I think it has to be assumed that only some prayers are 'effective' - and that there are many prayers that are 'wrong', and make no difference - for example being mere habitual repetitions, or askings for bad things.
But there is no doubt that some prayers are effective: all Christians know this from experience. This probably happens because prayer can be an act of creation: more precisely in prayer we can participate in God's ongoing creation.
That is how prayer can affect the future - we personally enter-into the creation, and add to it our personal creativity.
That is how we, individually, make a difference by our prayer. Creativity is always happening; and then we pray and introduce a new element by our prayer - so that the future is changed.
Changing the future is a creative act. Prayer is, in effect, each of us working-with God.
Prayer works by love: love is that which is aligned-with God's motivation in creation. It is love that 'ensures' our prayer is aligned with the goodness of divine creation.
This happens because love is the basis of creation - it is the cohesion of creation. Love is what allows personal creativity to be real - because by real I mean that our creativity is permanently woven-into creation.
Only loving prayer is effective - because unloving prayer is incompatible with creation.
Conversely, when we pray with Love - and only then; what we pray is intrinsically creative. And loving prayer is always effective - loving prayer changes the future.
This does not mean that the effect of prayer is predictable by us, nor that praying for some specific thing always gets us just what we ask-for.
But loving prayer always makes a difference, and that difference is always positive (when seen from a God's eye view).