Why opposition strength has to be priced into a batting rating

Unequal schedules are the normal case

International calendars are not balanced, and different teams face very different mixes of opposition across any given period of competition. A competitor whose fixtures fall disproportionately against weaker attacks accumulates favourable numbers without doing anything differently. The imbalance is not deliberate, and it arises from commercial scheduling, tournament structure and the practical geography of touring.

Any measure that ignores it inherits the schedule as a hidden component of the assessment, which is indefensible once stated plainly. The correction is conceptually simple and computationally awkward, which is why it is applied inconsistently across published measures. Until it is applied, a comparison between two competitors is partly a comparison between the tours their boards happened to arrange for them.

How the adjustment works

The method compares a performance against the expected performance of a reference competitor facing the same opposition in the same conditions. That expectation is estimated from all other performances against the same opposition, which pools a great deal of otherwise unused information. A score well above expectation raises the rating regardless of its absolute size, which correctly rewards difficult runs over easy ones.

Because opposition strength is itself estimated from performances, the system must be solved as a whole rather than competitor by competitor. Iterating until the estimates stop changing is standard, and the result is sensitive to how the process is initialised when data is thin.

Where the estimate becomes fragile

The adjustment relies on the opposition having faced enough other competitors for its level to be estimated with reasonable confidence. When a bowling attack has appeared rarely, its estimated level rests on a small sample and carries wide uncertainty into every adjustment that uses it. That uncertainty propagates, so a competitor assessed mostly against rarely seen opposition receives a rating with much larger error bars.

Published tables seldom display those bars, which encourages readers to treat all positions as equally well supported. Displaying them would change the tone of most rankings discussions considerably.

The changing-attack problem

A bowling attack is not a fixed entity, since personnel rotate and the same national side can present very different challenges within a single year. Rating the opposition as a team therefore blurs together configurations that a competitor experienced as quite distinct. Rating individual bowlers instead is more precise and requires far more data, since each pairing of batter and bowler is observed rarely.

Most systems compromise by rating the attack as it appeared in that match, which is better than a team constant and worse than full individual detail. The compromise is defensible provided the limitation is stated rather than quietly assumed away.

What adjustment can and cannot deliver

Adjustment removes a systematic bias, which is a genuine improvement, and it does not turn a noisy measure into a precise one. A competitor with a short record remains hard to assess however carefully the opposition is priced, because the sample is the binding constraint. The main value of adjustment is comparative, since it allows records built under different schedules to be placed on a common scale.

That common scale is exactly what a ranking needs, and it is why unadjusted averages should not be used for cross-era or cross-team comparison. Adjustment is a translation rather than a verdict, and treating it as the latter overstates what has been achieved.