{ "version": "https:\/\/jsonfeed.org\/version\/1.1", "title": "Ivan Baldin, Data Analyst: posts tagged call center", "_rss_description": "Data analytics, probability theory, and applied statistics — from the practitioner’s perspective. Ivan Baldin writes about sales funnels, call center performance, conversion analysis, confidence intervals, binomial distributions, Z-scores, and the math behind data-driven decisions. Years of hands-on experience turning raw CRM data into actionable insights for sales teams and business leaders.", "_rss_language": "en", "_itunes_email": "", "_itunes_categories_xml": "", "_itunes_image": "", "_itunes_explicit": "", "home_page_url": "https:\/\/ivanbaldin.blog\/tags\/call-center\/", "feed_url": "https:\/\/ivanbaldin.blog\/tags\/call-center\/json\/", "icon": "https:\/\/ivanbaldin.blog\/pictures\/userpic\/userpic@2x.jpg?1774085044", "authors": [ { "name": "Ivan Baldin", "url": "https:\/\/ivanbaldin.blog\/", "avatar": "https:\/\/ivanbaldin.blog\/pictures\/userpic\/userpic@2x.jpg?1774085044" } ], "items": [ { "id": "5", "url": "https:\/\/ivanbaldin.blog\/all\/kupivip-voice-bot-guessing-the-sample-size\/", "title": "KupiVIP’s Voice Robot: Guessing the Sample Size", "content_html": "

In the article “Case Study: On Black Friday, KupiVIP Replaced Their Call Center with a Robot, and Only 5 Out of 5,000 People Realized They Were Talking to a Neural Network<\/a>” on vc.ru, one phrase caught my attention above all else — the part where the author mentions a conversion rate increase from 6% to 8%:<\/p>\n

\n\""the\n<\/div>\n

Naturally, I started wondering: on what call volume was this conversion rate increase observed, and was that volume sufficient to make a reliable claim that the voice robot outperforms live call center agents?<\/p>\n

The question can be formulated precisely as follows: what is the minimum number of calls required to claim, with a confidence level of, say, 95%, that the conversion rate “increased from 6% to 8%”?<\/p>\n

Building the Experiment in Google Spreadsheets<\/h2>\n

Let’s lay out the available data in Google Spreadsheets. For the calculations that follow, we’ll need a “number of calls” parameter — let’s assume for now that both the robot and live agents each made 1,000 calls before the 6% and 8% conversion rates were obtained:<\/p>\n

\n\"\"\n<\/div>\n

Essentially, this is a standard A\/B split test, and we’ll need to walk through its algorithm to obtain the Z-score<\/i> and calculate the p-value<\/i>.<\/p>\n

Let’s calculate the standard errors (SD, or σ) for both conversion rates, along with the standard error of the difference between them. The formula for the standard error of a conversion rate:<\/p>\n

\n\"\"\n<\/div>\n

where p<\/i> is the conversion rate (6%, for example) and n<\/i> is the sample size (1,000 calls). Here’s the Google Spreadsheets calculation:<\/p>\n

\n\"\"\n<\/div>\n

The standard error of the difference between conversion rates is calculated using the formula:<\/p>\n

\n\"\"\n<\/div>\n

where σ<\/i> is the standard error of each conversion rate, A and B (live agent and robot). We’ll compute it just below in Google Spreadsheets:<\/p>\n

\n\"\"\n<\/div>\n

How much larger is the difference between conversions A and B compared to the standard error of that difference? This ratio is called the Z-score.<\/i><\/b> In Google Spreadsheets, it’s straightforward:<\/p>\n

\n\"\"\n<\/div>\n

So the Z-score = 1.7541. On the normal distribution curve, this corresponds to the 96th percentile — meaning the probability of the Z-score randomly exceeding 1.7541 is about 4% (in other words, 96% of the area under the bell curve falls within +1.7541 standard deviations):<\/p>\n

\n\"\"\n<\/div>\n

Where did we get 96%? The exact probability, the p-value<\/i>, is calculated using the formula:<\/p>\n

=NORM.DIST(1.7541,0,1,TRUE)<\/code><\/pre>
\n\"\"\n<\/div>\n
P-value = 96.03%.<\/p>\n
So here’s our interim conclusion: if, on a sample of 1,000 calls in each of the two groups, we observed conversion rates (promo code activations) of 6% and 8%, then we are 96% confident that this difference is not due to chance.<\/b> (There remains a 4% probability that the observed difference is random. In that case, perhaps the conversion rate is actually the same — say, 7% — and had we made more calls, the difference would have eventually disappeared.)<\/p>\n
Minimum Experiment Size<\/h2>\n
Now, let’s get back to the original question.<\/p>\n
We weren’t trying to prove that 8% is greater than 6%, and the figure of 1,000 calls for the robot and agents was chosen arbitrarily. What we wanted to calculate was the minimum number of calls needed to establish the statistical significance of the difference between 8% and 6% at a 95% confidence level.<\/b><\/p>\n
1,000 calls turned out to be more than enough. Now we just need to decrease this number until the p-value crosses the 95% threshold. (By the way, according to the normal distribution formula, this corresponds to a Z-score of 1.6449 — try verifying this yourself.)<\/p>\n
In theory, it would probably be possible to derive a large formula for the n<\/i> at which the p-value equals 0.95. In practice, it’s faster to manually find the minimum n through trial and error. Or, better yet, install a Goal Seek<\/b> add-on for Google Spreadsheets and use it to find the answer automatically:<\/p>\n
\n\"\"\n
(Just make sure the number of robot calls is exactly the same as the number of live agent calls, i.e., you’ve entered =C6 in cell C7.)<\/div>\n<\/div>\n
\n\"\"\n<\/div>\n
Conclusions<\/h2>\n
So, we’ve calculated the minimum experiment conditions for evaluating the effectiveness of the KupiVIP voice robot.<\/p>\n
You need at least 879 calls<\/b> in each of the two groups to confirm, with a 95% confidence level, that there is a difference between the 6% promo code activation rate in the control group (real live agents) and the 8% rate in the test group (voice robot).<\/p>\n
(The only caveat is that neither 6% nor 8% yields a whole number of activations on a sample of 879 calls, and in reality, of course, the numbers would be different — and the number of calls in the two groups could vary as well. But this doesn’t really matter much, since the conversion rates cited in the article were most likely rounded.)<\/p>\n
See also:<\/h2>\n
https:\/\/abtestguide.com\/calc\/?ua=1000&ub=1000&ca=60&cb=80<\/a><\/p>\n",
            "summary": "A voice robot beats call center with 8% vs. 6% promo code activations. But how many calls do you actually need to prove the difference is real? We walk through the A\/B test math and find the minimum sample size for 95% confidence using Goal Seek in Google Spreadsheets, Z-score and SD.",
            "date_published": "2019-07-20T13:18:00+03:00",
            "date_modified": "2026-04-12T03:31:13+03:00",
            "tags": [
                "A\/B test",
                "call center",
                "conversion",
                "Google Sheets",
                "statistics"
            ],
            "image": "https:\/\/ivanbaldin.blog\/pictures\/vc_quote.png",
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            "id": "8",
            "url": "https:\/\/ivanbaldin.blog\/all\/one-in-five-testing-a-connection-complaint\/",
            "title": "One in Five? Testing a Connection Complaint",
            "content_html": "
A contractor swears the phones drop out on every fifth call.<\/b> You make one — it’s fine. Another — also fine. How many do you need before you can confidently tell him he’s wrong?<\/p>\n
Our job is to check whether the claim that 20% of calls have connection problems holds up.<\/b> And as always, we’re not going to just make 100 test calls — we don’t have the resources for that. Instead, we’ll state a null hypothesis, an alternative hypothesis, and test it at a chosen confidence level.<\/p>\n
Stating the hypothesis and choosing a confidence level<\/h2>\n
The null hypothesis (H0<\/sub>)<\/i><\/b> is the contractor’s claim: at least 20% of calls have connection problems. This is the claim we’re putting on trial.<\/p>\n
The alternative hypothesis (H1<\/sub>)<\/i><\/b> is that the connection is fine — problems happen in fewer than 20% of calls. This is the position we’ll lean toward if the data supports it.<\/p>\n
(That framing matters. In hypothesis testing, you never “prove” H0<\/sub>; you either reject it or you fail to reject it. So when we say we want to side with the contractor or not, what we really mean is: can we gather enough evidence to reject<\/i> his claim?)<\/p>\n
The confidence level<\/b> is how sure we want to be about the outcome. The higher it is, the more test calls we’ll need to make, so we’ll budget 1% for error and go with 99% confidence<\/b> — leaving a 1% chance that we reject the contractor’s claim when problems really are there.<\/p>\n
Building the formula for the sample size<\/h2>\n
To reject H0<\/sub><\/i>, all we need is to pull off N<\/i> successful calls in a row with no signs of trouble — while keeping the probability at or below 1% that we simply got lucky and that real equipment problems just happened not to show up in any of the N<\/i> calls.<\/p>\n
If the contractor is right, 80% of calls go through cleanly. The probability of no issues across N<\/i> calls in a row is 0.80N<\/sup>. We need the smallest N<\/i> for which that probability drops to 1%:
\n0.80N<\/sup> = 0.01<\/p>\n
Which is exactly the logarithm of 1% to base 80%.<\/p>\n
\n\"\"\n<\/div>\n
Into Google Sheets it goes:<\/p>\n
\n\"\"\n<\/div>\n
The formula for cell C5 looks like<\/p>\n
=LOG(1-C2,1-C3)<\/code><\/pre>
We need 20.64 calls. (Check: 0.8020.64<\/sup> = 0.9995%, right on target.)
\nAll that’s left is rounding up:<\/p>\n
=ROUNDUP(C5)<\/code><\/pre>
or, in one shot,<\/p>\n
=ROUNDUP(LOG(1-C2,1-C3))<\/code><\/pre>
\n\"\"\n<\/div>\n
Testing the hypothesis<\/h2>\n
If the contractor’s claim H0<\/sub><\/i> is correct and every fifth call really does have trouble, then the probability of seeing zero problems across 21 test calls in a row is about 1%. In other words: either we just hit a one-in-a-hundred coincidence, or the claim that 20% of calls have problems doesn’t hold. At the 99% confidence level, we reject H0<\/sub><\/i> — in everyday terms, the connection is fine.<\/p>\n",
            "summary": "A contractor claims every fifth call has a bad connection. How many good calls in a row do you need to disprove him? This post uses a binomial hypothesis test to calculate the exact sample size for 99% confidence — with the Google Sheets formula included.",
            "date_published": "2019-06-09T16:45:58+03:00",
            "date_modified": "2026-04-24T21:06:41+03:00",
            "tags": [
                "binomial",
                "call center",
                "Google Sheets",
                "statistics"
            ],
            "image": "https:\/\/ivanbaldin.blog\/pictures\/every5th01.png",
            "_date_published_rfc2822": "Sun, 09 Jun 2019 16:45:58 +0300",
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        {
            "id": "30",
            "url": "https:\/\/ivanbaldin.blog\/all\/how-long-can-a-sales-phone-stay-silent\/",
            "title": "How Long Can a Sales Phone Stay Silent?",
            "content_html": "
Here’s another case. The middle of a busy day in the sales department, and the phone has been silent for half an hour.<\/p>\n
There are two possibilities: either something is broken, or this is just a lull that happened to run long, and the next customer call is about to come in.<\/p>\n
Let’s work out how many minutes you can sit in silence before you should start to worry.<\/p>\n
The least obvious parameter of a phone call<\/h2>\n
What parameters does a phone call in a sales department or a call center actually have? Date and time, speed of answer, duration, day of the week, line number, customer number<\/i> – those are the obvious characteristics you can analyze incoming calls by.<\/p>\n
One more hides in the shadows: the length of the pause<\/b> (the stretch of time with no calls) that came right before the call.<\/b> Say a call came in at 2:07 p.m. on February 13 and lasted 3 minutes 52 seconds. That’s what you see in an export, in the PBX logs, or in the CRM. What is no less interesting: if the previous call was logged at 2:01 p.m., then that six-minute gap is exactly the non-obvious parameter that could be analyzed too.<\/p>\n
Let’s take calls to a call center on weekdays between 10 a.m. and 7 p.m. We compute the difference in minutes between two adjacent calls – “0” if less than a minute passed, “1” for one to two minutes (from 01:00 to 01:59), and so on. Analyze thousands of calls, and you get roughly this table:<\/p>\n\n\n\n\n\n\n\n\n\n\n\n
Pause before the call, minutes<\/b><\/td>\nNumber of calls<\/b><\/td>\nShare of calls<\/b><\/td>\nCumulative share<\/b><\/td>\n<\/tr>\n
0<\/td>\n19,641<\/td>\n21.3%<\/td>\n21.3%<\/td>\n<\/tr>\n
1<\/td>\n16,299<\/td>\n17.7%<\/td>\n39.0%<\/td>\n<\/tr>\n
2<\/td>\n12,137<\/td>\n13.2%<\/td>\n52.2%<\/td>\n<\/tr>\n
3<\/td>\n9,251<\/td>\n10.0%<\/td>\n62.2%<\/td>\n<\/tr>\n
4<\/td>\n7,276<\/td>\n7.9%<\/td>\n70.1%<\/td>\n<\/tr>\n
...<\/td>\n...<\/td>\n...<\/td>\n...<\/td>\n<\/tr>\n
23<\/td>\n139<\/td>\n0.2%<\/td>\n99.4%<\/td>\n<\/tr>\n
...<\/td>\n...<\/td>\n...<\/td>\n...<\/td>\n<\/tr>\n
40<\/td>\n10<\/td>\n0.0%<\/td>\n100.0%<\/td>\n<\/tr>\n<\/table>\n
(Strictly speaking, pauses longer than 40 minutes occur as well, but their share is vanishingly small – which is why, rounding to the nearest tenth, we already reach 100% at 40 minutes.)<\/p>\n
The simple idea of “anomalous” pauses<\/h2>\n
So we now have a remarkably clean histogram of how pause lengths are distributed. What stands out is that they decay exponentially:<\/p>\n
\n\"\"\n<\/div>\n
Let’s come back to what we set out to calculate in the first place.<\/p>\n
The idea we started with: sooner or later, a gap between calls in the middle of the workday grows so long that it starts to worry the managers.<\/b> It stands to reason that the length that triggers the worry is different in every sales department and every call center – for a large call center, a five-minute gap is already very unlikely; for another, five minutes is the standard interval between calls, but 55 minutes is genuinely suspicious.<\/p>\n
What if we frame the idea of an “anomalously” long pause this way: it is a pause that occurs extremely rarely – say, once a week, or once a month, or once every six months. We pick the level of “anomaly” that seems reasonable to us, and then work out which pause lengths occur about as rarely as our definition says.<\/b><\/p>\n
For example, let an anomalous pause be one that, on average, happens once a week.<\/b><\/p>\n
If the calls in our table cover the past year, then the number of “anomalous” (“once a week”) pauses in it should be on the order of 52 – one for each week.<\/p>\n
So we need to count off the 52 calls with the longest pauses before them.<\/b> In my table there turned out to be 47 calls with pauses of 38 minutes or more, and after that 57 calls with pauses of 37 minutes or more.<\/p>\n
Which leads to the conclusion that a 37- to 38-minute gap between calls on a weekday should put you on alert: either you are looking at the weekly “anomaly,” the one that shows up about 52 times a year, or a technical failure has occurred and the calls have stopped coming in.<\/b><\/p>\n",
            "summary": "The phone in the sales department has been quiet for half an hour. Broken line, or just a long lull? Every call carries a hidden parameter – the pause before it. Count the 52 longest pauses in a year and you get a threshold: 37 minutes.",
            "date_published": "2019-06-09T12:10:35+03:00",
            "date_modified": "2026-08-17T02:05:27+03:00",
            "tags": [
                "call center",
                "statistics"
            ],
            "image": "https:\/\/ivanbaldin.blog\/pictures\/poisson01.png",
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        {
            "id": "7",
            "url": "https:\/\/ivanbaldin.blog\/all\/call-quality-audits-determining-your-sample-size\/",
            "title": "Call Quality Audits: Determining Your Sample Size",
            "content_html": "
Calculating Sample Size for Quality Call Audits<\/h2>\n
A common tool for assessing the quality of sales managers’ work is quality auditing of phone calls<\/b>, or “call monitoring.”<\/p>\n
Suppose your goal is not simply to measure<\/b> the quality of phone calls, but to document growth<\/i> in that quality.<\/b> For example, you conducted training for your managers, introduced new incentives for meeting quality standards, or implemented some other intervention.<\/p>\n
\n\"\"\n<\/div>\n
It’s reasonable to assume that an improvement in quality in the first random call recorded after the training won’t definitively prove that quality has improved across all calls. Likely, a second successful call won’t conclusively confirm the hypothesis either.<\/p>\n
Thus, you’ll need to listen to — if not all calls — at least a sufficient number<\/b> of calls after your changes, and the number of calls you’ll need to audit can, in fact, be calculated precisely.<\/b><\/p>\n
Calculating Sample Size<\/h2>\n
On page 35 of the paper “Introduction to Statistical Inference and Experimental Design<\/a>” I found a suitable example 1.9 and a formula for calculating such samples:<\/p>\n
\n\"\"\n<\/div>\n
In this example, an improvement in ACT<\/a> math test scores from 24.5 (variance 8.2) to 26.0 points is considered, with α = 0.05 and power = 0.90.<\/p>\n
For convenience, I assembled the formula in a Google Sheet:<\/p>\n
Sample Size Calculator<\/a><\/p>\n
\n\"\"\n
You simply need to copy the file and substitute your own values.
\nIt’s reasonable to choose a confidence level between 80% and 95%, and a statistical power between 60% and 80%. Enter the average call quality score before changes, the standard deviation (SD) of call scores “before,” and the expected average call quality score “after” your changes.<\/div>\n<\/div>\n
See also:<\/h2>\n
https:\/\/bpb-us-e1.wpmucdn.com\/sites.ucsc.edu\/dist\/2\/1389\/files\/2026\/03\/part1.pdf<\/a><\/p>\n",
            "summary": "Stop guessing how many calls to audit. Use this statistical formula to calculate the exact sample size needed for call audits that prove quality improvements. Learn about confidence levels, power calculations, and A\/B testing verification for your sales team.",
            "date_published": "2019-05-26T16:46:00+03:00",
            "date_modified": "2026-04-18T14:21:49+03:00",
            "tags": [
                "A\/B test",
                "call center",
                "equations",
                "Google Sheets",
                "Sales Department"
            ],
            "image": "https:\/\/ivanbaldin.blog\/pictures\/create-a-1080-1080-pixels-flat-style-cartoon-showi-(1).png",
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