After some testing, here are some numbers:
458 points for level 1 common, 703 points for level 10 common, 604 points for 2* level 1 common.
876 points for level 1 uncommon (so yes, rarity makes a difference too), 1275 points for level 20 uncommon, 1376 points for 3* level 1 uncommon.
29 points increase for a 1 level increase on a 5* rare.
168 points when you equip a 5* rare level 1 piece on a champion (gear doesn't affect your score while not being worn), 545 points when you equip a 5* rare level 16 gear piece on a champion. 21 points increase to level a 5* rare gear piece from level 9 to 10.
66 points increase for a tier 3 mastery being added.
So basically, if you want to reduce your player score to get you easier matchups in arena, you should get rid of champions that you don't use and don't plan to use in the future; you should not level up/ascend champions that you want to keep for future use but aren't using now, nor gear them, nor get them masteries; when you stop using a champion, you should strip their gear, even if you don't go so far as to feed the champion.