{ "version": "https:\/\/jsonfeed.org\/version\/1.1", "title": "Ivan Baldin, Data Analyst: posts tagged sales funnel", "_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\/sales-funnel\/", "feed_url": "https:\/\/ivanbaldin.blog\/tags\/sales-funnel\/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": "1", "url": "https:\/\/ivanbaldin.blog\/all\/conversion-chart-with-confidence-intervals\/", "title": "Conversion Chart with Confidence Intervals", "content_html": "

I’ve been happily using a more informative way to visualize conversion rates for a while now, by adding confidence interval bounds<\/b> to my charts.<\/p>\n

Sales office conversion rates<\/h2>\n

Say we’re evaluating the performance of regional sales offices. By performance<\/i><\/b> we mean the ratio of closed deals to incoming leads (lead-to-sale conversion, or simply “conversion”).<\/i><\/b> For example, if the “Midtown” office closed 19 deals out of 33 leads in a quarter, we consider their performance to be 19\/33 = 57.6%.<\/p>\n

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

Clearly, some offices outperform others: conversion rates range from 57.6% down to 17.6%. It is also apparent that the number of leads varies widely across offices: from 33 leads in “Midtown” to 706 leads in “Astoria.”<\/p>\n

Most people would stop here, but there is a straightforward way to use the concept of a “confidence interval” or “standard deviation (SD)” to reveal something that isn’t immediately obvious.<\/b><\/p>\n

Estimating sample size and SD<\/h2>\n

Because the number of leads differs dramatically across offices (“Midtown” and “Astoria” differ by a factor of nearly 22), our confidence in the calculated conversion rate will not be uniform. For “Astoria,” the 36.1% figure is based on a sample of 706 leads and can be considered quite reliable. For “Midtown,” the 57.6% result comes from a small sample of just 33 leads, so there is no guarantee that, given their own 706 leads over time, they would sustain the same conversion rate.<\/p>\n

Naturally, we need to estimate the confidence interval for each sales office based on the number of leads — that is, the sample size.<\/p>\n

Here is the familiar formula for the standard deviation (SD), or σ<\/i>:<\/p>\n

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

where p<\/i> is the conversion rate and n<\/i> is the number of leads.<\/p>\n

We compute it in column E:<\/p>\n

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

The resulting standard deviation shows the margin of error in the conversion estimate. As expected, it is larger where the sample is smaller. The less data we have, the less reliable the calculated result, and the less confident we can be in our assessment of the corresponding office’s performance.<\/p>\n

Computing the bounds of a 90% confidence interval<\/h2>\n

Let us extend our table with the lower and upper bounds of a 90% confidence interval. In other words, we estimate the range of conversion rates for each office such that there is a 90% probability the true<\/i> conversion rate falls within that range.<\/p>\n

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

Knowing that the bounds of a 90% confidence interval lie at ±1.645 SD, we subtract and add 1.645 SD to obtain the lower and upper bounds, respectively. For “Astoria,” this tells us that the true<\/i> conversion rate lies between 33.1% and 39.1%. (One time out of ten it may still fall outside our interval, but nine times out of ten our estimate holds.)<\/p>\n

Enhancing the chart with “candlesticks”<\/h2>\n

In Excel 2013 we can use a “stock chart,”<\/b> substituting the upper and lower confidence interval bounds for the high<\/i><\/b> and low prices,<\/i><\/b> and the conversion rate calculated earlier for the close price:<\/i><\/b><\/p>\n

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

The enhanced chart does not change the conclusions we drew at the outset. However, it subtly reminds an observant manager that the reported conversion rates are not final<\/b> — and are especially “not final” where the confidence bounds are wider.<\/p>\n

“Midtown” appears to have outperformed “SoHo”, but while “SoHo” strong result is reliable thanks to its narrow interval, the result for “Midtown” is highly approximate. Definitive conclusions can therefore only be drawn for some of the offices; for the rest, more data is needed, and until then their rankings should be considered preliminary — or, as noted above, not final.<\/p>\n", "summary": "Not all conversion rates are created equal. A 57% rate from 33 leads is not the same as 36% from 706. Ivan Baldin reflects on how to add confidence interval bounds to your sales conversion charts using standard deviation and Excel stock chart candlesticks.", "date_published": "2021-05-25T02:13:00+03:00", "date_modified": "2026-04-12T03:24:52+03:00", "tags": [ "analytics", "conversion", "diagrams and charts", "Excel", "sales funnel", "statistics" ], "image": "https:\/\/ivanbaldin.blog\/pictures\/conversion_simple.png", "_date_published_rfc2822": "Tue, 25 May 2021 02:13:00 +0300", "_rss_guid_is_permalink": "false", "_rss_guid": "1", "_e2_data": { "is_favourite": false, "links_required": [], "og_images": [ "https:\/\/ivanbaldin.blog\/pictures\/conversion_simple.png", "https:\/\/ivanbaldin.blog\/pictures\/conversion_simple_chart.png", "https:\/\/ivanbaldin.blog\/pictures\/CodeCogsEqn.png", "https:\/\/ivanbaldin.blog\/pictures\/conversion_SD.png", "https:\/\/ivanbaldin.blog\/pictures\/conversion_SD_max-min.png", "https:\/\/ivanbaldin.blog\/pictures\/conversion_simple_chart_type.png", "https:\/\/ivanbaldin.blog\/pictures\/conversion_simple_chart_modified.png" ] } }, { "id": "6", "url": "https:\/\/ivanbaldin.blog\/all\/the-cognitive-fallacy-of-conversion-rates\/", "title": "The Cognitive Fallacy of Conversion Rates", "content_html": "

A curious thing about working with the concept of conversion rate<\/i> is that, strictly speaking, a conversion rate is almost never precisely defined.<\/b><\/p>\n

All those “call-to-sale conversion of 18.4%,” “CTR of 3.1%,” “deal conversion of 30%” — it’s always a somewhat simplified approach, as if the conversion rate were reliably measured and, should it change, we’d explain it with objective factors, never entertaining the thought that there never was any “18.4%” to begin with — there were just 38 contracts we closed on 206 calls, and that doesn’t at all mean there couldn’t have been more or fewer.<\/p>\n

Much like the position of an electron around the nucleus of an atom isn’t defined by exact coordinates, but is merely described by a region where it’s most likely to be found, our conversion rate is not a specific number either. In reality, it is an interval within which it lies.<\/b><\/p>\n

Calculating Conversion Rates and Cognitive Bias<\/h2>\n

Consider a fictional sales department that started selling a new product this year. Let’s say, hmm, trucks.<\/b> The product isn’t in high demand, so, for now, there isn’t much data for analysis — or, better said, very little at all:<\/p>\n\n\n\n\n\n\n\n\n
Month<\/b><\/td>\nLeads<\/b><\/td>\nSales<\/b><\/td>\n<\/tr>\n
August<\/td>\n48<\/td>\n1<\/td>\n<\/tr>\n
September<\/td>\n35<\/td>\n1<\/td>\n<\/tr>\n
October<\/td>\n24<\/td>\n0<\/td>\n<\/tr>\n
November<\/td>\n61<\/td>\n2<\/td>\n<\/tr>\n
December<\/td>\n32<\/td>\n0<\/td>\n<\/tr>\n
TOTAL:<\/b><\/td>\n200<\/b><\/td>\n4<\/b><\/td>\n<\/tr>\n<\/table>\n

As the sales data shows, over several months we’ve got 4 deals out of 200 leads, i.e. our conversion rate is 4 \/ 200 = 2.0%.<\/p>\n

(Additionally, based on five months of data, we can roughly project 480 leads for the next year and, accordingly, 480 × 0.02 = 9.6 deals.)<\/p>\n

Given such scarce data, it’s impossible to go wrong, so, of course, such a forecast won’t be incorrect. However, it contains an important cognitive bias: 2.0% is not the exact value, but rather the most probable so far<\/i> value of our lead-to-sale conversion rate for trucks.<\/p>\n

In reality, the conversion rate cannot be determined precisely. It lies within a confidence interval from 0.4% to 3.6%.<\/b> And for the coming year, we should be projecting not 9.6 deals, but somewhere between 5 and 15 trucks sold. Unfortunately, narrowing this range any further would be overly optimistic.<\/p>\n

The Conversion Bell Curve<\/h2>\n

Assuming that our true<\/i> conversion rate is stable and exactly<\/i> equals 2.0%, we can estimate the possible range of deals out of 480 leads expected next year. Since we can only vouch for the consistency of our own<\/i> work but can’t account for randomness (customer moods, force majeure, a lucky sale to the CEO’s buddy), there’s always a chance the number of deals will differ slightly from the projected 480 × 0.02 = 9.6 deals — much like the number of tails in 480 coin flips may differ slightly from 240, coming out to 235, 248, or possibly even 223.<\/p>\n

Graphically, this looks like a normal distribution bell curve,<\/i> where the further we move from the expected value of 9 deals at the center of the bell, the lower the probability of closing significantly fewer or significantly more deals:<\/p>\n

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

Looking at the resulting graph, we have to admit that seeing fewer than 2 or more than 19 sales is practically impossible.<\/p>\n

But can we narrow our confidence interval?<\/i><\/p>\n

Confidence Interval of a Conversion Rate<\/h2>\n

The standard error (SD) for a binomial distribution is calculated using the formula:<\/p>\n

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

where n<\/i><\/b> is the number of trials, and p<\/i><\/b> is the probability of success.<\/p>\n

For our 200 leads this year, we get:<\/p>\n

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

SD = 1.98 deals.<\/b> In other words, according to the laws of normal distribution (and binomial distribution is a special case of normal distribution), in roughly 68% of cases, while operating with a true conversion rate of 2.0%, we’d land within the confidence interval of 2.02 to 5.98 deals, i.e. ±1SD.<\/p>\n

For the projected 480 leads next year, we get:<\/p>\n

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

SD = 3.07 deals.<\/b> By the laws of binomial (normal) distribution, it is known that in 68% of cases, next year’s sales will fall within ±1SD of the expected value of 9.6 deals, and in 90% of cases — within ±1.645SD of the expected value. 3.07 deals × 1.645 = 5.05 deals, meaning that in 90% of cases, if we work the entire next year at a 2% conversion rate, we won’t fall outside the confidence interval of “4.55 to 14.65 deals.” (Notably, conversely, in 1 out of 10 cases we will<\/i> fall outside these bounds, all while still operating at a “true” conversion rate of 2%.)<\/p>\n

One can only wonder what kind of uproar the sales manager would raise if, by year’s end, we sold just 4 trucks on 480 leads, formally showing a conversion rate of 0.83%... and what’s even more curious is that, statistically, this happens in 1 out of 27 sales departments.<\/p>\n

In one out of 27 cases, you get fired for missing your sales target, even though you were still operating at a “true” conversion rate of 2%.<\/p>\n

Three Conversion Rates at the Confidence Interval Boundary<\/h2>\n

So how should we interpret this year’s results, where we got 4 sales out of 200 leads?<\/p>\n

Case one, “2.00%.”<\/b> We covered this one right away. 4 \/ 200 = 0.02, meaning our conversion rate is 2%. At the same time, by the laws of binomial distribution, there’s still a chance of fluctuating within the 90% confidence interval of “±1.645SD,” i.e. within the range of 0.74 to 7.26 deals per 200 leads.<\/p>\n

It looks roughly like this:<\/p>\n

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

Our result of 4 deals matched the expected value for a 2.0% conversion rate, although, in general, it didn’t have to — it could have landed anywhere within the 90% confidence interval of 1 to 7 sales.<\/p>\n

Case two, “1.22%.”<\/b> In this scenario, our “true” conversion rate is actually lower, equaling, say, 1.22%.<\/b> Then the expected number of trucks sold is approximately 2, and we were lucky<\/b> to close 4 sales. Our luck was such that we could have made more<\/i> than 4 sales only in 10% of cases. That is, we remain within the 90% probability field, though we’re sitting at its boundary. A little more, and our luck would be too good — but for now, we’re lucky “within reason”:<\/p>\n

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

Case three, “3.31%.”<\/b> Now let’s suppose that this year we were unlucky,<\/b> even though our true conversion rate was above 2.0% all year and actually equaled 3.31%.<\/b> The expected value for 200 leads would then be approximately 6 trucks sold, and making fewer<\/i> than 4 sales would only be possible in 10% of cases. So we’d still be within the 90% probability field, but sitting at the left boundary with our unlucky 4 deals.<\/p>\n

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

Thus, the takeaway is clear: we don’t know for sure which of the 3 conversion rates is the true one.<\/b> We’re used to thinking it’s Case 1 — dividing 4 sales by 200 leads and getting a conversion rate of 2.00%. But nobody knows for certain whether the current year was typical or atypical, whether we were lucky or unlucky. In 90% of cases, it could have been a matter of luck,<\/b> and we were actually operating at a conversion rate of 1.22%, or a matter of bad luck,<\/b> where we were operating at a conversion rate of 3.31%. In all 3 cases, the probability of closing 4 sales out of 200 leads did not exceed the 90% threshold.<\/b><\/p>\n

Unfortunately, we simply don’t have enough data yet to make more precise claims.<\/p>\n

We Need More Data<\/h2>\n

A logical question to ask is — how much data do we need to accumulate before we can speak of a 2.0% conversion rate with any reliability? Let’s try gradually increasing the sample size (number of leads, and consequently, sales) until we see the 90% confidence interval converge around the 2.00% conversion rate value:<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
                    Leads<\/b><\/td>\n             Deals<\/b><\/td>\nLower bound of 90% confidence interval (-1.645SD)<\/b><\/td>\nUpper bound of 90% confidence interval (+1.645SD)<\/b><\/td>\nLower conversion bound<\/b><\/td>\nUpper conversion bound<\/b><\/td>\n<\/tr>\n
200<\/td>\n4<\/td>\n0.7<\/td>\n7.3<\/td>\n0.37%<\/td>\n3.63%<\/td>\n<\/tr>\n
500<\/td>\n10<\/td>\n4.9<\/td>\n15.1<\/td>\n0.97%<\/td>\n3.03%<\/td>\n<\/tr>\n
1,000<\/td>\n20<\/td>\n12.7<\/td>\n27.3<\/td>\n1.27%<\/td>\n2.73%<\/td>\n<\/tr>\n
5,000<\/td>\n100<\/td>\n83.7<\/td>\n116.3<\/td>\n1.67%<\/td>\n2.33%<\/td>\n<\/tr>\n
10,000<\/td>\n200<\/td>\n177.0<\/td>\n223.0<\/td>\n1.77%<\/td>\n2.23%<\/td>\n<\/tr>\n
50,000<\/td>\n1,000<\/td>\n948.5<\/td>\n1,051.5<\/td>\n1.90%<\/td>\n2.10%<\/td>\n<\/tr>\n
100,000<\/td>\n2,000<\/td>\n1,927.2<\/td>\n2,072.8<\/td>\n1.93%<\/td>\n2.07%<\/td>\n<\/tr>\n
500,000<\/td>\n10,000<\/td>\n9,837.2<\/td>\n10,162.8<\/td>\n1.97%<\/td>\n2.03%<\/td>\n<\/tr>\n
1,000,000<\/td>\n20,000<\/td>\n19,769.7<\/td>\n20,230.3<\/td>\n1.98%<\/td>\n2.02%<\/td>\n<\/tr>\n
10,000,000<\/td>\n200,000<\/td>\n199,271.7<\/td>\n200,728.3<\/td>\n1.99%<\/td>\n2.01%<\/td>\n<\/tr>\n
25,000,000<\/td>\n500,000<\/td>\n498,848.5<\/td>\n501,151.5<\/td>\n2.00%<\/td>\n2.00%<\/td>\n<\/tr>\n<\/table>\n

Needless to say, very few sales departments can generate more than a few tens of thousands of leads. Therefore, the truth is, setting sales targets and making promoting and firing decisions based on 1–5% conversion rates is madness — at these small numbers, math in sales simply doesn’t work.<\/b><\/p>\n", "summary": "Your conversion rate isn't a fixed number — it's a confidence interval. Using binomial distribution, this post shows why a 2% conversion rate on 200 leads could really be anywhere from 0.4% to 3.6%, and why setting sales targets on small samples is madness.", "date_published": "2019-05-07T12:39:07+03:00", "date_modified": "2026-04-12T11:39:08+03:00", "tags": [ "binomial", "conversion", "sales funnel" ], "image": "https:\/\/ivanbaldin.blog\/pictures\/norm_dist.png", "_date_published_rfc2822": "Tue, 07 May 2019 12:39:07 +0300", "_rss_guid_is_permalink": "false", "_rss_guid": "6", "_e2_data": { "is_favourite": false, "links_required": [], "og_images": [ "https:\/\/ivanbaldin.blog\/pictures\/norm_dist.png", "https:\/\/ivanbaldin.blog\/pictures\/CodeCogsEqn-1.png", "https:\/\/ivanbaldin.blog\/pictures\/sd01.png", "https:\/\/ivanbaldin.blog\/pictures\/sd02.png", "https:\/\/ivanbaldin.blog\/pictures\/001.png", "https:\/\/ivanbaldin.blog\/pictures\/002.png", "https:\/\/ivanbaldin.blog\/pictures\/003.png" ] } }, { "id": "4", "url": "https:\/\/ivanbaldin.blog\/all\/staff-decisions-or-lets-fire-grandma\/", "title": "Staff Decisions, or Let’s Fire Grandma", "content_html": "

It’s a Thursday morning, and the VP of Sales is staring at a spreadsheet. One number — 10.1% — is about to end someone’s career. He doesn’t know it yet, but he’s about to make a decision that mathematics would call premature.<\/p>\n

I would call this problem “Promote or Fire”, or “Let’s Fire Grandma”.<\/p>\n

Here we’re looking at our sales department’s results, and questions are arising about our new manager, Drennan:<\/p>\n

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

Matt Drennan joined the team two and a half months ago. He came from a smaller company, interviewed well, and his first few weeks were promising — he learned the product fast, clients liked him on the phone. His probation target was set at “16 deals per 100 calls”. Reason? Because historically, our VP of Sales observed a call-to-deal conversion rate of 16.1%.<\/p>\n

Now, with 89 calls behind him and only 9 deals to show for it, his conversion sits at 10.1%.<\/p>\n

“Fire him,” the VP of Sales decides.<\/p>\n

Here’s the question: is this decision justified?<\/b> Has enough time passed (enough data accumulated) to make this call? Has the “bad luck” factor been accounted for? Could it be that Drennan is simply performing no worse<\/b> than the other managers, actually converting at around the required 16%, but consistently running into clients’ force majeure events (5 clients “dropped off”), a “rough patch” in his personal life, and an unfortunately positioned Moon in the third house of Taurus?<\/p>\n

Rolling the Dice<\/h2>\n

Before we get to the spreadsheet formula that will settle this, let me take you on a brief detour.<\/p>\n

In 1913, at the Monte Carlo Casino, the roulette ball landed on black twenty-six times in a row<\/a>. Gamblers lost millions betting against the streak, convinced that red was “due.” They were wrong — not because the wheel was rigged, but because they could not intuitively grasp what randomness actually looks like. Streaks happen. Cold spells happen. And sometimes a perfectly good sales manager just has a bad quarter.<\/p>\n

This is the same trap the VP of Sales is walking into.<\/p>\n

Recalling the coin flip example, let’s switch things up this time and roll a 6-sided die. The probability of rolling a “1” is 1\/6, or roughly 16.7%.<\/p>\n

The expected value for 89 rolls of a die is 89 × 1\/6 = 14.8 “ones” (and the same number of “twos,” “threes,” and so on), but obviously you could get not just 14–15, but also 12, 17, or even 20. Getting none at all,<\/i> however, is virtually impossible (though, theoretically, the probability isn’t zero).<\/p>\n

Drennan’s work can be thought of as rolling a die, where the desired outcome — a “one” (a deal) — comes up roughly every sixth roll. Roughly,<\/i> because the historically observed conversion rate (excluding Drennan’s results) is 380 deals out of 2,361 calls, or 380\/2,361 = 16.1%. The expected value from his 89 “rolls” (calls) is 89 × 0.161 = 14.3 “ones” (deals), but intuitively, we understand there could be slightly more or slightly fewer.<\/p>\n

If we calculate (we’ll learn how shortly) the exact probabilities of “landing” a specific number of deals in 89 calls and plot them on a graph, the most likely outcome (the “expected value”)<\/i> of 14 deals will be in the center, with the remaining possible outcomes (13 and 15 deals, 12 and 16 deals, etc.) becoming progressively less likely each time, giving the graph its bell shape:<\/p>\n

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

We can’t say that 9 deals is entirely<\/i> improbable — the bar is visible, if modest, with a probability of 0.037. That is, it happens in 1 out of 27 cases — which may be unlikely, but not extremely<\/i> unlikely.<\/p>\n

All that’s left is to figure out how we arrived at “1 in 27,” and how this connects to difficult, “staff”, decisions in a sales department.<\/p>\n

Calculating the Binomial Distribution<\/h2>\n

Both Excel and Google Sheets have a built-in binomial distribution function.<\/b> It’s exactly what will give us the answer to whether it’s time to fire the unlucky Drennan.<\/p>\n

In the cell next to his 10.1% conversion rate, we calculate the function:<\/p>\n

=BINOM.DIST(D7,C7,$E$11,1)<\/code><\/pre>
\n\"\"\n<\/div>\n
In this function, we specify, in order: the number of successes (deals), the number of trials (calls), and the probability of success (the 16.1% conversion rate). The last, 4th parameter, we set to “1.”<\/p>\n
\n\"\"\n<\/div>\n
What is this 0.0763 we got? 0.0763 is the probability of getting no more than 9 deals out of 89 calls given a deal probability of 16.1%.<\/b> In other words, it’s the probability of getting anywhere from 0 to 9 deals inclusive<\/i> with these parameters. Conversely, 1 − 0.0763 = 0.9237 is the probability of getting 10 or more<\/i> deals.<\/p>\n
(By the way, if you change the 4th parameter to “0,” you get the probability of getting exactly<\/i> 9 deals.)<\/p>\n
\n\"\"\n<\/div>\n
You could say that, taking the sum of all bars on the graph as 1, the sum of bars “0” through “9” equals 0.0763, or 7.63%. As you can see, it’s far more likely to land in the blue portion of the bell curve than in the red one (92.37% vs. 7.63%).<\/p>\n
Conclusion:<\/b> the probability that Drennan, while actually converting at 16.1%, would randomly (remember the possibility of a “rough patch”?) end up with no more than 9 deals out of 89 calls is 7.63%.<\/p>\n
Conversely, there’s a 92.37% probability that he would have gotten 10 or more deals. Roughly speaking, there’s a 7.63% chance he was simply unlucky, and a 92.37% chance that bad luck alone doesn’t explain it, and he is most likely converting at a rate below 16.1%.<\/p>\n
Therefore, if a 90% confidence level<\/b> is enough for the VP of Sales, then Drennan can be let go at the end of his probation — the manager is, indeed, not meeting his target. If, however, a 95% confidence level<\/b> is required, the data is not yet sufficient, and it would be advisable to observe a bit longer.<\/p>\n
So what confidence level should we choose? There is no right answer here.<\/p>\n
If we set it too low,<\/b> we risk accidentally firing good managers, but we won’t lose deals by continuing to work with bad ones.<\/p>\n
If we set it too high,<\/b> we’ll have to accumulate data for too long before making a mathematically justified decision to fire a bad manager, but the probability of accidentally firing a good one will be lower. In my opinion, a 90% level is optimal for this case. Drennan can be fired.<\/p>\n
Wait, What About Whitfield’s 19.7%?<\/h2>\n
Indeed, if there are “bad” managers for whom there’s a 92.37% probability that their conversion is below the required 16.1%, then logically, there can also be “good” ones.<\/p>\n
\n\"\"\n<\/div>\n
Dan Whitfield is the quiet opposite of Drennan. He’s been with the company for six months, never makes a fuss, never asks for a raise. He just dials, talks, and closes. Over that time he put up 56 deals on 284 calls — a 19.7% conversion rate — compared to the projected 0.161 × 284 = 46 deals. Could he have been lucky this whole time? Could it be that, while actually performing like everyone else at a 16.1% conversion rate, he randomly ended up with more deals than the VP of Sales projected?<\/p>\n
The binomial distribution function returns 0.9563 — meaning that with a 95.63% probability, working like everyone else, he would have gotten no more than 56 deals... but he didn’t get more<\/i> than 56 deals... He got exactly<\/i> 56!<\/p>\n
Let’s simply refine the function by recalculating it for 56 − 1 = 55 deals:<\/p>\n
\n\"\"\n<\/div>\n
For 55 deals, the result is 0.9402. That is, with a 94.02% probability, Whitfield (working at a 16.1% conversion rate) would have gotten no more than<\/i> 55 deals. This means the probability of getting more than<\/i> 55 deals is the remaining 5.98%! It turns out our Whitfield landed in a sliver of his own bell curve — just on the opposite end — and the probability of landing there is only about 6%.<\/p>\n
\n\"\"\n<\/div>\n
The VP of Sales has already decided that before making staffing decisions, he wants to be at least 90% confident in the results. And in Whitfield’s results, he’s 94.02% confident! That leaves only 5.98% for the possibility that Whitfield was simply lucky.<\/p>\n
So either he got lucky, even though he actually performs like everyone else (at a 16.1% conversion rate) and doesn’t deserve a higher salary, or he truly converts at a rate above 16.1% and it would be fair to reward him.<\/p>\n
6% clearly loses to 94%, so Whitfield gets the promotion.<\/p>\n",
            "summary": "Your new sales rep is converting at 10% instead of the expected 16%. Fire him? Not so fast. Using the binomial distribution function built into Excel and Google Sheets, you can calculate the exact probability that poor results are just a cold streak — and make staffing decisions you can actually defend with math.",
            "date_published": "2019-03-29T18:03:00+03:00",
            "date_modified": "2026-04-12T03:09:44+03:00",
            "tags": [
                "binomial",
                "Sales Department",
                "sales funnel"
            ],
            "image": "https:\/\/ivanbaldin.blog\/pictures\/funnel01.png",
            "_date_published_rfc2822": "Fri, 29 Mar 2019 18:03:00 +0300",
            "_rss_guid_is_permalink": "false",
            "_rss_guid": "4",
            "_e2_data": {
                "is_favourite": true,
                "links_required": [
                    "highlight\/highlight.js",
                    "highlight\/highlight.css"
                ],
                "og_images": [
                    "https:\/\/ivanbaldin.blog\/pictures\/funnel01.png",
                    "https:\/\/ivanbaldin.blog\/pictures\/funnel_9.png",
                    "https:\/\/ivanbaldin.blog\/pictures\/funnel_binom.png",
                    "https:\/\/ivanbaldin.blog\/pictures\/funnel_0763.png",
                    "https:\/\/ivanbaldin.blog\/pictures\/funnel_1-9.png",
                    "https:\/\/ivanbaldin.blog\/pictures\/funnel_binom_d3c3_whit.png",
                    "https:\/\/ivanbaldin.blog\/pictures\/funnel_binom_whit.png",
                    "https:\/\/ivanbaldin.blog\/pictures\/funnel_56-67.png"
                ]
            }
        }
    ],
    "_e2_version": 4199,
    "_e2_ua_string": "Aegea 11.5 (v4199)"
}