df = pd.DataFrame({'Id': [102,103,104,303,305],'ExpG_Home':[1.8,1.5,1.6,1.8,2.9],
                  'ExpG_Away':[2.2,1.3,1.2,2.8,0.8],
                  'HomeG_Time':[[93, 109, 187],[169], [31, 159],[176],[16, 48, 66, 128]],
                  'AwayG_Time':[[90, 177],[],[],[123,136],[40]]})

y = [1 - (ExpG_Home + ExpG_Away), ExpG_Home, ExpG_Away]

`x1 = [1,0,0]`    `x2 = [0,1,0]`    `x3 = [0,0,1]`
     total_timeslot = 200 , number of timeslot per game.

For Id=102 with ExpG_Home=2.2 and ExpG_Away=1.8
HomeG_Time = [93, 109, 187],  AwayG_Time = [90, 177]

def squared_diff(x1, x2, x3, y):
    ssd = []
    for k in range(total_timeslot):
        if k in HomeG_Time:
            ssd.append(sum((x2 - y) ** 2))
        elif k in AwayG_Time:
            ssd.append(sum((x3 - y) ** 2))
        else:
            ssd.append(sum((x1 - y) ** 2))
    return ssd

sum(squared_diff(x1, x2, x3, y))
Out[37]: 9.822399999999993