Conversion-Rate Bridge Methodology

From Session Lift to Estimated Conversions

SpotLift's core engine measures incremental session lift — the additional web traffic (GA4 direct/organic sessions) attributable to each TV spot. But sessions are an intermediate metric: marketers need to know how many conversions (purchases, signups, leads) the spot drove.

The conversion-rate bridge closes this gap by estimating an hourly conversion rate (CR) from the same GA4 telemetry and multiplying it by the attributed session lift:

$${\text{key\_event\_response}}_k={\text{incremental\_lift}}_k\times \text{CR}(t_k)$$

where $\text{CR}(t_k)$ is the session-volume-weighted mean conversion rate in the ±1-hour neighborhood of spot $k$'s timestamp.

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How It Works

Step 1: Hourly Conversion Rate Aggregation

For each (day, hour) pair in the telemetry, SpotLift computes:

$${\text{CR}}_{d,h}=\frac{\sum _{\text{minutes in }(d,h)}\text{conversions}}{\sum _{\text{minutes in }(d,h)}\text{sessions}}$$

This requires the telemetry DataFrame to contain two channel sources:

Channel Source	What It Contains
ga4_direct_organic_sessions	Minute-level session counts (direct + organic traffic)
ga4_conversions	Minute-level conversion / key-event counts (purchases, signups, etc.)

If ga4_conversions is absent from the telemetry, the bridge silently skips — conversion_rate and key_event_response remain None. No error is raised, but no conversion estimate is produced.

Step 2: Session-Volume-Weighted CR per Spot

For a spot airing at timestamp $t_k$, the CR is estimated as the weighted mean of the hourly CR values in the continuous neighborhood $[h_k-1,h_k+1]$, weighted by session volume:

$$\text{CR}(t_k)=\frac{\sum _{h\in [h_k-1,h_k+1]}{\text{CR}}_{d_k,h}\times {\text{sessions}}_{d_k,h}}{\sum _{h\in [h_k-1,h_k+1]}{\text{sessions}}_{d_k,h}}$$

Why session-volume weighting? A flat average of hourly CRs would weight a 3 AM hour (few sessions, high noise) equally with an 8 PM hour (many sessions, stable CR). Session-volume weighting pulls the estimate toward the CR of hours that actually carry traffic, reducing noise from low-volume periods.

Why ±1 hour? TV response is immediate (within 5–15 minutes), but the conversion may happen slightly later (browsing → checkout takes 5–30 min). The ±1 hour window captures the CR of the surrounding traffic context without averaging across unrelated dayparts (e.g. daytime vs. prime time). The continuous window also seamlessly bridges across calendar-day boundaries at midnight (e.g. for spots airing at 23:45 or 00:15).

Step 3: Key Event Response

The estimated conversions for each spot:

$${\text{key\_event\_response}}_k={\text{incremental\_lift}}_k\times \text{CR}(t_k)$$

This is a linear scaling — it assumes the incremental sessions driven by TV convert at the same rate as the organic sessions in the surrounding hour. This is a reasonable baseline assumption: TV-driven visitors are typically brand-aware (they saw the ad), so their conversion behavior is similar to direct/organic visitors who also arrive with brand intent.

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Usage

Automatic (Default)

The bridge is enabled by default when ga4_conversions is present:

import spotlift as sl

airings = sl.load_airings("schaltplan.csv", tz="Europe/Berlin")
telemetry = sl.load_telemetry("ga4_export.parquet")

# apply_cr_model=True by default — bridge runs automatically
# if ga4_conversions is in the telemetry
results = sl.analyze_spots(
    airings=airings,
    web_telemetry=telemetry,
    window_minutes=8,
)

# results now contain: conversion_rate, key_event_response
print(results[["spot_id", "incremental_lift", "conversion_rate", "key_event_response"]].head())

Custom Conversion Source Label

If your conversions use a different channel_source label:

results = sl.analyze_spots(
    airings=airings,
    web_telemetry=telemetry,
    conversions_source="ga4_purchases",  # custom label
)

Disabled

To skip the bridge entirely (session lift only, no conversion estimate):

results = sl.analyze_spots(
    airings=airings,
    web_telemetry=telemetry,
    apply_cr_model=False,
)

Standalone Functions

The bridge components are also available as standalone functions for custom workflows:

from spotlift.core.conversion import (
    compute_hourly_conversion_rates,
    estimate_conversion_rate_for_spot,
    apply_conversion_model,
)

# Compute hourly CR table
hourly_cr = compute_hourly_conversion_rates(
    telemetry,
    sessions_source="ga4_direct_organic_sessions",
    conversions_source="ga4_conversions",
)

# Estimate CR for a specific spot timestamp
cr = estimate_conversion_rate_for_spot(
    spot_timestamp=airings.iloc[0]["timestamp"],
    hourly_cr=hourly_cr,
    window_hours=1,
)

# Or apply to an existing results DataFrame
annotated = apply_conversion_model(results, telemetry)

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Configurable Baseline Models

SpotLift defaults to a 21-day diurnal baseline (compute_diurnal_baseline) — a same-day-of-week median with weekday/weekend pooling and a 5-minute rolling median smoother. This works well for campaigns with ≥3 weeks of clean historical telemetry.

For campaigns with <7 days of history or markets without a clean diurnal pattern, use simple_mean_baseline:

from spotlift import simple_mean_baseline

results = sl.analyze_spots(
    airings=airings,
    web_telemetry=telemetry,
    baseline_fn=simple_mean_baseline,  # trailing 120-min rolling mean
)

Custom Baseline Functions

Any callable conforming to the BaselineFn protocol can be passed:

from spotlift.core.baseline import BaselineFn

def my_baseline(
    telemetry_series: pd.Series,
    spot_timestamps: list[datetime],
    **kwargs,
) -> tuple[pd.Series, dict[datetime, float]]:
    # Your baseline logic here
    # Must return (raw_baseline_series, alphas_dict)
    ...

results = sl.analyze_spots(
    airings=airings,
    web_telemetry=telemetry,
    baseline_fn=my_baseline,
)

The protocol requires:

• Input: telemetry_series (minute-indexed pd.Series), spot_timestamps (list of datetime), plus **kwargs (SpotLift passes window_minutes, pre_window_minutes, baseline_days).
• Output: (raw_baseline_series, alphas_dict) — a Series of expected organic traffic per minute, and a dict of per-spot multiplicative calibration factors.

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Limitations and Caveats

1. Linear assumption: The bridge assumes TV-driven sessions convert at the same rate as organic sessions in the same hour. If TV-driven visitors convert at a systematically different rate (e.g. higher brand intent), the estimate will be biased. For non-linear effects, use SpotLift Pro's EM deconvolution.

2. Continuous neighborhood across midnight: The CR is computed in a continuous ±1-hour window around the spot timestamp, bridging smoothly across midnight (e.g. 23:00 to 01:00). Delayed conversion paths that span multiple days (e.g. spot on Monday, conversion on Wednesday) are not captured by this immediate bridge (use SpotLift Pro's 36-hour distributed lag solver for delayed response).

3. Requires both channels: If ga4_conversions is missing from the telemetry, no estimate is produced. Ensure your GA4 export includes conversion events as a separate channel_source.

4. Hourly granularity: The CR is computed at hour granularity. Sub-hourly CR variation (e.g. a 15-minute checkout spike) is smoothed by aggregation.