When does the tortoise beat the hare?

More shipping is useful when you can check the result

A small release gives you another chance to move activation, conversion, or retention. If the result tells you what to try next, a rough first attempt can be better than waiting for a polished one. In this model, every new step gets a fresh bearing toward the same goal.

Activity alone is not progress. At 110° aiming error, the fast hare won only 0.1%. It was busy, but most of that movement did not help. In business, counting releases can hide the same problem: you still need to check whether customers are doing the thing you wanted.

Metrics and taste solve different problems

A metric tells you whether something changed. Taste helps you decide what to try and what is worth making. A metric can reward the wrong behavior; a good-looking product can fail to retain anyone. Use judgment to pick a change, then look for evidence that it helped.

The simulation represents better judgment as lower aiming error and repeated misjudgment as a fixed offset. It does not decide whether metrics or taste produce better judgment. In the equal-accuracy scenario, the hare won all 2,000 races and traveled almost the same median distance as the tortoise. Better aim and more attempts can go together.

When the tortoise makes sense

1. The next move is expensive to undo. A production rollout or pricing change can affect more customers before you see the result. The equal-speed race shows why smaller commitments let you correct sooner.
2. Your feedback is unreliable. If the retention data is too noisy to choose the next move, adding more releases may just add more guesses. Check the signal before speeding up.
3. You are close to a precise target. A large adjustment can overshoot. Smaller final moves can reduce detours, although they may also take longer.
4. Wasted work matters more than the deadline. The tortoise’s shorter route is an advantage if extra attempts are costly. This model counts distance, not dollars or engineering hours.

The choice depends on the decision. Prototype quickly when another test is cheap. Check carefully before a mistake reaches every customer. The race does not establish which company style is best, and it does not model learning, harm, or the cost of an experiment.

Smaller near the goal is not automatically better

I added two controls for each racer: Near-goal step size and Start adapting within. A 0.25× setting gradually shrinks the step toward one quarter of its usual size. A 3× setting gradually grows it. A 1× setting keeps it fixed. The step interval stays the same, so changing length also changes travel speed.

In the staged-rollout setup, shrinking the hare’s steps near the goal reduced its median route from 415.9 to 362.2 units, but increased its median time from 17.33 to 18.15 seconds. In a separate equal-speed setup, growing the hare’s steps near the goal won 99.2% of trials. The two examples use different starting settings; they are not a direct smaller-versus-larger comparison.

What “repeated aim offset” means

It is an angle, not a belief. A racer first points at the actual goal, then adds this same error every time. At 90°, every intended move gets a quarter-turn off course. Random aiming error varies from step to step; the repeated offset does not. Set it to 0° to remove it.

A business analogy is consistently treating clicks as proof of retention. The model does not contain a second metric or a hidden goal. The offset simply shows why a persistent wrong assumption can survive lots of activity.

1. Worse aim can still win

Start with the same 6-unit step size. The tortoise steps 4 times per second with 10° aiming error. The hare steps 12 times per second, but its aim is much noisier.

At 60° error, the hare won all 2,000 trials. Its median finishing time was 7.34 seconds, compared with 12.50 for the tortoise.

Then I kept increasing only the hare’s aiming error:

The winner changed around 83–84° of hare error. These percentages are estimates from 2,000 trials per setting. At 83°, the 95% interval was 49.5–53.9%; at 84°, it was 43.7–48.0%.

2. Enough error erases the speed advantage

At 110° error, the hare won only 0.1% of trials. Too much of its travel went sideways or backward.

At 85° error, increasing the hare’s frequency from 12 to 16 steps per second raised its win rate from 39.2% to 93.9%. Its aim did not improve. It moved faster and aimed again more often.

3. Shorter steps help at the same travel speed

A longer step increases travel speed but also takes you farther in a mistaken direction. To separate those effects, I gave both racers the same speed: 24 units per second, with 30° aiming error.

The tortoise took 6-unit steps 4 times per second. The hare took 48-unit steps once every 2 seconds. The tortoise won 87.3% of trials.

The tortoise could change direction sooner, and its smaller steps made the finish area easier to hit. Median finishing times were 14.26 seconds for the tortoise and 17.33 for the hare.

At a fixed frequency of 12 steps per second and 85° error, increasing the hare’s step size from 6 to 20 raised wins from 39.2% to 100%. That change also increased its travel speed. At 80-unit steps, wins fell to 96.0%, with little median-time improvement over 40-unit steps.

Download the original 65 settings · Download the 12 scenario results · Try your own race