When analyzing the card, why is it more accurate to use total hands rather than printed hands?
Often, misleading data is published when hands are analyzed. For example, we may read something along the lines of "x% of hands contain y". But each hand on the card corresponds to many actual hands (sometimes hundreds) once expanded out into all its permutations. This affects the calculations significantly, and without using the total number of hands, any percentage calculated would be somewhat misleading.
The hands as written on the card are just a notation to express the actual hands, because it'd be cumbersome to list them all. But that notation is arbitrary. Depending on whether the League decides to spell out some hands or use a note to express them, the number of hands on the card is different, but the real number of hands is the same.
The examples below use the NMJL 2023 card.
Consecutive Run line 5 are considered 2 hands. But the League could have shown 1 hand and said in the note "1 or 3 suits". Either way, it's the same number of expanded hands (63), but if you count hands written on the card, it'd be 1 instead of 2, and the percentages calculated would be different.
Another example would be 369 line 5. That's considered 1 hand, and the note says you can use 3s, 6s or 9s for your kongs. Instead of adding that note, they could have spelled out the 3 hands on separate lines (ignoring the real estate constraints). Either way the number of real hands is the same. But for those who are analyzing the card using just the hands marked on the card, they would count 1 or 3 depending on the chosen notation, and come up with different percentages for "x% of hands contain y".
The key point is that the hands as written on the card are an arbitrary notation, and if used without expansion, they can lead to inconsistent or erroneous calculations.