It was my former colleague Raj Chande who first asked me the question “What does the graph at the end of the project look like?”. Raj is an economist by training. I am a literature graduate. The question was not remotely intuitive to me. But it’s something I come back to again and again: when all the work is done, what’s the story I will be able to tell in a single chart? And will I know what to make of that story if the chart doesn’t turn out as I expect?

I’ve recently been thinking about this question in relation to doing mission-driven work where the goal is fixed but the means of achieving it changes as we learn more. When we set up a mission, our imagined version of the graph-at-the-end should be able to tell us about the magnitude of change it achieved and the trajectory that got us there. Referring back to this graph throughout the work forces us to subordinate our attachment to any given project, method or team to the larger goal. It also forces us to think through how those projects add up to a plausible pathway to create impact at scale.

Across our three missions at Nesta, we are aiming to improve millions of lives and we have specific targets to help us. In our fairer start mission we aim to close the school readiness gap between disadvantaged children and their more affluent peers; in a healthy life, halving obesity to improve our health means reducing daily calorie intake by around 8.5% on average across the population; and in our sustainable future mission we need to reliably reduce household emissions by around 19 million tonnes a year by 2030.

In practice, this means that we know the x axis (between now and 2030), the y axes (the size of the school readiness gap, calorie intake or tonnes of carbon) and the target for our endline measure for all three missions. Our theories of change for each mission also allow us to make a best guess at what we think the trajectory of change would look like. In our healthy life mission, for example, our working hypothesis is that the graph-at-the-end looks something like the below.

I say “working hypothesis” because, of course, this graph is wrong. After all, we can’t know the exact projects we will run over the years or how they will ultimately ladder up to hit our three mission goals. But having stylised versions of the end result helps to push us in the right direction. To paraphrase the poker player and researcher Annie Duke: waiting for perfect information is like not shooting the arrow for fear you won’t hit the bullseye. What we’re doing by pre-specifying what we need to happen is giving ourselves a continual reference point to come back to, making sure we at least “get on the target”, even if it’s not a bullseye.

“How big a change could this piece of work make?” is probably the most important question at the outset of a project. This is because all the choices we make – what part of the problem to tackle, what types of solution to explore, what the delivery mechanism looks like, what our gateways are for advancing the project – flow from this.

Put differently, right at the start of a project we need a hypothesis about how the work is going to contribute to the mission’s graph-at-the-end. If we don’t think it will then we should bank the lessons learned and put the remaining resources somewhere else.

This doesn’t mean a project can’t be green-lit if it won’t drive large scale impact all by itself. In fact, most projects won’t generate enough impact in their initial phases and we should be sceptical of any project that claims otherwise.

Often we are doing indirect exploratory work that may throw up an insight we can use to directly transform outcomes. Sometimes the work does have a direct impact but the outcome we can observe isn’t measured in the same way as the overall mission goal. And even where a project is scoped to make a direct impact we are usually not in control of the levers that need to be pulled to scale it. Despite all this, thinking about how each project contributes to the graph-at-the-end forces us to think all the way through the theory of change to see whether we have a plausible account of how it could lead to impactful work at scale.

To give an example, we’re currently working with large food and beverage retailers to test how changes in their online and physical stores alter customer purchases. We are specifically interested in two outcomes from this work: the healthiness of the food purchased and the effect on the retailers’ bottom line. Each individual project we do will measure the effect of one or more interventions on these outcomes.

It’s easy to think of the results of these trials as an endpoint. But that’s the start, not the end. The chart below shows what would need to happen after to make a significant dent in the mission goal.

We often tend to think of change as linear. In linear relationships the rate of change is stable across time - you get the same amount of output for a fixed amount of input from start to end. Graphed, a linear relationship produces a neat diagonal line; the steeper the line, the faster the rate of change. As the charts above show, this is not what we expect to happen when we think about how our work might scale over time. It is, however, the way in which we think the continued trend of increases in calories sold will look in the absence of intervention.

The journey to impact for each mission and project is more likely to follow a version of the classic S-curve. Since we are seeking reductions in all three missions (emissions, obesity, the size of the school readiness gap) the S is in mirror image like the blue line in the example above.

The S-curve is the most familiar type of change curve. As you can see from the examples above, it is made of three parts, each of which can occur with or without the others:

1. the slow start
2. the steep slope
3. diminishing returns

The second part of the S-curve – the steep slope – is the bit that gets you to scale. But it takes a trigger to transition into it and out of the slow start. In the example above, legislation triggers mass adoption of calorie-reducing in-store policies. But technological advances in medication and food production, shifts in consumer demand and new dietary trends (see, for example, the rising interest in oat milk) could also prompt such inflections. There are many routes to scale (more on that in this excellent report from my colleague Madeleine Gabriel) but if you don’t have a credible plan for following one of them it’s unlikely you will make any difference to your graph-at-the-end.

When it comes to social innovation, we also need to look at our change curve through the lens of who is affected when. If you're a business this really doesn’t matter: a sale is a sale and anyone willing to pay the price is a welcome customer.

It’s often people who are already disadvantaged in some way who are hit hardest by change. At the front end, the burden of advocacy can fall on those for whom things are so bad that sticking their neck feels like the most appealing option. Civil rights movements, for example, are often started by activists who are directly affected by societal prejudice.

At the tail end of change, those who have the least resources often get left behind while those who had the means to adopt early enjoy new and sometimes compounding benefits.

When it comes to legislating to make supermarket shelves healthier, for example, we should design out potentially damaging effects of increased food prices resulting from intervention. Increased prices are not bad in themselves. They can be a helpful way to sway consumer choice where the price of healthy alternatives decreases in parallel. But where no cheaper substitute is available, the poorest consumers will be hit relatively harder by price increases.

By thinking about who is likely to be left behind without intervention we can:

• devise mitigation strategies, for example, identifying and overcoming barriers to take up for those at highest risk of being left behind
• deliberately phase rollout to target those who would benefit most, sooner. The Covid-19 vaccine rollout is a good example of this in action: those who would benefit most from increased immunity were moved to the front of the queue
• be explicit about who will be excluded. We won’t always be able to help everyone and so we should be clear who is likely to be left behind and how we think they could be supported.

So, in summary, thinking about the graph-at-the-end can help us choose projects today that are more likely to give us the kind of pay-off we need to see to meet our goals. This means thinking about how we get the scale of impact we are targeting, what the journey to impact at scale is likely to look and feel like, and how those affected experience that change curve.

To conclude, the graph-at-the-end is pointless if you only make it at the end. We should be planning and monitoring projects based on how they are going to help us draw the line we need to see. This is tricky because the end of the project is often nowhere close to the end of the impact trajectory. By continuing to track progress after projects close we can figure out when to deploy additional resources to push adoption and when to stop.

Our Money Saving Boiler Challenge – a campaign that aimed to get people to turn down their boiler flow temperature – followed a somewhat wonky looking S-curve (note – to create this graph I’ve taken the specific data on when people registered turning down their boiler on the campaign website and used it to create the trajectory for all boiler turn downs we attributed to the campaign, most of which are not logged on the website).

The trigger event into steep growth was the launch of the final campaign site. Sign-ups blew up in the first weeks before diminishing. As growth slowed, though, there were miniature S-curves. These describe a "Martin Lewis effect". When Martin Lewis referenced the campaign we saw large surges in users logging that they had taken action on our site.

The Money Saving Boiler Challenge had a return of around 33:1, generating millions of pounds in savings to consumers and government and saving half a million tonnes of carbon dioxide annually.

This is clearly meaningful and worthwhile but when we overlay this onto the mission graph-at-the-end, we can see that it only accounts for around 2% of the mission goal.

Indeed, if all ten million combi-boiler owners in the UK turned down their flow temperature we would achieve a little less than 10% of the goal. This is a helpful reminder that even the big cut-through moments won’t be enough on their own: we need to keep pushing a number of different approaches to hit the target.