Pivot DataFrame while calculating new values
The magic word is "pivoting":

records = [(1871,"SS",0.0,3.0,1.0), (1871,"2B",30.0,1.0,0.0)]
pandas.DataFrame.from_records(records, columns=("yearID", "POS", "PO", "A", "E")
     ).assign(result = df.apply(lambda x: x['E']/(x['PO']+x['A']+x['E']), 1)
     ).pivot(index='yearID', columns='POS', values='result')


Result:

| POS    | 2B | SS   |
|--------|----|------|
| yearID |    |      |
| 1871   | 0  | 0.25 |


I went to the trouble of looking at your file now that you linked to it, and the problem is that you have removed to much information, so your index is not unique. Indices always have to be unique, so either you add that information back, or you preprocess the data before pivoting such that the duplication is resolved. I chose to retain the extra columns; I don't know if this is what you want, but it should help you understand what it takes to make pivoting work:

from pandas import read_csv

field_cols = ("playerID", "yearID", "teamID", "POS", "PO", "A", "E")
df = read_csv('Fielding.csv', usecols=field_cols).dropna(
             ).query('not PO == A == E == 0')

df.assign(ID = df[['playerID', 'yearID', 'teamID']].apply(tuple, 1), 
          FP = df.apply(lambda x: 1-x['E']/(x['PO']+x['A']+x['E']), 1)
          ).drop(set(df.columns) - {'POS'}, 1).drop_duplicates('ID'
          ).pivot(index='ID', values='FP', columns='POS')


Result:

| POS                    | 1B  | 2B  | 3B  | C   | CF  | LF  | OF  | P        | RF  | SS  |
|------------------------|-----|-----|-----|-----|-----|-----|-----|----------|-----|-----|
| ID                     |     |     |     |     |     |     |     |          |     |     |
| (aardsda01, 2006, CHN) | NaN | NaN | NaN | NaN | NaN | NaN | NaN | 1.000000 | NaN | NaN |
| (aardsda01, 2007, CHA) | NaN | NaN | NaN | NaN | NaN | NaN | NaN | 0.857143 | NaN | NaN |
| (aardsda01, 2008, BOS) | NaN | NaN | NaN | NaN | NaN | NaN | NaN | 1.000000 | NaN | NaN |
| (aardsda01, 2009, SEA) | NaN | NaN | NaN | NaN | NaN | NaN | NaN | 1.000000 | NaN | NaN |
| (aardsda01, 2010, SEA) | NaN | NaN | NaN | NaN | NaN | NaN | NaN | 0.833333 | NaN | NaN |
  ...