Stage 07 · Measurement: Last-Click Is a Story You Tell Yourself

Ariadne's seventh stage promises attribution from source to closed customer, and "qualified conversations not vanity clicks." This post is why that phrasing is worth the extra words.

Why last-click survives

It survives because it is cheap, unambiguous, and produces a number nobody argues with. It also assigns 100% of credit to a single event in a sequence, which is defensible only if the earlier events did nothing — a claim nobody would defend out loud.

Shao and Li opened the data-driven attribution literature at KDD 2011 with a framing that still holds: rather than giving all credit to the last ad, allocate credit across channels by estimated contribution Shao & Li 2011. Their more subtle contribution was methodological. They proposed a bivariate metric scoring a model on both classification accuracy and the stability of its estimated channel weights, because channels are severely multicollinear — a model can classify conversions well while its per-channel coefficients swing wildly between refits. Their bagged logistic regression achieved comparable accuracy to ordinary logistic regression with far more stable channel contributions.

If your attribution report changes materially every time it is recomputed, that is not new information. That is variance, and Shao and Li built a metric specifically to detect it.

Removal effect: the Markov approach

The peer-reviewed anchor for graph-based attribution is Anderl and colleagues in the International Journal of Research in Marketing Anderl et al. 2016. Model each customer journey as a path through a Markov graph whose states are channels, plus a start state and two absorbing states — conversion and null.

Credit for a channel is its removal effect: delete that channel's state from the graph, recompute the probability of reaching conversion from the start, and measure the drop.

Attributed conversions follow by normalising removal effects across channels and multiplying by total conversions.

Shapley: the axiomatic alternative

The other principled approach comes from cooperative game theory. Shapley derived a unique allocation of a coalition's value from three axioms — efficiency (allocations sum to the total), symmetry (identical marginal contributions receive identical value), and the null-player axiom (a player contributing nothing receives nothing) Shapley 1953. Treating channels as players and conversions as the coalition's value:

The obvious objection is combinatorial: this sums over subsets, which is intractable for many channels. Zhao, Mahboobi and Bagheri give a reformulation that collapses the naive enumeration into a far cheaper computation, which is what makes Shapley attribution usable at realistic channel counts Zhao et al. 2018.

Dalessandro and colleagues connect both approaches to what we actually want, arguing attribution should be posed as causal estimation — the credit due a touchpoint is the causal lift it produced — and offering cooperative-game approximations because randomised per-channel holdouts are usually infeasible Dalessandro et al. 2012.

The part that is about incentives, not statistics

Here is the finding that changed how I think about this. Ron Berman modelled multiple publishers delivering ads to a consumer, where each exposure creates an externality on the others, and showed that last-touch attribution over-incentivises ad exposures — publishers rationally over-serve impressions to win the last touch — "often resulting in lower advertiser profits" Berman 2018.

What I would actually build for a service business

Multi-touch attribution at 40 inquiries a month is statistically hopeless, and I will not pretend otherwise. The models above need path volume that owner-led firms do not have.

What is achievable, and what I build:

One identity, end to end. A single record from first touch to closed deal. Without this nothing else is possible, and with it even simple analysis becomes useful.

Store the full path, not the last touch. Even if you cannot model it today, you cannot recover what you never recorded. This is the cheapest irreversible decision on the list.

Report first-touch and last-touch side by side. Not because either is right, but because the gap between them is informative: channels that look strong on first and weak on last are your discovery channels, and last-click will starve them.

Use holdouts where you can. Turning a channel off for a defined period is a genuine experiment, and it is available even at low volume. Blake and colleagues did precisely this at eBay and found the experimental return on paid search was −63% where ordinary regression had estimated over 4000% Blake et al. 2015.

That last number is the honest summary of this whole stage. The gap between what your dashboard says and what an experiment says is not small, and it does not favour the dashboard.

References

1. Shao, X., & Li, L. (2011). Data-driven multi-touch attribution models. Proceedings of KDD 2011, 258–264. https://doi.org/10.1145/2020408.2020453
2. Anderl, E., Becker, I., von Wangenheim, F., & Schumann, J. H. (2016). Mapping the customer journey: Lessons learned from graph-based online attribution modeling. International Journal of Research in Marketing, 33(3), 457–474. https://doi.org/10.1016/j.ijresmar.2016.03.001
3. Shapley, L. S. (1953). A value for n-person games. In H. W. Kuhn & A. W. Tucker (eds.), Contributions to the Theory of Games II, Annals of Mathematics Studies 28, Princeton University Press, 307–318. https://doi.org/10.1515/9781400881970-018
4. Zhao, K., Mahboobi, S. H., & Bagheri, S. R. (2018). Shapley value methods for attribution modeling in online advertising. arXiv preprint arXiv:1804.05327. https://arxiv.org/abs/1804.05327Working paper; not peer-reviewed.
5. Dalessandro, B., Perlich, C., Stitelman, O., & Provost, F. (2012). Causally motivated attribution for online advertising. Proceedings of ADKDD '12, Article 7, 1–9. https://doi.org/10.1145/2351356.2351363
6. Berman, R. (2018). Beyond the last touch: Attribution in online advertising. Marketing Science, 37(5), 771–792. https://doi.org/10.1287/mksc.2018.1104
7. Blake, T., Nosko, C., & Tadelis, S. (2015). Consumer heterogeneity and paid search effectiveness: A large-scale field experiment. Econometrica, 83(1), 155–174. https://doi.org/10.3982/ECTA12423
8. Altomare, D., & Loris, D. (2026). ChannelAttribution: Markov model for online multi-channel attribution (R package v2.2.5). CRAN. https://cran.r-project.org/package=ChannelAttributionSoftware and accompanying white paper; not peer-reviewed.