Matching Speed vs. Matching Position: Visualising the Triple Lock's Mathematical Flaw

Imagine that you've been tasked with instructing a camera drone to follow the leader in a race.

Without thinking too much, you write down the instructions:

At any moment, match the speed of whichever racer is currently going fastest.

Before too long, the drone is flying around more than a full lap ahead of every racer.

What went wrong? The drone continuously matched whichever racer was going fastest at that moment. Whenever a racer sped up and pulled away, the drone gained ground over the pack. When the front-runner slowed for corners, the drone matched a car still on the straight.

Any distance gained on the leader was baked in permanently. It kept every advantage, never giving any back, because the front-runner could never go faster than the drone and therefore could never make up lost ground.

The mistake made is confusing matching speed with matching position. The drone was mathematically guaranteed to fly ahead by cherry-picking the best speed.

The UK Treasury made this same mistake, and it has been costing the UK billions. Watch the pension (in red) run the race below. It only ever copies the speed of one of the three racers it is "locked" to — and ends up ahead of all of them:

2011 — baseline
Everyone starts level at 100. Press Start, or drag the slider.
Track uses a logarithmic scale, so constant percentage growth appears as constant speed. The shaded red band is the pension's lead over the front-runner — the overshoot a true lock would not have.
2011 2026
Pension index
100.0
as implemented
True‑lock index
100.0
highest of the three measures
Gap
0.0
index points of overshoot
Cumulative overspend
£0bn
our estimate, since 2012
The pension ends the race ahead of all three measures it is supposedly "locked" to. The UK government made exactly this mistake, and it has cost taxpayers an estimated £85 billion so far.

The same race as a chart

Every index starts at 100 in 2011. The red pension line borrows the best growth rate every year and never gives it back, so it climbs above the envelope of all three measures. The shaded band is the overshoot — growth beyond even the best-performing measure.

What went wrong, precisely

A multi-billion pound mistake: The UK state pension "triple lock" contains a mathematical design mistake that has cost taxpayers tens of billions since 2012. The policy sounds simple: increase pensions each year by whichever is highest — CPI inflation, average earnings growth, or 2.5%. But there's a critical flaw in the mathematical formulation.

What "triple lock" should mean: If pensions are "locked" to three measures, you'd expect: Pension = MAX(CPI index, Earnings index, 2.5% index). This would ensure pensions genuinely track the highest measure.

What it actually does: Instead, it takes the rate (delta) from whichever is highest each year: Pensiont = Pensiont-1 × (1 + MAX(CPI rate, Earnings rate, 2.5%)). This creates a ratchet effect where pensions borrow growth from whichever grows fastest, but never gives it back, compounding ahead of all three measures.

The mathematical mistake: By locking to rates instead of indexes, the policy cherry-picks the best performance from each measure annually. A true "lock" would mean matching the position of the leader. Instead, pensions exceed all three measures they're supposedly locked to. The Resolution Foundation describes the same structural effect in "What a ratchet!", and the OBR estimates triple-lock uprating will cost roughly £12.6bn per year more than earnings-linking by 2029–30 — the same order of magnitude as our per-year estimate below.

Estimated cumulative overspend (2012–2026):
Our estimate: each year's overspend = pension spend × (1 − true‑lock index ÷ pension index). Figures are current as of the April 2026 uprating (4.8%, earnings), confirmed in November 2025.

Historical UK triple lock data (2012–2026)

CPI data: ONS Consumer Price Inflation · Analysis: IFS — Effects of the Triple Lock · Spending figures: DWP Benefit Expenditure and Caseload Tables (outturn 2012/13–2023/24, forecast thereafter)

Year CPI (%) Earnings (%) Floor Applied (%) CPI index Earnings index 2.5% index Pension index
(as implemented)
True‑lock index
(what it should be)
Gap
(points)
Spend
(£bn)
Overspend
(£bn)

*In 2022, the triple lock was temporarily suspended and the earnings element was excluded. Pensions increased by 3.1% (CPI) instead of 8.3% (earnings growth), which was unusually high due to pandemic-related statistical distortions. Struck-through figures were not applied.