Traffic - Light at Newton and River St intersection

When turning left off of River St to head south on Newton St, there is a delayed green light for the opposite side of the traffic heading east on River. Why is there no arrow on the traffic light to indicate when it is safe to turn left or not. If you are familiar with the area, then you know you have a few seconds to take a left before the cars on the opposite side get their green light. What if you are new to the area? You would have no idea you are allowed to take a left and the other traffic still has red. Half the time, you have to guess if it is ok to take a left or not before the other traffic guns it through the intersection. This is an intersection that should clearly have an arrow but does not. What's the deal?