Troublesome residual plot from linear mixed model

I have fitted the following linear mixed model based on the results of an economic game:

lmer(TotalScore~perOOgivenP+Game+(1|Subject),REML=T,data=mdl1table)->m1

TotalScore is a integer. perOOgivenP is a proportion between 0 and 1 (most of which are 0). Game is numeric and tells us if it is the 1st or 2nd game played by the participant

The qq plot looks good so I am confident the residuals are normally distributed. The fitted vs. residuals plot does not look so good. To me it looks like the residuals are biased. I am not sure what Is causing this or what to do about it?

Could it be caused by the amount of 0's in perOOgivenP (32/46 data points). perOOgivenP is the proportion of times a particular behaviour was made. Would anyone suggest making this binary as in 0 or 1 (actual value not 0).

perOOgivenP is as follows: [1] 0.5000000 1.0000000 0.3333333 0.0000000 0.0000000 0.0000000 NaN 0.1666667 0.2500000 0.8000000 0.1666667 0.0000000 0.3333333 [14] 0.0000000 0.0000000 NaN NaN 0.0000000 0.0000000 0.0000000 NaN 1.0000000 NaN 0.0000000 NaN 0.0000000 [27] 0.0000000 NaN NaN NaN NaN 0.0000000 NaN 0.0000000 0.0000000 0.0000000 NaN NaN NaN [40] 1.0000000 NaN 0.0000000 0.4117647 0.0000000 0.0000000 NaN NaN 0.0000000 0.2000000 0.0000000 NaN 0.0000000 [53] 0.3333333 0.0000000 0.2500000 NaN 0.0000000 NaN NaN NaN 0.0000000 NaN 0.0000000 0.0000000 NaN [66] 0.0000000 NaN NaN NaN 0.0000000 0.0000000 0.0000000 0.0000000 NaN NaN NaN NaN NaN [79] NaN NaN

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 What do you mean by "biased residuals" ? If you compute the average value of the residuals, you find 0. – Stéphane Laurent Jan 16 at 18:59