---
title: Smart Fast Finish (SFF) in Ad Budget Pacing
url: https://www.emergentmind.com/topics/smart-fast-finish-sff
type: topic
---

# Smart Fast Finish (SFF) in Ad Budget Pacing

Smart Fast Finish (SFF) is a budget pacing feature for daily advertising spend that extends the industry-standard Fast Finish (FF) mechanism by making the onset of the fast-finish phase campaign-specific and by replacing an abrupt end-of-day throttle release with a short transition window. In the reported DoorDash deployment, SFF is part of the platform’s budget pacing system and is intended to mitigate overdelivery caused by delayed attribution and late-day spend spikes; the reported offline simulations and online budget-split experiments show reduced overdelivery together with longer campaign live hours [2509.07929].

## 1. Problem setting and design objective

Daily budget pacing seeks to spend an advertiser’s daily goal over the course of a day rather than exhausting budget too early or failing to spend it. The cited formulation emphasizes a tension between underdelivery and overdelivery: pacing that is too conservative early in the day risks failing to spend, while pacing that is too aggressive late in the day risks exceeding the advertiser’s daily goal [2509.07929].

At DoorDash, the overdelivery problem is aggravated by delayed attribution. An ad impression or click served before the daily cap may convert into a purchase hours later, after the cap has already been reached. Those post-cap conversions continue to be billed against the advertiser’s monthly budget, so the realized daily spend can exceed the target. The paper further notes that even a small systematic daily overdelivery can exhaust a campaign’s budget early in the month, producing blackout days at month’s end and degrading advertiser experience.

Traditional FF is described as a hard switch in intraday pacing systems. During most of the day, the pacing controller throttles or shapes bid participation to track a target cumulative spend curve. At a fixed time, often 22:00 in a 24-hour day, any remaining budget triggers an “ASAP pacing” mode in which throttling is removed and the system attempts to deplete the residual budget immediately. The reported limitation is that this abrupt switch produces a spike in conversions during the last couple of hours, which amplifies delayed-attribution overdelivery.

The design goals of SFF are correspondingly specific: dynamically delay or advance the start of fast finish using campaign-specific historical overdelivery behavior; smoothly ramp down throttle rates over a short transition window instead of dropping throttling to zero instantaneously; prevent feedback loops so that a delayed FF start cannot immediately move earlier the next day due only to a single day’s outcome; and integrate into the existing DoorDash pacing pipeline under tight latency SLAs.

## 2. Control formulation and pacing equations

The formulation introduces the following notation. $B(t)$ is the remaining daily budget at time $t$, $T(t)$ is the remaining normalized time until the end of the billing window with $T(0)=1$ and $T(1)=0$, $r \coloneqq B(0)$ is the initial daily budget, and $\lambda(t)\in[0,1]$ is the throttle rate, interpreted as the probability that an ad request is allowed to enter auction. In this notation, $\lambda=1$ denotes no throttling and $\lambda=0$ denotes complete blocking. A calibration constant $C$ is used to keep $\lambda$ within the allowable range [2509.07929].

Over a small interval $\Delta t$, if the instantaneous unthrottled expected spend rate is $s(t)$, actual spend is modeled as $\lambda(t)\,s(t)$. The remaining budget therefore evolves as

$$
B(t+\Delta t)=B(t)-\lambda(t)s(t)\Delta t.
$$

Under the normalized simplification $s(t)=1$, this becomes

$$
B(t+\Delta t)=B(t)-\lambda(t)\Delta t.
$$

The baseline “ideal” throttle rate is defined as

$$
\lambda^*(t)=\frac{B(t)}{T(t)},
$$

which would deplete the remaining budget linearly to zero at $t=1$. In practice, the deployed controller clamps this quantity:

$$
\lambda(t)=\min\Bigl(1,\;C\frac{B(t)}{T(t)}\Bigr).
$$

This proportional form is also the stated implementation of `IntradayThrottle(·)` in the paper’s pseudocode.

SFF modifies the end-of-day behavior. Once the campaign reaches the SFF start time $t_{\mathrm{start}}$, the system no longer performs a hard transition to an unthrottled mode. Instead, over a transition window of length $\Delta$, for example one hour or $1/24$ day, the throttle is specified as

$$
\lambda(t)=1-\frac{t-t_{\mathrm{start}}}{\Delta},
\qquad
t\in[t_{\mathrm{start}},\,t_{\mathrm{start}}+\Delta],
$$

with $\lambda(t)=0$ for $t>t_{\mathrm{start}}+\Delta$. As presented, this turns the final phase into a deterministic linear schedule rather than an instantaneous switch.

## 3. Dynamic start-time computation and stabilization

The principal campaign-specific input to SFF is the historical overspend ratio, denoted $OR$, defined as actual spend divided by goal and averaged over a lookback window, such as six months [2509.07929].

The system sets campaign-level lower and upper bounds on historical overspend, $OR_{\min}$ and $OR_{\max}$, together with corresponding earliest and latest start fractions, $t_{\min}$ and $t_{\max}$. The paper gives example values of $1.03$ and $1.50$ for the overspend bounds and $0.85$ and $0.95$ for the start fractions. A non-linear mapping is then used:

$$
D \leftarrow \frac{t_{\max}-t_{\min}}{\sqrt{\max(0,\;OR_{\max}-OR_{\min})}},
$$

$$
\text{raw\_}t_{\mathrm{start}} \leftarrow t_{\min} + D\sqrt{\max(0,\;OR_c-OR_{\min})}.
$$

Campaigns with low historical overspend, near $OR_{\min}$, receive start times near the earliest bound, whereas heavily overspending campaigns move toward the latest bound. The paper also states that $OR_c$ is floored at $OR_{\min}$ and capped at $OR_{\max}$ so that extreme outliers do not skew $t_{\mathrm{start}}$.

A central stabilization mechanism is the monotone update rule:

$$
t_{\mathrm{start},c}\leftarrow \max(\text{previous\_}t_{\mathrm{start},c},\;\text{raw\_}t_{\mathrm{start}}).
$$

This means the campaign’s fast-finish start time may move later but not earlier. The stated purpose is to break the feedback loop that would otherwise allow a single day’s outcome to pull the start time back toward an earlier FF. The refresh cadence is correspondingly coarse, such as weekly or monthly rather than daily. Historical paced-versus-actual spend curves are used offline to fit $C$, $\Delta$, and the non-linear mapping’s overspend bounds.

A common misunderstanding would be to treat SFF as merely a later FF switch. The reported design is more specific: it couples a non-linear campaign-specific start-time mapping to a transition window and a one-directional update rule. This suggests that its behavior is determined as much by temporal smoothing and update stability as by the absolute location of the start time.

## 4. Runtime architecture in the DoorDash pacing stack

SFF is described as the final stage in the daily pacing pipeline. Early in the day, campaigns remain under the intraday pacing service; near $t_{\mathrm{start}}$, they are passed into the SFF throttle service. The campaign-specific start time $t_{\mathrm{start},c}$ is computed in a nightly batch job and stored in an in-memory key–value store, with Redis given as an example, keyed by campaign ID [2509.07929].

At request time, the bidding service executes a short sequence. It looks up remaining budget $B(t)$ from streaming state, looks up $t_{\mathrm{start},c}$ and transition window $\Delta$ from cache with $O(1)$ access, computes $\lambda(t)$ in-line using simple arithmetic, and samples a uniform random variable $u\in[0,1]$; the request proceeds if $u\le \lambda(t)$. The use of probabilistic admission at the request level is consistent with the interpretation of $\lambda(t)$ as an auction-entry probability.

The reported latency overhead is approximately $100\,\mu s$, and this is stated to satisfy sub-$5$ ms SLAs. Within the paper’s framing, the significance of this result is operational rather than theoretical: SFF is presented not as a stand-alone pacing framework but as a low-latency modification that can be inserted into an existing production bidding path without materially changing the surrounding serving architecture.

## 5. Experimental evaluation

The offline simulator uses historical traces of minute-level ad-request volumes together with estimated conversion probabilities. For each minute, it applies the throttle $\lambda(t)$, samples conversions with noise, decrements $B(t)$, and accumulates the resulting daily spend curve. Four configurations are compared: baseline intraday pacing plus static FF with a hard switch at 22:00; SFF with dynamic start time only; SFF with transition window only; and full SFF combining both mechanisms. The reported evaluation metrics are campaign live hours, defined as time until the daily goal is reached, and smoothness, characterized as the absence of late-day spikes [2509.07929].

For a single high-spend campaign in offline simulation, dynamic start time alone yielded a $+6\%$ change in live hours, transition window alone yielded $+3\%$ live hours together with a smoother curve, and full SFF yielded $+8\%$ live hours with a dramatically reduced end-of-day spike.

The online budget-split A/B test ran for one week over all campaigns eligible for intraday pacing. The control arm used intraday pacing plus traditional FF, while the treatment arm used intraday pacing plus Smart Fast Finish. Aggregated across approximately $10$ K campaigns, campaign live hours rose from an average of $10$ h $45$ m in control to $11$ h $30$ m in treatment, a gain of $45$ m or $4.2\%$. The reported overdelivery rate, defined in the paper as soft overdelivery $=(\text{actual spend}-\text{goal})/\text{goal}$, fell from $7.0\%$ to $4.7\%$, a reduction of $2.3\%$ absolute. For the top $28$ highest-spend campaigns, live hours increased by $48$ m, or $4.6\%$, and overdelivery fell from $7.7\%$ to $4.1\%$, a reduction of $3.6\%$. The paper states that these changes occurred with no measurable increase in underdelivery or impression jitter.

These measurements support a narrow empirical conclusion: in the reported environment, the combined dynamic-start and transition-window design outperformed both a static hard-switch FF baseline and the two partial ablations. A plausible implication is that overdelivery mitigation depended on the interaction of campaign-specific timing and late-day smoothing rather than on either component in isolation.

## 6. Limitations, tuning, and broader interpretation

The stated takeaways are that campaign-specific data matters, that a smooth throttle drop over roughly an hour prevents sharp spend spikes that worsen delayed-attribution overshoot, and that constraining start-time updates to move only later stabilizes long-run pacing behavior by breaking the positive feedback loop [2509.07929].

The paper also states several limitations. First, SFF relies solely on the historical overspend ratio, whereas other signals such as time-of-day demand curves and competitive bid density could further refine $t_{\mathrm{start}}$. Second, the mechanism uses hard throttling rather than a soft method based on bid multipliers. The authors suggest that a soft approach might blend more gracefully with modern DSPs.

The reported tuning recommendations follow directly from these constraints. For low-traffic or unpredictable campaigns, the transition window $\Delta$ may be shortened to reduce underdelivery risk. For highly seasonal campaigns, such as sporting events, tighter $OR_{\min}$ and $OR_{\max}$ bounds are recommended so that temporary extreme overdelivery does not miscalibrate $t_{\mathrm{start}}$. The paper also proposes investigating integration with a soft-pacing system, exemplified by Mystique’s bid-shading approach, so that auction participation could be maintained at greatly reduced bids rather than through full blocking.

In summary, SFF is presented as a pair of data-driven modifications to conventional FF: a campaign-specific, non-linear shift of fast-finish start time derived from historical overdelivery, and a gradual throttle-rate ramp-down during the terminal phase. The reported production deployment at DoorDash since mid 2024 associates these mechanisms with reductions of roughly $2$–$3$ percentage points in overdelivery and extensions of campaign live hours in the $4$–$8\%$ range, while preserving low serving-path latency and limited engineering complexity.

Source: https://www.emergentmind.com/topics/smart-fast-finish-sff