Aggregate stats summary
GET
/v1/email/stats/summary
curl -X GET "https://us1.platform.bird.com/v1/email/stats/summary" \
-H "Authorization: Bearer $TOKEN"Returns a single-row aggregate across the requested period covering delivery, bounce, complaint, open, and click counts plus the derived rates, along with processing, delivery, and total latency percentiles (p50/p95/p99) for the period. Suitable for KPI tiles, dashboard headers, and email digests.
Rows are computed against event time (not send time), so engagement received during the period for messages sent earlier is included.
Rate fields are null when their denominator is zero — for example, open_rate is null in a period where nothing was delivered.
from and to accept either calendar days (YYYY-MM-DD) or RFC 3339 instants. With days the window covers whole calendar days, up to 365 days. With instants the window is hour-grain — bounds round down to the hour, both inclusive — so a rolling window such as the last 24 hours is a single request; hour windows may span up to 720 hours (30 days), and compare=previous_period compares against the preceding equal-length hour window. Both bounds must use the same form; mixing a day and an instant returns 422. Set timezone to report in a local zone instead of UTC (it then governs the day and hour boundaries; see timezone). The full window is available in any timezone.
Parameter Kueri
from
string
Inclusive start of the window: a calendar day (YYYY-MM-DD) or an RFC 3339 instant (rounded down to the hour). Interpreted in timezone -- a calendar day names a local day and an instant is rounded down to the local hour -- or in UTC when timezone is omitted. A numeric UTC offset (for example +05:45) is rejected when timezone is set; use a calendar day or a Z (UTC) instant. Must use the same form as to. Defaults to 30 days before to for day windows, or 168 hours (7 days) before to for hour windows, when omitted.
to
string
Inclusive end of the window: a calendar day (YYYY-MM-DD) or an RFC 3339 instant (rounded down to the hour). Interpreted in timezone -- a calendar day names a local day and an instant is rounded down to the local hour -- or in UTC when timezone is omitted. A numeric UTC offset is rejected when timezone is set; use a calendar day or a Z (UTC) instant. Must use the same form as from. Defaults to today for day windows, or the current hour for hour windows, in that timezone, when omitted. Day windows may not exceed 365 days; hour windows may not exceed 720 hours (30 days).
timezone
string
IANA timezone identifier (for example Asia/Kathmandu or America/New_York) to report the statistics in. It is the single source of timezone: day and hour boundaries, and the relative window defaults used when from and to are omitted, are computed in this timezone instead of UTC, so a timezone with a sub-hour offset (such as India at +05:30 or Nepal at +05:45) still gets correct local-day and local-hour totals. When it is set, a from or to given as a calendar day names a local day in this timezone, and one given as an instant stays an absolute point in time but is rounded down to its hour and bucketed in this timezone (so the hour boundaries are local, not UTC). To avoid specifying the zone twice, a from or to that carries its own numeric UTC offset (for example +05:45) is rejected when timezone is set; use a calendar day or a Z (UTC) instant instead. Defaults to UTC.
category
string
Restrict the statistics to a single category: transactional or marketing. Mutually exclusive with the other dimension filters; only one may be set per request.
sending_domain
string
Restrict the statistics to a single sending domain (the part of the From address after @). Mutually exclusive with the other dimension filters; only one may be set per request.
tag
string
Restrict the statistics to a single tag. Use name to match any value of a tag, or name:value for a specific pair (for example campaign:spring_launch). Mutually exclusive with the other dimension filters; only one may be set per request.
sending_ip
string
Restrict the statistics to a single sending IP. Mutually exclusive with the other dimension filters; only one may be set per request. A sending IP is only assigned once a message reaches delivery, so an IP-filtered result reports delivery-side metrics only: accepted, processed, rejected, complaint, and engagement counts are 0 and the processing latency is null; complaint, open, and click rates read 0 when there were deliveries and null when there were none.
recipient_domain
string
Restrict the statistics to a single recipient mailbox domain (the part of the recipient address after the @, for example gmail.com). Mutually exclusive with the other dimension filters; only one may be set per request.
template
string
Restrict the statistics to a single template, by its ID (emt_…) or its name. Mutually exclusive with the other dimension filters; only one may be set per request.
compare
string
Set to previous_period to also include the same statistics for the immediately preceding window of equal length, plus the change between the two, so you can show "+X% vs last period" without a second request.
Payload Respons
period
object
wajib
Tampilkan atribut turunan
period.from
string
wajib
Inclusive start of the window the response covers -- a calendar day (YYYY-MM-DD, UTC) for day windows, or an hour boundary (RFC 3339) for hour windows.
period.to
string
wajib
Inclusive end of the window the response covers -- a calendar day (YYYY-MM-DD, UTC) for day windows, or an hour boundary (RFC 3339) for hour windows.
period.data_as_of
nullable string
The instant the statistics in this response are current to: events recorded up to roughly this time are reflected, while more recent events may not be yet. Statistics are served from a rolling aggregation that refreshes every few seconds, so a response is near-real-time but not live; use this field to label data freshness (for example "as of 14:03") rather than assuming the numbers are to-the-second. Null when the freshness boundary is not being reported.
sends_accepted
integer
wajib
Distinct email messages accepted, counted at the message level (one per accepted send regardless of recipient count) and summed per day across the period. This counts messages, not recipients, so it is not comparable to delivery.accepted, which counts recipients -- a single message to 500 recipients is 1 here and up to 500 there.
delivery
object
wajib
Tampilkan atribut turunan
delivery.accepted
integer
Distinct recipients accepted for delivery after suppression filtering. Reported on time buckets and the period summary; omitted on breakdown rows, whose rollups do not carry it.
delivery.processed
integer
wajib
Distinct recipients whose message was processed and handed off for delivery.
delivery.delivered
integer
wajib
Distinct recipients whose message the receiving mail server accepted.
delivery.bounced
integer
wajib
Distinct recipients whose delivery failed. Approximately the sum of the five bounces.* sub-counts (hard, soft, admin, block, undetermined); the totals are computed independently so they may differ slightly at the approximation error.
delivery.bounces
object
wajib
Tampilkan atribut turunan
delivery.bounces.hard
integer
wajib
Distinct recipients with a permanent delivery failure (invalid address or non-existent domain).
delivery.bounces.soft
integer
wajib
Distinct recipients with a transient delivery failure (mailbox full or server temporarily unavailable).
delivery.bounces.admin
integer
wajib
Distinct recipients bounced by an upstream policy block (relaying denied, blocklisted domain).
delivery.bounces.block
integer
wajib
Distinct recipients bounced because the receiving mail server blocked the sending IP for reputation reasons.
delivery.bounces.undetermined
integer
wajib
Distinct recipients bounced where the receiving server's response did not allow precise classification.
delivery.bounces.hard_rate
nullable number
wajib
Fraction of bounced recipients that hard bounced, computed as hard / bounced. Null when bounced is zero.
delivery.bounces.soft_rate
nullable number
wajib
Fraction of bounced recipients that soft bounced, computed as soft / bounced. Null when bounced is zero.
delivery.bounces.admin_rate
nullable number
wajib
Fraction of bounced recipients that admin bounced, computed as admin / bounced. Null when bounced is zero.
delivery.bounces.block_rate
nullable number
wajib
Fraction of bounced recipients that block bounced, computed as block / bounced. Null when bounced is zero.
delivery.bounces.undetermined_rate
nullable number
wajib
Fraction of bounced recipients with undetermined classification, computed as undetermined / bounced. Null when bounced is zero.
delivery.complained
integer
wajib
Distinct recipients who reported the message as spam via a feedback loop.
delivery.deferred
integer
wajib
Distinct recipients whose delivery the receiving server temporarily delayed and is still being retried.
delivery.rejected
integer
wajib
Distinct recipients rejected before any delivery attempt. Includes recipients on the workspace suppression list, transmissions that could not be completed, message-generation failures, and recipients refused by sending policy. The per-recipient rejection_reason field on GET /v1/email/messages/{message_id}/recipients surfaces the specific cause.
delivery.oob_bounces
integer
wajib
Out-of-band bounce events: distinct failure notifications received after the receiving server had initially confirmed delivery. Counted as deduplicated events, not unique recipients.
delivery.effective_delivered
integer
wajib
Recipients who remain in-inbox in this scope after all bounce signals resolve, computed as delivered - oob_bounces. Use this as the base for engagement-rate denominators. Clamped to 0 when oob_bounces exceeds delivered.
delivery.all_bounces
integer
wajib
Total recipients in this scope who did not receive the message, computed as bounced + oob_bounces.
delivery.oob_rate
nullable number
wajib
Share of this scope's delivery attempts that resulted in an out-of-band bounce, computed as oob_bounces / (delivered + bounced). Null when there were no attempts.
delivery.delivery_rate
nullable number
wajib
Share of this scope's delivery attempts that resulted in a message remaining in-inbox, computed as effective_delivered / (delivered + bounced). Null when there were no attempts.
delivery.bounce_rate
nullable number
wajib
Share of this scope's delivery attempts that ultimately failed (inband or out-of-band), computed as all_bounces / (delivered + bounced). Null when there were no attempts.
delivery.complaint_rate
nullable number
wajib
Spam complaints in this scope relative to effectively delivered recipients, computed as complained / effective_delivered. Complaints are attributed by event time, so a scope can record more of them than it effectively delivered, pushing the rate above 1. Null when effective_delivered is zero.
engagement
object
wajib
Tampilkan atribut turunan
engagement.opens
integer
wajib
Distinct open events, counting repeat opens from the same recipient and opens auto-fetched by inbox privacy features (such as Apple Mail Privacy Protection and the Gmail image proxy).
engagement.opens_non_prefetched
integer
wajib
Distinct open events excluding those auto-fetched by inbox privacy features. Same event-counting semantics as opens (repeat opens from the same recipient count separately), with prefetched opens removed.
engagement.unique_opens
integer
wajib
Distinct recipients who opened at least once, including opens auto-fetched by inbox privacy features.
engagement.unique_opens_non_prefetched
integer
wajib
Distinct recipients who opened at least once, excluding opens auto-fetched by inbox privacy features. This is the numerator used for open rate, so iOS-heavy audiences (Apple Mail Privacy Protection and similar) do not inflate it.
engagement.clicks
integer
wajib
Distinct click events, counting repeat clicks from the same recipient.
engagement.unique_clicks
integer
wajib
Distinct recipients who clicked at least once.
engagement.unsubscribes
integer
wajib
Distinct unsubscribe events, recorded via the list-unsubscribe header or the footer link.
engagement.open_rate
nullable number
wajib
Distinct non-prefetched openers relative to recipients delivered in the same scope, computed as unique_opens_non_prefetched / delivery.delivered. The numerator excludes opens auto-fetched by inbox privacy features. Opens are attributed by event time, so engagement earned by earlier deliveries can push the rate above 1. Null when delivery.delivered is zero.
engagement.click_rate
nullable number
wajib
Distinct clickers relative to recipients delivered in the same scope, computed as unique_clicks / delivery.delivered. Clicks are attributed by event time, so engagement earned by earlier deliveries can push the rate above 1. Null when delivery.delivered is zero.
engagement.unsubscribe_rate
nullable number
wajib
Unsubscribes relative to recipients delivered in the same scope, computed as unsubscribes / delivery.delivered. Unsubscribes are attributed by event time, so the rate can exceed 1. Null when delivery.delivered is zero.
latency
object
wajib
Tampilkan atribut turunan
latency.processing
object
p50, p95, and p99 latency percentiles in milliseconds for one latency family over the bucket. Percentiles are approximate (computed from a high-volume aggregation pipeline). All three are null together when no qualifying event contributed a latency measurement in the bucket.
Tampilkan atribut turunan
latency.processing.p50_ms
nullable integer
wajib
Median (50th percentile) latency in milliseconds. Null when no qualifying event contributed a measurement.
latency.processing.p95_ms
nullable integer
wajib
95th percentile latency in milliseconds. Null when no qualifying event contributed a measurement.
latency.processing.p99_ms
nullable integer
wajib
99th percentile latency in milliseconds. Null when no qualifying event contributed a measurement.
latency.delivery
object
p50, p95, and p99 latency percentiles in milliseconds for one latency family over the bucket. Percentiles are approximate (computed from a high-volume aggregation pipeline). All three are null together when no qualifying event contributed a latency measurement in the bucket.
Tampilkan atribut turunan
latency.delivery.p50_ms
nullable integer
wajib
Median (50th percentile) latency in milliseconds. Null when no qualifying event contributed a measurement.
latency.delivery.p95_ms
nullable integer
wajib
95th percentile latency in milliseconds. Null when no qualifying event contributed a measurement.
latency.delivery.p99_ms
nullable integer
wajib
99th percentile latency in milliseconds. Null when no qualifying event contributed a measurement.
latency.total
object
p50, p95, and p99 latency percentiles in milliseconds for one latency family over the bucket. Percentiles are approximate (computed from a high-volume aggregation pipeline). All three are null together when no qualifying event contributed a latency measurement in the bucket.
Tampilkan atribut turunan
latency.total.p50_ms
nullable integer
wajib
Median (50th percentile) latency in milliseconds. Null when no qualifying event contributed a measurement.
latency.total.p95_ms
nullable integer
wajib
95th percentile latency in milliseconds. Null when no qualifying event contributed a measurement.
latency.total.p99_ms
nullable integer
wajib
99th percentile latency in milliseconds. Null when no qualifying event contributed a measurement.
comparison
object
Tampilkan atribut turunan
comparison.period
object
wajib
Tampilkan atribut turunan
comparison.period.from
string
wajib
Inclusive start of the window the response covers -- a calendar day (YYYY-MM-DD, UTC) for day windows, or an hour boundary (RFC 3339) for hour windows.
comparison.period.to
string
wajib
Inclusive end of the window the response covers -- a calendar day (YYYY-MM-DD, UTC) for day windows, or an hour boundary (RFC 3339) for hour windows.
comparison.period.data_as_of
nullable string
The instant the statistics in this response are current to: events recorded up to roughly this time are reflected, while more recent events may not be yet. Statistics are served from a rolling aggregation that refreshes every few seconds, so a response is near-real-time but not live; use this field to label data freshness (for example "as of 14:03") rather than assuming the numbers are to-the-second. Null when the freshness boundary is not being reported.
comparison.sends_accepted
integer
wajib
Distinct email messages accepted in the preceding period, counted at the message level.
comparison.delivery
object
wajib
Tampilkan atribut turunan
comparison.delivery.accepted
integer
Distinct recipients accepted for delivery after suppression filtering. Reported on time buckets and the period summary; omitted on breakdown rows, whose rollups do not carry it.
comparison.delivery.processed
integer
wajib
Distinct recipients whose message was processed and handed off for delivery.
comparison.delivery.delivered
integer
wajib
Distinct recipients whose message the receiving mail server accepted.
comparison.delivery.bounced
integer
wajib
Distinct recipients whose delivery failed. Approximately the sum of the five bounces.* sub-counts (hard, soft, admin, block, undetermined); the totals are computed independently so they may differ slightly at the approximation error.
comparison.delivery.bounces
object
wajib
Tampilkan atribut turunan
comparison.delivery.bounces.hard
integer
wajib
Distinct recipients with a permanent delivery failure (invalid address or non-existent domain).
comparison.delivery.bounces.soft
integer
wajib
Distinct recipients with a transient delivery failure (mailbox full or server temporarily unavailable).
comparison.delivery.bounces.admin
integer
wajib
Distinct recipients bounced by an upstream policy block (relaying denied, blocklisted domain).
comparison.delivery.bounces.block
integer
wajib
Distinct recipients bounced because the receiving mail server blocked the sending IP for reputation reasons.
comparison.delivery.bounces.undetermined
integer
wajib
Distinct recipients bounced where the receiving server's response did not allow precise classification.
comparison.delivery.bounces.hard_rate
nullable number
wajib
Fraction of bounced recipients that hard bounced, computed as hard / bounced. Null when bounced is zero.
comparison.delivery.bounces.soft_rate
nullable number
wajib
Fraction of bounced recipients that soft bounced, computed as soft / bounced. Null when bounced is zero.
comparison.delivery.bounces.admin_rate
nullable number
wajib
Fraction of bounced recipients that admin bounced, computed as admin / bounced. Null when bounced is zero.
comparison.delivery.bounces.block_rate
nullable number
wajib
Fraction of bounced recipients that block bounced, computed as block / bounced. Null when bounced is zero.
comparison.delivery.bounces.undetermined_rate
nullable number
wajib
Fraction of bounced recipients with undetermined classification, computed as undetermined / bounced. Null when bounced is zero.
comparison.delivery.complained
integer
wajib
Distinct recipients who reported the message as spam via a feedback loop.
comparison.delivery.deferred
integer
wajib
Distinct recipients whose delivery the receiving server temporarily delayed and is still being retried.
comparison.delivery.rejected
integer
wajib
Distinct recipients rejected before any delivery attempt. Includes recipients on the workspace suppression list, transmissions that could not be completed, message-generation failures, and recipients refused by sending policy. The per-recipient rejection_reason field on GET /v1/email/messages/{message_id}/recipients surfaces the specific cause.
comparison.delivery.oob_bounces
integer
wajib
Out-of-band bounce events: distinct failure notifications received after the receiving server had initially confirmed delivery. Counted as deduplicated events, not unique recipients.
comparison.delivery.effective_delivered
integer
wajib
Recipients who remain in-inbox in this scope after all bounce signals resolve, computed as delivered - oob_bounces. Use this as the base for engagement-rate denominators. Clamped to 0 when oob_bounces exceeds delivered.
comparison.delivery.all_bounces
integer
wajib
Total recipients in this scope who did not receive the message, computed as bounced + oob_bounces.
comparison.delivery.oob_rate
nullable number
wajib
Share of this scope's delivery attempts that resulted in an out-of-band bounce, computed as oob_bounces / (delivered + bounced). Null when there were no attempts.
comparison.delivery.delivery_rate
nullable number
wajib
Share of this scope's delivery attempts that resulted in a message remaining in-inbox, computed as effective_delivered / (delivered + bounced). Null when there were no attempts.
comparison.delivery.bounce_rate
nullable number
wajib
Share of this scope's delivery attempts that ultimately failed (inband or out-of-band), computed as all_bounces / (delivered + bounced). Null when there were no attempts.
comparison.delivery.complaint_rate
nullable number
wajib
Spam complaints in this scope relative to effectively delivered recipients, computed as complained / effective_delivered. Complaints are attributed by event time, so a scope can record more of them than it effectively delivered, pushing the rate above 1. Null when effective_delivered is zero.
comparison.engagement
object
wajib
Tampilkan atribut turunan
comparison.engagement.opens
integer
wajib
Distinct open events, counting repeat opens from the same recipient and opens auto-fetched by inbox privacy features (such as Apple Mail Privacy Protection and the Gmail image proxy).
comparison.engagement.opens_non_prefetched
integer
wajib
Distinct open events excluding those auto-fetched by inbox privacy features. Same event-counting semantics as opens (repeat opens from the same recipient count separately), with prefetched opens removed.
comparison.engagement.unique_opens
integer
wajib
Distinct recipients who opened at least once, including opens auto-fetched by inbox privacy features.
comparison.engagement.unique_opens_non_prefetched
integer
wajib
Distinct recipients who opened at least once, excluding opens auto-fetched by inbox privacy features. This is the numerator used for open rate, so iOS-heavy audiences (Apple Mail Privacy Protection and similar) do not inflate it.
comparison.engagement.clicks
integer
wajib
Distinct click events, counting repeat clicks from the same recipient.
comparison.engagement.unique_clicks
integer
wajib
Distinct recipients who clicked at least once.
comparison.engagement.unsubscribes
integer
wajib
Distinct unsubscribe events, recorded via the list-unsubscribe header or the footer link.
comparison.engagement.open_rate
nullable number
wajib
Distinct non-prefetched openers relative to recipients delivered in the same scope, computed as unique_opens_non_prefetched / delivery.delivered. The numerator excludes opens auto-fetched by inbox privacy features. Opens are attributed by event time, so engagement earned by earlier deliveries can push the rate above 1. Null when delivery.delivered is zero.
comparison.engagement.click_rate
nullable number
wajib
Distinct clickers relative to recipients delivered in the same scope, computed as unique_clicks / delivery.delivered. Clicks are attributed by event time, so engagement earned by earlier deliveries can push the rate above 1. Null when delivery.delivered is zero.
comparison.engagement.unsubscribe_rate
nullable number
wajib
Unsubscribes relative to recipients delivered in the same scope, computed as unsubscribes / delivery.delivered. Unsubscribes are attributed by event time, so the rate can exceed 1. Null when delivery.delivered is zero.
comparison.latency
object
wajib
Tampilkan atribut turunan
comparison.latency.processing
object
p50, p95, and p99 latency percentiles in milliseconds for one latency family over the bucket. Percentiles are approximate (computed from a high-volume aggregation pipeline). All three are null together when no qualifying event contributed a latency measurement in the bucket.
Tampilkan atribut turunan
comparison.latency.processing.p50_ms
nullable integer
wajib
Median (50th percentile) latency in milliseconds. Null when no qualifying event contributed a measurement.
comparison.latency.processing.p95_ms
nullable integer
wajib
95th percentile latency in milliseconds. Null when no qualifying event contributed a measurement.
comparison.latency.processing.p99_ms
nullable integer
wajib
99th percentile latency in milliseconds. Null when no qualifying event contributed a measurement.
comparison.latency.delivery
object
p50, p95, and p99 latency percentiles in milliseconds for one latency family over the bucket. Percentiles are approximate (computed from a high-volume aggregation pipeline). All three are null together when no qualifying event contributed a latency measurement in the bucket.
Tampilkan atribut turunan
comparison.latency.delivery.p50_ms
nullable integer
wajib
Median (50th percentile) latency in milliseconds. Null when no qualifying event contributed a measurement.
comparison.latency.delivery.p95_ms
nullable integer
wajib
95th percentile latency in milliseconds. Null when no qualifying event contributed a measurement.
comparison.latency.delivery.p99_ms
nullable integer
wajib
99th percentile latency in milliseconds. Null when no qualifying event contributed a measurement.
comparison.latency.total
object
p50, p95, and p99 latency percentiles in milliseconds for one latency family over the bucket. Percentiles are approximate (computed from a high-volume aggregation pipeline). All three are null together when no qualifying event contributed a latency measurement in the bucket.
Tampilkan atribut turunan
comparison.latency.total.p50_ms
nullable integer
wajib
Median (50th percentile) latency in milliseconds. Null when no qualifying event contributed a measurement.
comparison.latency.total.p95_ms
nullable integer
wajib
95th percentile latency in milliseconds. Null when no qualifying event contributed a measurement.
comparison.latency.total.p99_ms
nullable integer
wajib
99th percentile latency in milliseconds. Null when no qualifying event contributed a measurement.
comparison.delta
object
wajib
Tampilkan atribut turunan
comparison.delta.sends_accepted_pct_change
nullable number
wajib
Relative change in accepted messages (the sends_accepted count) versus the previous period, as a signed fraction. Null when the previous period accepted none.
comparison.delta.delivered_pct_change
nullable number
wajib
Relative change in delivered recipients (delivery.delivered) versus the previous period, as a signed fraction. Null when the previous period delivered none.
comparison.delta.bounced_pct_change
nullable number
wajib
Relative change in bounced recipients (delivery.bounced) versus the previous period, as a signed fraction. Null when the previous period had none.
comparison.delta.complained_pct_change
nullable number
wajib
Relative change in spam complaints (delivery.complained) versus the previous period, as a signed fraction. Null when the previous period had none.
comparison.delta.opened_pct_change
nullable number
wajib
Relative change in unique non-prefetched opens (engagement.unique_opens_non_prefetched, the same count the open rate uses) versus the previous period, as a signed fraction. Null when the previous period had none.
comparison.delta.delivery_rate_pp
nullable number
wajib
Signed difference between this period's and the previous period's delivery rate, both fractions in [0,1] (multiply by 100 for percentage points). Null when either period's delivery rate is undefined.
comparison.delta.open_rate_pp
nullable number
wajib
Signed difference between this period's and the previous period's open rate, both fractions (multiply by 100 for percentage points). Null when either period's open rate is undefined.
comparison.delta.click_rate_pp
nullable number
wajib
Signed difference between this period's and the previous period's click rate, both fractions (multiply by 100 for percentage points). Null when either period's click rate is undefined.
comparison.delta.bounce_rate_pp
nullable number
wajib
Signed difference between this period's and the previous period's bounce rate, both fractions in [0,1] (multiply by 100 for percentage points). Null when either period's bounce rate is undefined.
comparison.delta.complaint_rate_pp
nullable number
wajib
Signed difference between this period's and the previous period's complaint rate, both fractions (multiply by 100 for percentage points). Null when either period's complaint rate is undefined.
comparison.delta.unsubscribe_rate_pp
nullable number
wajib
Signed difference between this period's and the previous period's unsubscribe rate, both fractions (multiply by 100 for percentage points). Null when either period's unsubscribe rate is undefined.