Improving the model of base card value

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So while the previous model had a good fit, we can do better.

First, it's worth noting that we were training only off of creatures; weapons with no text were not modelled, and we were modelling those after the creatures.

By adding a categorical value for the card type, we can include both sets of data in the model, and provide a better prediction for both creatures and weapons.

Lastly, we add something to the model to account for card balance, penalizing cards that have are "lopsided" towards attack or health.

Predicted vs actual for fitted values.  Remember that horizontal values (actual) are quantized integers; vertical values (predicted cost) are not.

Predicted vs actual for fitted values.  Remember that horizontal values (actual) are quantized integers; vertical values (predicted cost) are not.

An updated poisson(link="identity") model, including the card type as a categorical (factor) attribute of the model.

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-0.80723  -0.05861   0.03219   0.11557   0.88626  

Coefficients:
                                              Estimate Std. Error z value Pr(>|z|)
(Intercept)                                    0.05952    0.45112   0.132    0.895
Attack                                         0.06746    1.17126   0.058    0.954
Health                                         0.81846    1.14619   0.714    0.475
sqrt(abs(Attack - Health))                    -0.29185    0.98007  -0.298    0.766
CardType_q2                                   -2.39374    3.99784  -0.599    0.549
Attack:sqrt(abs(Attack - Health))              0.25817    0.53455   0.483    0.629
Health:sqrt(abs(Attack - Health))             -0.18654    0.64174  -0.291    0.771
Attack:CardType_q2                             0.07223    2.55269   0.028    0.977
Health:CardType_q2                             0.98153    2.49477   0.393    0.694
sqrt(abs(Attack - Health)):CardType_q2         0.73281    2.73863   0.268    0.789
Attack:sqrt(abs(Attack - Health)):CardType_q2  0.46050    1.66056   0.277    0.782
Health:sqrt(abs(Attack - Health)):CardType_q2 -0.67290    1.20226  -0.560    0.576

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 59.0578  on 45  degrees of freedom
Residual deviance:  3.7054  on 34  degrees of freedom
AIC: 148.7

Number of Fisher Scoring iterations: 6

...and for a preview of just how much card mechanics beyond the Mana/Attack/Health relationship affect the true card cost, here's a plot of the predicted base vs actual for all minions and weapons.

Predicted "base value" vs the actual value, highlighting the effects of other card mechanics on the true cost of a card.