In every field โ whether it be sports, weather observations, or economic indicators โ there is a concept of a "historical record." Many consider records to be simply the result of luck or supernatural skill; however, from a statistical point of view, the breaking of records follows certain mathematical laws.
The basis of record theory relies on the analysis of "extreme values." If we examine a sequence of random variables, the probability that each new piece of data will be higher than the previous maximum value decreases over time. For example, if the data are independent and identically distributed, the probability that the $n$-th observation is a record equals $1/n$. This means that as time passes, setting a new record becomes increasingly difficult.
However, in real life, we work with "non-stationary" systems. For instance, athletes' results improve with the development of technology, training methods, and medicine. In this case, a "trend" (tendency) is added to the mathematical model. When a trend exists, the frequency of records being broken does not decrease but continues at a certain pace. In the example of global warming, the fact that maximum temperature records are updated every year indicates a structural change (trend) in the climate system.
To predict the breaking of records, "Extreme Value Theory" (EVT) is used. Through this model, we can calculate not only whether a record will be broken, but also by how much it will increase. This is of vital importance, especially for insurance companies and in the field of engineering (for example, when analyzing records of floods or earthquakes).
In conclusion, the breaking of historical records is not merely a coincidence, but a result of system dynamics and statistical distribution. If a system is static, records seem "eternal"; if a system is evolving, today's record becomes tomorrow's ordinary indicator. Mathematics helps us understand not only the possibility of records but also when they reach a point where they can no longer be broken.
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