The funnel bench

Cost per lead turns money into leads. It is never flat: the first leads from a channel come from the people most ready to respond, and each extra dollar reaches people slightly less ready. The bench models that with a curve that starts at the stated cost per lead and flattens toward a cap, set by default at twice the channel's real monthly lead volume. That curve is constructed and labelled; the shape is the standard one, the numbers are not anybody's measurements.

Close rate turns leads into customers. It is measured, per channel, from which of the 5,998 leads in the 2018 cohort became sellers. It varies by more than three to one across the channels: paid search 14.8 percent, social 6.3 percent, email 4.0 percent.

CAC is the budget divided by the deals. A channel with cheap leads and a poor close rate can have a worse CAC than one with expensive leads that close. Social's assumed cost per lead is $25 against paid search's $60; at the first dollar, social's CAC is about $25 / 0.063, roughly $400, and paid search's is about $60 / 0.148, roughly $405. Nearly a tie, from very different routes.

The closed-deal records begin on 5 December 2017. Leads that arrived in 2017 had their deals logged, if at all, only from that date on, so the 2,002 leads from 2017 show just 61 closes, 3.0 percent, against 13.0 percent for the 5,998 leads from January to May 2018. The 2017 leads did not get worse. The deal log started late.

The bench defaults to the 2018 cohort for that reason, and gives you a checkbox to include 2017 anyway. Tick it and every CAC on the ladder rises, the even split from $524 to $742, because a third of the leads now look as if they never close. The ordering of the presets survives. The dollar figures do not, which is the general rule for any funnel number taken from a log whose start date you have not checked.

Weighting by leads and weighting by deals give the same answer wherever a channel's share of leads equals its share of deals. Organic search is 28.9 percent of the 2018 leads and 32.7 percent of the deals; paid search 19.7 and 22.4. Close. Social is 17.5 and 8.5. Not close. The lead-weighted split sends social roughly twice the money its deals justify, and that is the whole $16.

So the honest lesson is not "volume is always a trap". It is that volume is the right signal only to the extent that conversion is uniform, and you cannot know whether it is uniform without looking. On a funnel where the biggest lead source is also the worst closer, the same sentence would cost far more than 4.3 percent. Check the second column before the first one wins the meeting.

Cost per lead is the metric ad platforms report first, and the cheapest-leads preset follows it: email at an assumed $15 and social at $25 get the most money. They are the two worst closers in the table, so the split buys 412.1 leads and only 31.9 customers, CAC $627, 70.4 percent above the best split. A lower cost per lead bought a higher cost per customer.

The fix is the same in both traps: rank channels by what a customer costs, never by what a lead costs, and treat cost per lead as an input to CAC rather than a result.

The dataset has a field called declared monthly revenue on each closed deal. It would be the obvious source for payback. It cannot be used: 797 of the 842 closed deals declare 0, and the 45 that declare something range from 6 to 50,000,000 reais. The median of all closed deals is zero. The table on the bench shows the counts per channel, "12 of 255 declared" for organic, so you can see why.

So payback uses one stated assumption for every channel: $80 a month of revenue per new seller at a 65 percent gross margin, $52 a month of gross profit, and payback is CAC divided by 52. Because the assumption is the same everywhere, payback ranks the presets exactly as CAC does. Session 5 is where revenue per customer becomes the subject rather than a constant.

A bench that can only ever report the answer you hoped for measures nothing. The break button takes the 781 closed flags and deals them back out across the 5,998 leads with a fixed random seed, so the number of deals stays 781 but which channel they land in is now arbitrary. If the bench's ranking came from the channels, the ranking should collapse. It does: lead-weighted and deal-weighted tie at $316, because with conversion uniform, volume is the right signal after all.

It also moves the "best split" toward the cheap-lead channels, social and email, which is what you would expect once every channel converts alike: then cost per lead is the only difference left. That is the mirror image of step 6, and the reason step 6 loses on the real data.