# Towards Adaptive Gamification: A Method Using Dynamic Player Profile and a Case Study
## 5 Adaptive Method Evaluation
### Results
Moreover, both cases of method \(B\) have similar errors (\(Err=0.08024\) and \(Err=0.08027\) in accurate and inaccurate answers, respectively), because there is a random selection of player type ratings and thus, they are almost independent of the reliability (accurate or inaccurate) of the answers. Finally, except in method \(A\) with accurate answers, method \(C\) behaves better than \(A\) and \(B\) (\(Err=0.0070\) and \(Err=0.0243\) in accurate and inaccurate answers, respectively) even in its worst scenario (\(Err=0.0333\)). Note that themean errors should be interpreted in the interval [0, 0.2857] since the maximum distance between two normalized points in a Unit Hypercube is 2/7 (approximately 0.2857). This indicates, for example, that the value of the error 0.0827 in case B-Random represents approximately 28%. Regarding the results of the mean error in inaccurate answers, the difference between method A (Constant Player Type) and method C (Dynamic Player Type) is 0.0068. To analyze this difference, we conducted a statistical study. As the data are not normally distributed (Shapiro-Wilk \(p\)-value: 0.00005421, with an effect size large ES = 0.239), we used the Wilcoxon signed-rank test for paired samples. Results indicate that we can reject the null hypothesis (\(mean_{A}=mean_{C}\), \(p<0.0001\), ES = 0.87) and then the difference is significant. On the other hand, the player profiles of the worst (0.0333) and best (0.0146) cases of C in inaccurate answers were disruptor in both cases. Indeed, the disruptors, free spirit and philanthropists/achievers player types represent the most frequent results from the [PERSON] questionnaire. Figure 9 shows the values of a bot's player ratings \(PR^{(t)}\) along 180 iterations for the best case of method C in inaccurate answers, as shown in Table 3. The real player type, \(RPT_{0}\), is represented by dotted lines and colored stars (red--disruptor; green--free spirit; yellow--philanthropist) at the end of the X axis. As can be appreciated, the disruptor player type is the one that achieves the lowest error (distance between the red star and the end of the red line). The first values, 0.14 and 0.21, of the two initial vectors (\(PR^{(0)}\) : [0.14, 0.2, 0.17, 0.16, 0.15, 0.17, 0] \(RPT_{0}\):: [0.21, 0.17, 0.16, 0.16, 0.14, 0.15, 0]), and the final value obtained, 0.21, in the vector \(PR^{(180)}\) :: [0.21, 0.185, 0.156, 0.149, 0.136, 0.162, 0], are the vector of player ratings in the following order :: (disruptor, free spirit, achiever, player, socializer, philanthropist, non-player). Additionally, not only does the predominant player type converge to its real value, but other player types that are not predominant, such as the free spirit rating (initially at 0.20), also evolve by slightly decreasing their values with regard to the real one (0.17). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Cases/Methods**} & **A—Constant** & **B—Random** & **C—Our Method** \\  & **Constant \(PR^{(0)}\)** & **Dynamic \(PR^{(t)}\)** & **Dynamic \(PR^{(t)}\)** \\ \hline \hline \multicolumn{3}{c}{**Accurate Answers Case: \(RPT_{0}\simeq PR^{(0)}\)**} \\ \hline Mean Error (SD) & 0 & 0.08024 (0.00052) & 0.0070 (0.00166) \\ Worst Scenario of C & 0 & 0.0804 & 0.0105 \\ Best Scenario of C & 0 & 0.0797 & 0.0029 \\ \hline \multicolumn{3}{c}{**Inaccurate Answers Case: \(RPT_{0}\
eq PR^{(0)}\)**} \\ \hline Mean Error (SD) & 0.0311(0.00404) & 0.08027 (0.00040) & 0.0243 (0.00475) \\ Worst Scenario of C & 0.0367 & 0.08012 & 0.0333 \\ Best Scenario of C & 0.0233 & 0.08018 & 0.0146 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Table of mean errors of methods A-Constant Player Type, B-Random Dynamic Player Type, and C-Our Method-Dynamic Player Type, when the questionnaire is accurately and inaccurately answered (the two cases in rows), together with the best and worst errors obtained with method C.