*As the auto industry enters version 2.0, forecasting future sales of EVs is a crucial piece of work. But most projections, especially from the oil industry, use the wrong curve, and so underestimate demand.*

**The Missing S Curve**

Here’s a funny thing.

Most analysis of technological innovation refers to a chart like this at some point.

It’s referred to often as the “S curve” effect, as the curve resembles a shallow S.

Throughout history, many critical inventions – electricity, the automobile, colour TVs, refrigerators, mobile phones – have followed this type of curve. Never exactly, but often pretty close.

This is no accident. Technically, the S curve belongs to a maths category called the logistic function, or slightly more accessibly “resource-limited exponential growth.”

Its genesis is in modeling population growth, where steady, and then rapid expansion has to ultimately give way to much slower growth, as support resources become scarcer and scarcer. Its equation (which is shown in the notes only, not here) has a limiting factor that makes growth slow as it reaches its natural saturation point or “carrying capacity”.

Intuitively, such a function makes sense when modelling or forecasting rapid technological growth: at some point, when the technology manages to reach a critical mass, it starts to show rapid, explosive (exponential) growth. But, as limits such as market share or manufacturing capacity then slow development, the innovations revert to the S curve, with the growth phase petering out to a plateau, or decline if replaced by a future innovation.

The S curve thus provides mathematical compactness to the well-known Roger’s curve of innovation diffusion – with Early Adopters and Early Majorities and so on – defining probabilistic accumulation with a peak value.

So how do most analysts model the future of new innovations? Do they use the maths of an S curve?

No, the funny thing is, they almost always use a J curve, based on simple exponential growth’s J-like appearance, also known as compound annual growth rates (CAGR). See here from BNEF

The compound growth curve is a simple, one-dimensional cousin of the S curve, showing unrestrained exponential growth, but with no in-built limits on how far the curve may rise, or with any of the S curve continuous change structure.

**Underestimating Demand**

A comparison of S curve and J curve is shown below, based on 1-10 units of time (weeks, quarters, years etc), with an arbitrary limiting value of 100.

There are similarities of course, but its clear that beyond a narrow timeframe, the J curve will abandon control and increase without limit.

So note the following key principle from the very humble charts above:

- The aggregate sum under the S curve is 550 units – e.g. of demand
- The aggregate sum under the J curve is 275 units, or 50% less
- At the midpoint, 5, demand is 50 units for the S curve but only 10 for the J curve

They arrive at the same destination, buts it’s a very different journey, especially if you are depending on the total demand numbers. J curves will almost always underestimate the early stage demand, and often the total demand too for these reasons.

This is more than semantics and mathematical esoterica.

By their nature, exponential curves tend to focus on back-end loaded growth (slow to start and then very rapid).

Not only does this not mimic empirical reality – it almost always underestimates early and total demand. The real-life S curve tends to show steady then rapid growth quite early on in its development. So the amount of demand is greater (the area under the curve in mathematical jargon).

This means that the volatile nature of the J curve can tend to miss actual demand by some distance.

So – why by-pass the known outcome of the S curve, and opt for simple exponential growth charts?

**More accessible – but synthetic**

It can be argued that over limited timeframes (eg 3-5 years) a simple exponential curve functions just as well as the S curve, or that multiple-rate exponential curves can be used to mimic the S curve pattern.

Also, the simple exponential curve is simpler to explain, and people encounter it every day eg compound interest rates. Plus when growth is low, gradual percentage changes make sense, and simple growth curves are used all the time for e.g. business indices or government projections.

Perhaps. But we are in the world of looking for transformational growth here. And even in low-growth situations choosing the wrong annual growth number, unchecked, leads to very large errors over time.

In the domain of rapid change forecasting, exponential growth is an extreme modeling device – and little in nature or business grows unrestrained long-term; (exponential decay is another matter, but that is because it does have a limit, zero).

Even compound interest, which is ultimately unrestrained, has an indirect limit of human life-span (although, efficient inherited wealth tests this limit via generations, and it’s likely why a greater and greater proportion of global wealth is concentrated in fewer hands).

**The S curve**

A key point to note straight way- the S curve is not a wonder-panacea to these J curve limitations.

Whilst the S curve is more flexible and intuitive to use for forecasting, it still relies on key assumptions and estimates such as final market share which could be very inaccurate.

But for the practicalities of simulating real-life technology diffusion, the slightly more complicated resource-limited growth equation offers a decent payback: it is more adaptable, more intuitive and, crucially, provides the known-shape of actual technology development histories.

**Application to Electric Vehicle Demand**

In the context of energy transformation, we can apply the S curve and J curve models to EV demand to see what each offers.

EVs are generally accepted to be at the tipping point between low initial growth and widespread adoption.

**Beyond a Tipping Point**: An empirical rule-of-thumb, but linked to the maths we’ve discussed, is that the technology in question needs to at least breach 1% market share before it becomes viable for powerful growth and uptake.

That may not sound like much, but to get to 1% of a national or international market (relatively quickly) the technology under review has likely gone well beyond prototype, has achieved a baseline adoption, and is starting to acquire economies of scale that can propel the next stage of growth.

Thus, the global light vehicle market today is about 900 million, and annual new sales are around 80million units. The global fleet of EVs is currently 2.1million, and annual sales around 800k pa.

On an annual sales basis EVs have therefore reached the 1% mark. At current growth rates, they will reach 1% of the total cumulative global fleet by 2019.

This means the likelihood of EVs growing rapidly as a technology innovation are high, and applying high-growth forecasts are valid.

**Global EV Demand Forecasts compared with Actuals (2010-2016)**

Although we can trace EVs back to the 1890s, and “revivals” ever since, the latest EV development can be dated more or less to 2010 when mainstream automotive companies, possibly catalyzed by Tesla, started to offer plug-in options under their own badge.

Note the importance of this development. When the mainstream automotive companies, who control global production, decide to offer EVs as alternatives to conventional thermal fuel engines, you do not have the traditional model of plucky new entrant fighting the establishment.

You have the establishment converting en masse to a new technology to preserve dominance.

This may change the shape of the traditional S curve.

So below we look at three scenarios.

Conventional S curve versus J curve based on latest assessments of EV demand and actual global sales, 2010-16.

And two further outlier scenarios – EV demand suffers a great reversal, or EV demand accelerates far faster than we imagined.

J curves can only model these in one dimension (annual growth rates), but the S curve can use a couple of other tools such as final market share and smoothness of growth.

**Forecasting Conventional EV Demand**

Between 2010 and 2016 we have actual data on global EV (Plug-in EV and Plug-In Hybrid) sales.

In addition, for a central scenario we can call on a host of forecasts for estimated future demand.

Here we will assume 35 million EV sales pa by 2035, or about 30% of total sales estimated in that year. It is more or less in line with the BNEF forecast (but we’ll get there via an S curve).

The three charts below show three curves over the period 2010-2016; 2010-25 and 2010-35.

This is to highlight the changes in the forecast models in hindsight, over a short-term forecast period and a longer-term projection.

The three curves used are:

– actual EV sales plus actual sales extended using simple composite exponential growth at 50% pa until 2022, then 15% until 2030, and 5% thereafter (a typical model)

– an S curve assuming a saturation point of 35 million sales by 2035 and relatively shallow S as substitution of conventional cars may not happen quickly due to reasons discussed below

– A single exponential curve of exceptional 90% annual growth starting with actual sales in 2010

**EV Demand – Central Scenario – 35m pa sales by 2035**

The first chart, 2010-2016, with actual sales data, shows how at the early stages of expansion, even a high-growth exponential curve does not mimic the actual sales well. However, the S curve at least keeps pace with the initial progress.

Out to 2025, the limitation of a simple exponential are obvious and typically analysts have to crow-bar actual data with composite CAGRs as shown here. The S curve maintains a middle way, but clearly shows far higher growth than predicted by simple exponentials.

In the long-term analysis, the S curve shows that by 2035 most growth is complete and 35million EVs is a steady state sales rate. The exponential curve continues to grow – but any final saturation point is unclear. (NB – the 90% exponential curve is not shown as it is completely off-scale, a reminder of its limitations).

Whatever the accuracy of each forecast, a couple of key points should be considered comparing the two types of curve.

**First, demand speed:** as noted simple J curves underestimate early demand.

Here, in 2010-2016 even relying on 90% growth from 2010’s actual data underestimates sales in this short period by a cumulative 50% or 500,000 units.

We know much of this was in China, but for any global manufacturer the trend in under-estimation ought to be a red flag for future analysis, and current readiness for expansion planning.

**Second, total weight of demand**: relying on adjusted exponential curves predicts aggregate sales to 2035 of about 300m vehicles: using the S curves, the comparative figure is over 420m, with much of the difference in the earlier years of growth.

**Alternative Scenario 1: BP / XOM – Demand is DOA**

The likelihood of far lower EV demand (eg predicted by oil companies Exxon and BP , here) can also be quickly tested by the S curve model using current sales data.

BP’s central projection assumes aggregate 100m EV demand by 2035-40, which given such low growth we can assume is a saturation point. This equates to about 8m EV sales per annum at that point.

The chart of this low-level growth with current actual data is shown below, up to 2016 and out to 2035.

**BP’s DOA Scenario – 8mpa sales by 2035**

Although its early in the technology life-cycle, the BP-implied S curve looks way below actual demand. It also suggests that EVs will only occupy a niche role within the whole automotive industry. This is discussed below, but it is an unstable scenario, without much precedent.

**Alternative Scenario 2 – Demand Takes Off**

This is shown below, again using 2016 actual and the charts out to 2035.

**EV High Sales Scenario – 50m pa sales by 2035**

It assumes a saturation point of 50m EVs at 2035, which would be around 45-50% of total estimated market. For a long-cycle product such as automobiles this is still a major achievement in market capture within 20 years, and would require aggregate demand of over 700m vehicles.

In fact the early stage chart is a relatively good fit with actual data, but clearly sales diverge significantly by 2021 or so from the composite CAGR curve.

This could be reasonable if 2021 marked the entry of a wide range of new, competitive lower-cost EV models, with a denser structure of electrical infrastructure to support it, especially in urban areas, and near arterial roads.

Thus in the 50 million S-curve model, the implied annual growth rate in the 2020-2030 period is 25%, not irrational if this era marked the surge in EV growth as the early and late majority adopted the technology.

**Implications for the Real World**

**Planning & Forecasting: S plus J is greater than J**

It’s easy to get carried away with maths and neat models, but they are important guides. My colleague Kingsmill Bond refers to the S curve as a little bit like a black box, and so using its comes with a health warning.

Annual growth curves ought to have one too.

One key implication is that analysts should at least use S curve models in conjunction with standard compound growth models to wider insights, and checks on core assumptions.

**Predicting EV Demand**

Using S curves provides these predictions:

**– Current EV sales are in line with S curve longer-term projections of 30-50m EV sales pa by 2035**. However, note the S curve assumes market saturation at this point (ie very low growth) – exponential curves will see continued expansion.

**– The S-curves are not consistent with the lower ranges of EV demand proposed, mostly by oil companies**. These are increasingly low probability. In turn this means aggregate EV demand to 2035 is likely to be closer to the 400-500 range than 100-150m.

– The S curve used here has quite a shallow neck to fit actual data implying that the **very high growth rates are likeliest around from 2020 until 2030.**

**Do ****these make real-world sense? **

We have to be careful.

The maths of S curves and J curves are both volatile – small changes in annual percentages or assumed capacity levels can make the charts produce outrageous results.

That is why outlier testing of scenarios is useful.

On balance, the analysis suggests that the stronger evidence is weighted to a high-level of growth for EVs.

The alternative would be that EVs remain forever niche, and run in parallel with ICE vehicles for many decades to come.

The history of technology does not provide much support for this type of phenomenon.

However, there are three other issues regarding the growth of EVs that ought to be considered, each one reflected in the maths of the S curve:

**Why the Low Percentage Saturation Level of 30-50% ?**

It’s possible that the long life-cycle of automobiles and their relatively high cost might prohibit major market gains globally: some countries could choose to avoid the necessary investment for decades. However, in other countries such as China the saturation level may be much higher and much quicker.

A market share value of over 80%, especially with a later increase in high-growth demand is still feasible with the current actual sales data.

This analysis may have potentially erred on the conservative so far.

**Why a Shallow Neck ?**

The rise of EV demand represents a major change in global technology, aiming to displace a robust and effective incumbent. As replacement life-cycles of cars can be a decade or longer, and many policy and cultural elements may inhibit the transformation, a shallow S curve has been used in this analysis, to account for slower adoption than recent information-based technologies.

However, there is an alternative. The “tsunami” scenario is one in which with cost, efficiency and convenience cracked by the auto-manufacturers, consumers adopt EVs en masse, via a steep S curve, not least to avoid plummeting re-sale values of gasoline vehicles.

**Does Capability Match Growth? (yes)**

None of the maths of the S curve analysis breaches practical manufacturing issues such as car production capacity, although moving from 1 million EVs pa to 10 million pa in 4-5 years may prove a stretch – but crucially not to an industry grouping that is used to mass production and sales.

As noted, this is not just gutsy Tesla against the world – this is the whole auto industry upgrading simultaneously to version 2.0.

**Oil Demand Impact**

Does S curve vs J curve growth impact overall oil demand impact?

Front-end loaded EV sales of 50m by 2035 would pull down oil demand slightly quicker than exponential curves would suggest. Perhaps by a further 1-2m b/d by 2025, and bring peak gasoline forward by a year to 2019.

The bigger impact, however, will be the presence of EVs as a normal feature of road use, forcing down the fuel consumption of ICE cars more rapidly than anticipated (a clear sailing ship effect).

This can only reduce oil demand more rapidly than currently predicted.

**Finally, will it really happen? (Most likely, yes).**

Mathematically, and historically, we have the 1% market share level breached, plus plausible demand projections based on actual sales figures.

But will the century-old dominance of thermal combustion engines really be removed by their electric doppelgangers?

Technology and economics are closing in on parity of choice.

And the historical mathematical charts suggest this now heads in the direction of more rapid adoption.

The probabilities are increasingly weighted toward mainstream EV adoption.

We’ll follow the S curve as it develops.

———— ————-

**Notes – the maths**

*The standard form of the simple exponential curve used is:*

*f(x) = (1+r) ^{x}*

*where r is the interest rate. I used 90% for the simple curve, so 1.9 to the power x, where x is the time in years. In the composite growth curve I used 1.5. 1.15 and 1.05 as noted.*

*Now the S curve logistic equation. You can see why folk are put off, but it repays a little effort. A straightforward version is shown below.*

*f(x) = N / 1 + e ^{–kx}*

*So, in fact the curve relies on just two simple values: N – the limiting value, and k the slope of the curve. See here.*

*In the central case I used here, N is the limiting capacity e.g. 35 million (35), and I simplified the equation slightly by assuming the mid point of the S curve was half-way between the start values and the limiting value.*

*x ranges over 25 years (2010-35), so the shape of the curve is generated from x values of -12 to 12. Finally, I set k at 0.5 for the reasons noted – a slower growth than standard due to headwinds of life-cycle and so on. So my equation placed into excel was:*

*f(x) = 35 / 1 + e ^{–0.5x}*

*That’s it.*