For single seasons, From 1901 to 2008, (requiring whip≤1.06, W≤9, and At least 162 Innings Pitched), sorted by most recent date

  Cnt Player            Year  WHIP  W   IP  Age Tm  Lg  G   GS CG SHO GF  L  W-L% SV  H   R   ER  BB  SO   ERA  ERA  HR  BF   AB  2B 3B IBB HBP  SH  SF GDP  SB CS Pk BK WP   BA   OBP   SLG   OPS  OPS   Pit  Str
 ----+-----------------+----+-----+--+-----+---+---+--+---+---+--+---+--+--+-----+--+---+---+---+---+---+------+----+--+----+----+--+--+---+---+---+---+---+---+--+--+--+--+-----+-----+-----+-----+----+----+---- 
    1 Curt Schilling    2003 1.048  8 168    36 ARI NL  24  24  3   2  0  9  .471  0 144  58  55  32 194   2.95  159 17  673  626 27  1   2   3  11   1   9   3  3  0  0  4  .230  .270  .358  .628   61 2450 1705 
    2 Ed Halicki        1978 1.060  9 199    27 SFG NL  29  28  9   4  1 10  .474  1 166  74  63  45 105   2.85  121 11  819  751 21  2   9   7  12   3   6  36  2  0  3  1  .221  .270  .298  .568   66           
    3 Bob Moose         1968 1.033  8 171.1  20 PIT NL  38  22  3   3  7 12  .400  3 136  61  52  41 126   2.73  106  5  685  624 21  3   7   3  14   3  13   9  1  0  1  3  .218  .268  .285  .553   66           
    4 Fred Anderson     1917 0.963  8 162    31 NYG NL  38  18  8   1 15  8  .500  3 122  40  26  34  69   1.44  176  1  632                  2                        0  5                            0           
    5 Pat Ragan         1916 1.044  9 182    30 BSN NL  28  23 14   3  4  9  .500  0 143  53  42  47  94   2.08  118  3  717                  0                        0  1                            0           
    6 Frank Miller      1916 1.064  7 173    30 PIT NL  30  20 10   2  7 10  .412  1 135  55  44  49  88   2.29  116  4  677                  7                        0  3                            0           
    7 George McConnell  1916 1.004  4 171.1  38 CHC NL  28  21  8   1  7 12  .250  0 137  66  49  35  82   2.57  113  8  682                  5                        0  8                            0           
    8 Jack Warhop       1914 1.043  8 216.2  29 NYY AL  37  23 15   0 10 15  .348  0 182  75  57  44  56   2.37  117  8  829                 11                        0  4                            0           
    9 Bill Burns        1908 0.927  6 165    28 WSH AL  23  19 11   2  1 11  .353  0 135  58  31  18  55   1.69  136  3  612                  4                        0  1                            0           
   10 Roy Patterson     1904 1.042  9 165    27 CHW AL  22  17 14   4  5  9  .500  0 148  52  42  24  64   2.29  108  1  681                  7                        0  2                            0           
   11 Ed Siever         1902 1.051  8 188.1  27 DET AL  25  23 17   4  2 11  .421  1 166  73  40  32  36   1.91  196  0    0                  2                        1  0                            0           

Seasons/Careers found: 11.

 Photos from the George Grantham Bain Collection at the Library of Congress.