“Why is the prayer of the righteous like a shovel ?
Just as a shovel [ehtehr/עתר] moves grain from one place to another,
the prayer [ahtahr/עתר] of the righteous turns G-d’s trait of anger to the trait of mercy.” 
Is this only true of the prayer of “the righteous?” Do the rabbis extol saints at the expense of ordinary people? No, I don’t think so. Elsewhere they say, “Whoever prays much will be answered.”  It’s prayer, not saints, that the rabbis extol.
Still, the analogy raises other questions.
Does G-d “change”? Can G-d be angry and punitive at one moment, then happy and loving at another? If so, it would contradict everything we’re told about G-d being changeless.
It would also mean that G-d’s reactions are determined by our actions – that we can “push G-d’s buttons.” Yet, when we tell even small children, “We choose our reactions, and can always choose better ones,” we mean: “No one else can ‘push your buttons’ unless you let them.” If we can choose to let someone “push our buttons” or not, then “kal v’homer” — how much more must it be true that G-d can choose!
To understand the rabbis, we must first realize that phrases like G-d’s “trait of anger” (Judgment/Din) or “trait of mercy” (Kindness/Hesed) don’t describe changes in G-d. Rather, they describe changing human perceptions of G-d. G-d, we’re taught, always gives the perfect, Loving response. As Rabbi Boruch Leff wrote:
“God through His judgment shows us that He cares about everything that we do…Through judgment, we are made aware that every little thing that we do makes a difference…We are significant and responsible. And responsibility is a tremendous cause for celebration.” 
We name that response as either “anger” or “mercy” depending on how it seems to us. In fact, the Talmud addresses this directly: Now (“in this world”), we say the brachah “Dayan ha-Emet” for seemingly bad news, and “ha-Tov v’ha-Mei’tiv” for seemingly good news,  but in a future time of higher, clearer awareness of G-d – we’ll say only “ha-Tov v’ha-Mei’tiv” for Good that’s done, because that’s how we’ll see everything that G-d does. 
Our own thinking creates the way G-d appears to us. Comparing praying with using a shovel (in Hebrew, a pun based on the similarity of the linguistic roots of both words), the rabbis are describing a change in our own thinking that comes about as a result of our repeated personal experiences of G-d’s Presence and Goodness in the course of praying.
As with all change, this is gradual; incremental -– like moving a large pile of grain with a shovel. Just as each “shovelful” moves some of the grain from one place to another, until it has all been moved, each sincere prayer — in which we experience Divine Love, even a little — can gradually change our thinking and our awareness of G-d from One who is “punishing” us, to One Who is always loving us. With each sincere prayer, G-d’s Goodness in our lives can become increasingly clear to us outside of prayer, too.
The rabbis suggest even more: as G-d’s Goodness becomes more and more undeniable to us, more happiness, health, calmness and patience, even more material abundance, can fill us. That’s “G-d’s trait of ‘Mercy’.”
But this is only true when, in each prayer, we stop insisting that G-d do what we want, and instead make each prayer invoke what is Divinely known to be best for us. When first, “b’Yado af’kid ru’chi…”  – “I put my soul in [Your] Hands,” then “…v’lo ih’rah”  – “I don’t fear” follows. In order not to fear, we must first sincerely place ourselves in the Presence of G-d and G-d’s Goodness, then let go of our problem. Fear disappears by itself, and we know only Divine Goodness filling every aspect of our lives.