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The definition is the number

One month of a support desk, one stylised log of 43 events, and a headline that wording alone can move a long way. Set the numerator, the denominator and the window, and every figure is recounted from the log. Nothing about the service changes while you do it.

Reported by this definition
81.8%
Spread across every setting
43.8 pp
rateselected 81.8%0%25%50%75%100%band lowest 56.3%band highest 100.0%

The shaded band is the range every one of the 24 switch settings can produce from this same log at a 28-day window. The thick line is the setting selected on the right.

Over unique customers 81.8%Over sessions 78.6%Over tickets 75.0%

The highest of the three reads 81.8% over unique customers, and the lowest reads 75.0% over tickets opened. A unit is counted as served once any one of its tickets qualifies, so which grain reads highest turns on whether the customers and sessions that came back more than once are the ones being served.

Numerator

This switch is not read while the numerator counts resolutions, because an acknowledgement resolves nothing.

Denominator
Work that finishes after the window closes
Window length28 days (to hour 672)
The log, 43 rows. Hours are offsets from a fixed origin, not a clock.
HourEventTicketSessionCustomerUnder this definition
3ticket openedT01S1C1in window
5first response (agent)T01S1C1not used
14ticket openedT02S2C2in window
15first response (automated)T02S2C2not used
16ticket openedT03S2C2in window
20resolvedT01S1C1counts
28first response (agent)T03S2C2not used
31ticket openedT04S3C3in window
33first response (agent)T04S3C3not used
46resolvedT02S2C2counts
52resolvedT03S2C2counts
58ticket openedT05S4C4in window
59first response (automated)T05S4C4not used
95ticket openedT06S5C5in window
101first response (agent)T06S5C5not used
120ticket openedT07S6C6in window
121first response (automated)T07S6C6not used
126ticket openedT08S6C6in window
130resolvedT06S5C5counts
162ticket openedT09S7C7in window
166first response (agent)T09S7C7not used
172resolvedT09S7C7counts
190resolvedT07S6C6counts
205ticket openedT10S8C8in window
208first response (agent)T10S8C8not used
236resolvedT10S8C8counts
268ticket openedT11S9C1in window
270first response (automated)T11S9C1not used
300resolvedT11S9C1counts
331ticket openedT12S10C4in window
340first response (agent)T12S10C4not used
402ticket openedT13S11C9in window
404first response (agent)T13S11C9not used
430resolvedT13S11C9counts
511ticket openedT14S12C10in window
512first response (automated)T14S12C10not used
553resolvedT14S12C10counts
640ticket openedT15S13C10in window
645first response (agent)T15S13C10not used
665ticket openedT16S14C11in window
690first response (agent)T16S14C11not used
700resolvedT15S13C10counts
712resolvedT16S14C11counts
The desk reports 81.8%, which is 9 of 11 unique customers. Counting the same qualifying work over the three grains gives 81.8% over unique customers, 78.6% over sessions and 75.0% over tickets. The highest of the three reads 81.8% over unique customers, and the lowest reads 75.0% over tickets opened. A unit is counted as served once any one of its tickets qualifies, so which grain reads highest turns on whether the customers and sessions that came back more than once are the ones being served. The automated acknowledgement switch is not read here, because the numerator counts resolutions. Crediting work that finished after the window closed gives 81.8% against 72.7% for counting only what happened inside it. The 2 tickets that opened inside the window and finished after it are the whole argument. Across the 24 settings these switches can take, the same desk over this window reports anywhere from 56.3% to 100.0%, a spread of 43.8 points. The highest is tickets with any first response, automated ones included over unique customers, crediting work that finished after the window closed. The lowest is tickets with a human first response over tickets opened, crediting only what happened inside the window. Neither is dishonest and the desk did the same work in both. That spread is the argument an organisation has when the definition is not written down.
Stylised log. The 43 rows are written for teaching rather than drawn from a real service desk, and the hours are offsets from a fixed origin rather than dates. Every figure above is recounted from those rows by one classifier, so the table markers and the headline cannot disagree.
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