pMana and Base Card Value
/So, once you've scrubbed out zero-mana cards from scoring (which are a problem disconnected from value - it costs you in the deck build, but the card in isolation is always a pretty good deal), you clean up a few of the outliers and end up with a pretty solid qqplot.
QQ plot of predicted vs. actual, monsters > 0 mana with no additional mechanics.
QQ plot of predicted vs. actual, for *all* monsters and weapons (including those with mechanics)
Our goal in computing a base card value is to look purely at the numbers on the card, without considering the effects of the card mechanics, the rule violations that appear on the card. You do this for a few reasons:
- Many mechanical effects have dependencies that are situational or may just not go off the way you hope they would when you built the deck.
- Some cards have a "Silence" mechanic that wipe the card text, leaving you with just the base minion.
- Dependencies on combos and card synergies requires careful deck engineering.
Most of your deck should be stable, dependable, and work towards a single goal; every card in your deck should help you reach that goal. Like building your first boat, or house, the temptation is to throw every cool thing you ever saw into a deck; what usually happens next is a catastrophic chain of losses.
What makes building a valuation like this interesting is the stuff at either end, the outliers on the outskirts of Value Town. I'm also pleasantly surprised to find a fairly normal distribution.
The outliers are more-or-less who you'd expect them to be.
At the bottom of the value pile is the Molten Giant, at a mana cost of 20 for an 8/8 creature that's really only worth 7-8 mana. It's all in the rule violation of the card text: Costs (1) less for each damage your hero has taken.
At the top of the heap is Mukla's Big Brother... a massive 10/10 creature that costs 6 mana but should cost 9. Again, the card text says it all: So strong! And only 6 Mana?!
Two more cards without card text do well, here:
- Emerald Drake, costing 4 for a 7/6 creature, is well known to be great value and at a 92/100 rating for value is a great choice.
- Blood Fury is a great value at 3 mana for a 3/8 card.
Its brethren above 90% are all either great value or have debilitating problems with their additional mechanics.
- Ancient Watcher at 2 mana for a 4/5 looks good until you see that its big restriction is that it can't attack.
- Injured Blademaster has a debilitating Battlecry that deals 4 damage to himself, a 4/7 creature that becomes a 4/3 when you play him.
- Earth's Elemental is great value at 5 for a 7/8, but has an Overload: (3) that takes out three of your mana for a whole turn.
Millhouse Manastorm and Flame Imp are right up there with Ancient Watcher , but again, those debilitating mechanical violations come in to destroy their utility.
Even the Oasis Snapjaw and Chillwind Yeti appear in the correct order. (Yeti > Snapjaw, in case you didn't know.)
A cursory review of cards shows a pretty good match for general consensus on perceived value, so I'm going to roll with this for a V1.
Note that it's hard to read too much from the distribution here; this is data that came out of the model, which iteself presumes a normal distribution of the source data. I'd have to switch to a glm or bayesian model to avoid making that assumption about the source data...
Which is something I'll look at in future passes. For now, I'm comfortable that the fit passes basic sniff tests.