Assuming your W & L are in row 1 starting in column A (Adjust the ranges for your data)
These are array formulas so you need to enter them using CTRL-SHIFT-ENTER rather than just ENTER. If successful a pair of {} will be put around the formula
For wins
=MAX(FREQUENCY(IF(A1:P1="W",COLUMN(A1:P1)),IF(A1:P1<>"W",COLUMN(A1:P1))))
For Losses
=MAX(FREQUENCY(IF(A1:P1="L",COLUMN(A1:P1)),IF(A1:P1<>"L",COLUMN(A1:P1))))