I would assume that Random is based on the total amount of sP you've won.
Actually, I just won a snowball and my score went up so I'm not certain on that one :P
I'm certain that Slots is based on the number of items you've won
I had a score of 271 and it went to 272 when I won a Slots Coin just now
I've always been curious on the quest ones
My wizard score is 80,210 and I won a 15 point wizard token and 22,400 sP and my score is still 80,210
So, I dunno :P
sorry I cannot help, as I have wondered that myself.
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For random you get a set amount when you win an item - 800 pts. When you win sPs you get 20% of the value of sPs as points. For Slots you get 1 point every time you win a prize - be it a slots spork or the grand prize. Quests - I don't know.
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