.0125 formula	Documentary: S1, combo taker fees	Scope
The fee share applies to combo fills that the standard schedule governs	Conditional analysis: S1 with S2, pp. 1 and 3	Scope
The standard comparison decreases 16.6% at 15% before rounding	Derived: 0.15 × 0.0695 / 0.0125 = 0.834	The algebra
The top-rate combo reward exceeds today's below about 29.8 cents	Derived, conditional on the combo scope	The algebra
The 5% and 10% rates cannot exceed today's combo formula	Derived, conditional on the combo scope	The algebra
Today's maker rebate is $1.12 for 1,000 contracts at 10 cents	Reproduced from S1 examples	The finding and its limits
The 15% entitlements are $0.939 and $1.332 on that fill	Derived, conditional on the combo scope	The finding and its limits
Credited amounts will be $0.94 and $1.33	Not established: one hypothetical credit rule	Rounding and fill splitting
The 5% and 10% standard comparisons decrease 72.2% and 44.4%	Derived	The algebra
The surcharge adds about 42% at 10 cents and 7% at 50 cents	Derived	The algebra
Table Tennis gains 20% at 15%	Conditional: S1 announcement with the S2 tiers	The algebra
Ordinary maker tiers start at $10 million, $50 million and $200 million	Documentary: S2, p. 3	Eligibility and fee flows
Maker and taker volumes count separately	Documentary: S2, p. 1	Eligibility and fee flows
First-month placement uses the greatest of three inputs	Documentary: S2, pp. 1 and 3	Eligibility and fee flows
A maker with no qualifying tier loses the current rebate	Documentary comparison: S1 and S2, p. 3	Eligibility and fee flows
The maker's amount does not depend on the taker's rebate	Documentary: S2 uses fees before taker rebates	Eligibility and fee flows
The whole combo fee applies to the combo as a unit	Documentary: S1, combo taker fees	Eligibility and fee flows
The example's gross combo fee does not change	Documentary comparison: S1 and S2	Eligibility and fee flows
Four previously rebated taker bands lose rebate	Documentary comparison: S1 and S2, Exhibit A	Eligibility and fee flows
Larger maker rewards improve execution	Not tested: a hypothesis	Unresolved questions
This is the first published crossover calculation	Not established	Sources and prior work

Sources and prior work

Primary sources:

S1: PM-US fee documentation, labeled effective September 25 and read on September 30 at 01:13:25 UTC. Sections on standard trading fees, standard fee rules and combo taker fees, and both price tables. It also announces the Table Tennis taker coefficient of 0.10.
S2: September 22 fee schedule update, page 1 and Exhibit A on page 3. The maker share uses the corresponding fees before taker rebates. The filing names no combo family. It intends an October 6 start, subject to review.
S3: September 21 weekly notice. The standard taker coefficient became 0.0695 on September 17. The maker rebate did not change.
S4: Official notice index. At the source cutoff, it listed no fee update later than September 22, and one September weekly notice.
S5: Liquidity incentive program. Resting-order rewards are separate from maker fill rebates.
S6: Volume program and user programs. These separate incentives also affect what makers can offer.
S7: Politics combo amendment of September 22, cover page and Attachment A, pages 2 to 4. It was read again on September 30.

Unresolved questions

Does the proposed standard maker fee share replace the 0.0125 maker formula on the relevant non-crypto combo executions, with no product-specific exception? This controls the conditional headline. A retained 0.0125 exception removes the gain for those fills.
What becomes effective, and when? The current documents still show a proposed October start. A later notice or an effective schedule can change the scope or the rates.
How do the percentage credits aggregate, round and pay out? This affects account-level amounts and the direction for small fills. A public specification or a worked multi-fill credit example can answer it.
How do local maker volume and external proof map to tiers? This affects who receives the top rate. The proposal gives no explicit normalization equations.
Does the proposed maker share apply to Table Tennis without a category-specific exception? The 0.10 taker coefficient is announced, but the future maker treatment is not stated.
Do the changed incentives alter quotes, depth or the cost of completed orders? This question is separate from the rule result. It needs time-stamped book and execution data that identify the product, price, size, fill pattern, fee regime and other rewards.

The smallest piece of evidence that can strengthen the article is the effective combo rebate rule. Market data is not needed to verify the algebra. It is needed for any claim about trader behavior or execution quality.

What was checked

The calculation reproduces all 198 published 100-contract fee rows, including the 99 maker values. It also reproduces five standard examples and two combo examples from the fee page. A separate check recomputes every displayed number with exact rational arithmetic.

Splitrule keeps dated copies of the public sources, with retrieval times and file hashes.

No live order, account statement, payout or market-quality effect was checked. The largest remaining uncertainty is the effective combo scope, then the actual implementation and credit treatment.