The open cases were left out of the average

# Self-authored for the EML case corpus (no external origin). A report gives the
# average time to resolve a ticket, and it averages the real resolution times of
# every resolved ticket correctly. Which tickets can be in the average is computed
# below.
#
# The measurement is careful. It reads the real close timestamps, not estimates;
# it covers every ticket that has a resolution time; the mean is the honest
# average of days-to-close; and the intent is exactly 'how long does a ticket take
# to resolve'.
#
# A ticket contributes a resolution time only once it is closed, and the slowest
# tickets are the ones still open, so they are absent from the average by virtue of
# not being done.

100000 => tickets_opened
70000 => tickets_resolved
30000 => tickets_still_open
5 => avg_days_over_resolved
12 => estimate_including_the_open_tail
20 => days_the_open_ones_have_already_waited

estimate_including_the_open_tail - avg_days_over_resolved => days_the_censoring_hid
int(days_the_censoring_hid * 10000 / estimate_including_the_open_tail) => understated_share_per_myriad

"tickets opened                  : " + str(tickets_opened) ^0
"  resolved (have a close time)  : " + str(tickets_resolved) ^0
"  still open (no close time yet) : " + str(tickets_still_open) ^0
"" ^0
"average days over resolved      : " + str(avg_days_over_resolved) ^0
"open ones already waited (min)  : " + str(days_the_open_ones_have_already_waited) ^0
"estimate including the open tail : " + str(estimate_including_the_open_tail) ^0
"understated share of the truth  : " + str(understated_share_per_myriad) + " per ten thousand" ^0
"" ^0

# ---- what the measurement verified ----

"the resolution-time average" ^0
"  reads : the real close timestamps, not estimates" ^0
"  covers : every ticket that has a resolution time" ^0
"  mean : the honest average of days-to-close" ^0
"  intent : how long does a ticket take to resolve" ^0
"  resolved tickets omitted : 0" ^0
"  verdict : RESOLVED TICKETS AVERAGE 5 DAYS" ^0
"" ^0
"  averaging real close times over every resolved ticket is" ^0
"  the part done right here, and it is why the 5 days is a" ^0
"  true statement about the tickets that closed" ^0
"" ^0

# ---- which tickets can be in the average ----

"who contributes a resolution time" ^0
"  requirement : the ticket must be closed" ^0
"  which tickets are still open : the 30000 slowest" ^0
"  how long they have already waited : at least 20 days, and" ^0
"    counting" ^0
"  so the tail longer than the mean : is entirely excluded" ^0
"  what the average therefore measures : the ones fast" ^0
"    enough to have finished" ^0
"" ^0

# ---- what the caller got ----

"the result of the report" ^0
"  reported average : " + str(avg_days_over_resolved) + " days" ^0
"  the open tickets already exceed : " + str(days_the_open_ones_have_already_waited) + " days each" ^0
"  estimate that counts the open ones : " + str(estimate_including_the_open_tail) + " days" ^0
"  is the mean over resolved wrong : no; it is exact for them" ^0
"  is it the time a ticket takes : no; the slow half is" ^0
"    right-censored, invisible until it closes" ^0
"" ^0

# ---- null control ----

# The same tickets, with a survival estimate that counts the open tickets'
# elapsed time as a lower bound instead of dropping them.
5 => nc_mean_over_resolved_only
12 => nc_estimate_with_censored_included
30000 => nc_open_tickets_the_estimate_stops_dropping

"null control - include the open tickets' elapsed time" ^0
"  mean over resolved only : " + str(nc_mean_over_resolved_only) ^0
"  estimate with the censored included : " + str(nc_estimate_with_censored_included) ^0
"  open tickets the estimate stops dropping : " + str(nc_open_tickets_the_estimate_stops_dropping) ^0
"  no ticket and no timestamp changed; the slow tail stopped" ^0
"  being excluded for not being finished and started" ^0
"  counting as at-least-this-long" ^0
"" ^0

# ---- the rule ----

"what an average over resolved tickets guarantees" ^0
"  the resolved tickets took that long on average : exactly," ^0
"    real close times, every resolved ticket, honest mean" ^0
"  a ticket takes that long to resolve : not addressed; a" ^0
"    ticket enters the average only by closing, so the " + str(tickets_still_open) ^0
"    slowest are censored out and the mean sees the fast ones" ^0
"" ^0

"an average of the finished is an average of the fast; whatever is still running" ^0
"is exactly the part that runs long, and leaving it out because it has no end time" ^0
"yet removes the tail that the question was about" ^0
"" ^0

"It averages real close times over every resolved ticket - the 5 days is true for" ^0
"them. But a ticket enters the average only by closing, and the " + str(tickets_still_open) + " still open" ^0
"are the slow tail; an estimate that counts their elapsed time gives " + str(estimate_including_the_open_tail) + " days," ^0
"" + str(understated_share_per_myriad) + " per ten thousand understated by the right-censoring." ^0

tickets_opened = 100000
tickets_resolved = 70000
tickets_still_open = 30000
avg_days_over_resolved = 5
estimate_including_the_open_tail = 12
days_the_open_ones_have_already_waited = 20
days_the_censoring_hid = estimate_including_the_open_tail - avg_days_over_resolved
understated_share_per_myriad = int(days_the_censoring_hid * 10000 / estimate_including_the_open_tail)
print("tickets opened                  : " + str(tickets_opened))
print("  resolved (have a close time)  : " + str(tickets_resolved))
print("  still open (no close time yet) : " + str(tickets_still_open))
print("")
print("average days over resolved      : " + str(avg_days_over_resolved))
print("open ones already waited (min)  : " + str(days_the_open_ones_have_already_waited))
print("estimate including the open tail : " + str(estimate_including_the_open_tail))
print("understated share of the truth  : " + str(understated_share_per_myriad) + " per ten thousand")
print("")
print("the resolution-time average")
print("  reads : the real close timestamps, not estimates")
print("  covers : every ticket that has a resolution time")
print("  mean : the honest average of days-to-close")
print("  intent : how long does a ticket take to resolve")
print("  resolved tickets omitted : 0")
print("  verdict : RESOLVED TICKETS AVERAGE 5 DAYS")
print("")
print("  averaging real close times over every resolved ticket is")
print("  the part done right here, and it is why the 5 days is a")
print("  true statement about the tickets that closed")
print("")
print("who contributes a resolution time")
print("  requirement : the ticket must be closed")
print("  which tickets are still open : the 30000 slowest")
print("  how long they have already waited : at least 20 days, and")
print("    counting")
print("  so the tail longer than the mean : is entirely excluded")
print("  what the average therefore measures : the ones fast")
print("    enough to have finished")
print("")
print("the result of the report")
print("  reported average : " + str(avg_days_over_resolved) + " days")
print("  the open tickets already exceed : " + str(days_the_open_ones_have_already_waited) + " days each")
print("  estimate that counts the open ones : " + str(estimate_including_the_open_tail) + " days")
print("  is the mean over resolved wrong : no; it is exact for them")
print("  is it the time a ticket takes : no; the slow half is")
print("    right-censored, invisible until it closes")
print("")
nc_mean_over_resolved_only = 5
nc_estimate_with_censored_included = 12
nc_open_tickets_the_estimate_stops_dropping = 30000
print("null control - include the open tickets' elapsed time")
print("  mean over resolved only : " + str(nc_mean_over_resolved_only))
print("  estimate with the censored included : " + str(nc_estimate_with_censored_included))
print("  open tickets the estimate stops dropping : " + str(nc_open_tickets_the_estimate_stops_dropping))
print("  no ticket and no timestamp changed; the slow tail stopped")
print("  being excluded for not being finished and started")
print("  counting as at-least-this-long")
print("")
print("what an average over resolved tickets guarantees")
print("  the resolved tickets took that long on average : exactly,")
print("    real close times, every resolved ticket, honest mean")
print("  a ticket takes that long to resolve : not addressed; a")
print("    ticket enters the average only by closing, so the " + str(tickets_still_open))
print("    slowest are censored out and the mean sees the fast ones")
print("")
print("an average of the finished is an average of the fast; whatever is still running")
print("is exactly the part that runs long, and leaving it out because it has no end time")
print("yet removes the tail that the question was about")
print("")
print("It averages real close times over every resolved ticket - the 5 days is true for")
print("them. But a ticket enters the average only by closing, and the " + str(tickets_still_open) + " still open")
print("are the slow tail; an estimate that counts their elapsed time gives " + str(estimate_including_the_open_tail) + " days,")
print("" + str(understated_share_per_myriad) + " per ten thousand understated by the right-censoring.")

tickets opened                  : 100000
  resolved (have a close time)  : 70000
  still open (no close time yet) : 30000

average days over resolved      : 5
open ones already waited (min)  : 20
estimate including the open tail : 12
understated share of the truth  : 5833 per ten thousand

the resolution-time average
  reads : the real close timestamps, not estimates
  covers : every ticket that has a resolution time
  mean : the honest average of days-to-close
  intent : how long does a ticket take to resolve
  resolved tickets omitted : 0
  verdict : RESOLVED TICKETS AVERAGE 5 DAYS

  averaging real close times over every resolved ticket is
  the part done right here, and it is why the 5 days is a
  true statement about the tickets that closed

who contributes a resolution time
  requirement : the ticket must be closed
  which tickets are still open : the 30000 slowest
  how long they have already waited : at least 20 days, and
    counting
  so the tail longer than the mean : is entirely excluded
  what the average therefore measures : the ones fast
    enough to have finished

the result of the report
  reported average : 5 days
  the open tickets already exceed : 20 days each
  estimate that counts the open ones : 12 days
  is the mean over resolved wrong : no; it is exact for them
  is it the time a ticket takes : no; the slow half is
    right-censored, invisible until it closes

null control - include the open tickets' elapsed time
  mean over resolved only : 5
  estimate with the censored included : 12
  open tickets the estimate stops dropping : 30000
  no ticket and no timestamp changed; the slow tail stopped
  being excluded for not being finished and started
  counting as at-least-this-long

what an average over resolved tickets guarantees
  the resolved tickets took that long on average : exactly,
    real close times, every resolved ticket, honest mean
  a ticket takes that long to resolve : not addressed; a
    ticket enters the average only by closing, so the 30000
    slowest are censored out and the mean sees the fast ones

an average of the finished is an average of the fast; whatever is still running
is exactly the part that runs long, and leaving it out because it has no end time
yet removes the tail that the question was about

It averages real close times over every resolved ticket - the 5 days is true for
them. But a ticket enters the average only by closing, and the 30000 still open
are the slow tail; an estimate that counts their elapsed time gives 12 days,
5833 per ten thousand understated by the right-censoring.

Trace event types