Sorting and Ranking

Rank Values

Assign a rank to each value in a column — the largest gets rank 1. By hand, each value's rank is 1 plus the count of values strictly greater than it. With pandas, Series.rank(ascending=False) does this in one call.

By hand

For each score, count how many other scores are strictly greater than it — that count plus 1 is the rank. All values are distinct, so there are no ties and the formula produces gap-free integer ranks.

naive.py
Replay: real traced execution (multi-file project)
scores = [80, 55, 90, 70]
ranks = []
for s in scores:
    rank = 1
    for other in scores:
        if other > s:
            rank += 1
    ranks.append(rank)
print('RESULT:', ranks)

  1. scores ← [80, 55, 90, 70]

    1scores = [80, 55, 90, 70]2ranks = []
    values this step[80, 55, 90, 70]scores

  2. ranks ← []

    1scores = [80, 55, 90, 70]2ranks = []3for s in scores:
    values this step[]ranks

  3. s ← 80

    2ranks = []3for s in scores:4    rank = 1
    values this step80s

  4. rank ← 1

    3for s in scores:4    rank = 15    for other in scores:
    values this step1rank

  5. other ← 80

    pass 1 of 3
    4rank = 15for other in scores:6    if other > s:7        rank += 1
    values this step80other
    All 3 passes — pass 1 is the card above
    passother
    180
    280 → 55
    355 → 90

  6. rank ← 2

    6    if other > s:7        rank += 18ranks.append(rank)
    values this step1 → 2rank

  7. other ← 70

    4rank = 15for other in scores:6    if other > s:
    values this step90 → 70other

  8. if other > s:

    5for other in scores:6    if other > s:7        rank += 1

  9. for other in scores:

    4rank = 15for other in scores:6    if other > s:

  10. ranks ← [2]

    7            rank += 18    ranks.append(rank)9print('RESULT:', ranks)
    values this step[] → [2]ranks

  11. s ← 55

    2ranks = []3for s in scores:4    rank = 1
    values this step80 → 55s

  12. rank ← 1

    3for s in scores:4    rank = 15    for other in scores:
    values this step2 → 1rank

  13. other ← 55, rank ← 2

    pass 1 of 2
    4rank = 15for other in scores:6    if other > s:7        rank += 18ranks.append(rank)
    values this step80 → 55other1 → 2rank

  14. other ← 70, rank ← 3

    pass 2 of 2
    4rank = 15for other in scores:6    if other > s:7        rank += 18ranks.append(rank)
    values this step90 → 70other2 → 3rank

  15. rank ← 4

    6    if other > s:7        rank += 18ranks.append(rank)
    values this step3 → 4rank

  16. for other in scores:

    4rank = 15for other in scores:6    if other > s:

  17. ranks ← [2, 4]

    7            rank += 18    ranks.append(rank)9print('RESULT:', ranks)
    values this step[2] → [2, 4]ranks

  18. s ← 90

    2ranks = []3for s in scores:4    rank = 1
    values this step55 → 90s

  19. rank ← 1

    3for s in scores:4    rank = 15    for other in scores:
    values this step4 → 1rank

  20. other ← 80

    pass 1 of 4
    4rank = 15for other in scores:6    if other > s:7        rank += 1
    values this step70 → 80other
    All 4 passes — pass 1 is the card above
    passother
    170 → 80
    280 → 55
    355 → 90
    490 → 70

  21. for other in scores:

    4rank = 15for other in scores:6    if other > s:

  22. ranks ← [2, 4, 1]

    7            rank += 18    ranks.append(rank)9print('RESULT:', ranks)
    values this step[2, 4] → [2, 4, 1]ranks

  23. s ← 70

    2ranks = []3for s in scores:4    rank = 1
    values this step90 → 70s

  24. rank = 1

    3for s in scores:4    rank = 15    for other in scores:

  25. other ← 55, rank ← 2

    pass 1 of 2
    4rank = 15for other in scores:6    if other > s:7        rank += 18ranks.append(rank)
    values this step80 → 55other1 → 2rank

  26. other ← 70, rank ← 3

    pass 2 of 2
    4rank = 15for other in scores:6    if other > s:7        rank += 18ranks.append(rank)
    values this step90 → 70other2 → 3rank

  27. for other in scores:

    4rank = 15for other in scores:6    if other > s:

  28. ranks ← [2, 4, 1, 3]

    7            rank += 18    ranks.append(rank)9print('RESULT:', ranks)
    values this step[2, 4, 1] → [2, 4, 1, 3]ranks

  29. for s in scores:

    2ranks = []3for s in scores:4    rank = 1

  30. stdout ← RESULT: [2, 4, 1, 3]

    8    ranks.append(rank)9print('RESULT:', ranks)
    values this stepRESULT: [2, 4, 1, 3]stdout

With pandas

df['score'].rank(ascending=False) assigns rank 1 to the largest value. rank() always returns float64; with distinct values the fractional part is always .0, so casting to int is safe.

library.py 
import pandas as pd
from dalib.display import set_display
set_display()

scores = [80, 55, 90, 70]
df = pd.DataFrame({'score': scores})
r = df['score'].rank(ascending=False)
ranks = [int(x) for x in r.tolist()]
print('index:', r.index.tolist())
print('values:', r.tolist())
print('dtype:', r.dtype)
print('RESULT:', ranks)

index: [0, 1, 2, 3]
values: [2.0, 4.0, 1.0, 3.0]
dtype: float64
RESULT: [2, 4, 1, 3]

Implementation notes

  • rank(ascending=True) (the default) assigns rank 1 to the smallest value. Pass ascending=False to rank largest-first, as done here — this matches the naive formula (1 + count of values greater).
  • With distinct values all tie methods agree. When ties exist, pandas offers: method='average' (default — mean of tied ranks), method='min' (lowest rank in the tie group), method='dense' (no gaps — [1,2,2,3] rather than [1,2,2,4]).
  • rank() always returns float64 regardless of the input dtype; cast with int() or .astype(int) only after confirming no NaN values.
  • Cross-reference: rank-assign (python-data-basics) for the pure-Python version.