Hi, today I want to share an interesting topic, "why does the feeling of failure increase even though the ratio is 99.0% and 99.9%, The main reason why I chose this topic is because many people experience a shift in cognitive function when there is a difference in the failure ratio. The feeling of incongruity I describe where the difference between 99% and 99.9% success seems larger than the difference between 1 in 100 and 1 in 1000 failure rates,
Failure arises comes from several cognitive biases and aspects of how we perceive numbers:
1. Framing Effects and Reference Points:
* Success Rate as a "Goal": When we hear "success rate," our mental reference point is often 100% perfection. A 99% success rate means we're "only" 1% away from perfect, while 99.9% means we're "only" 0.1% away. That 0.9% difference feels significant because it's narrowing the gap to an ideal.
* Failure Rate as an "Avoidance": When we hear "failure rate," our mental reference point is often 0% failure. A 1 in 100 failure rate means there's a small chance of something bad happening. A 1 in 1000 failure rate means that chance is even smaller. The absolute difference (1 in 100 vs. 1 in 1000) might seem small because both are already quite low.
2. Absolute vs. Relative Thinking:
* Success Rates (Relative to 100%): When comparing 99% and 99.9%, we are implicitly thinking about the remaining 1% and 0.1%. The change from 1% to 0.1% is a 90% reduction in the failure rate (1% is ten times 0.1%). This relative reduction in the negative outcome feels very significant.
* Failure Rates (Absolute Difference): When comparing 1 in 100 and 1 in 1000, we're focused on the absolute numbers of failures. While 1 in 1000 is indeed ten times better than 1 in 100, our brains don't always immediately perform that multiplicative comparison in the same way they do with percentages nearing perfection. It's an improvement, but perhaps not as dramatically felt.
3. The "Last Mile" Problem / Diminishing Returns:
* Improving from 50% to 60% success might feel good, but the impact of improving from 99% to 99.9% often feels disproportionately large. This is because getting closer to perfection often requires significantly more effort, precision, and cost for smaller absolute gains. We intuitively understand that these "last few points" are the hardest to achieve, making their attainment feel more significant.
4. Cognitive Ease and Vividness:
* "1 in 100" is easy to grasp. "1 in 1000" is also relatively easy. The difference between them might not immediately trigger a strong emotional response because both are fairly rare events.
* However, when we think of 99.9% success, we might mentally picture "almost perfect" or "barely any mistakes," which is a very desirable and vivid outcome. The mental image associated with 99% might still include a noticeable number of errors, making the leap to 99.9% feel more substantial.
5. Anchoring and Adjustment:
* When you hear 99%, your brain might "anchor" to that number. Then, when you hear 99.9%, you "adjust" your perception. Because the numbers are so close to 100%, even small absolute differences (like 0.9%) can feel large in that context.
* With failure rates, if you're anchored at 1 in 100, moving to 1 in 1000 is an improvement, but it's still a relatively rare event, so the adjustment might not feel as impactful.
In essence, our brains are not always perfectly rational computers. We are influenced by how information is presented (framing), what we consider the ideal outcome (reference points), and the psychological weight we assign to "getting closer to perfect" versus "reducing rare occurrences." The "last mile" of improvement often carries a disproportionately high psychological value.
