# Analytical Modeling and Empirical Analysis of Binary Options Strategies
## 3 Results
### Strategy C  
In Figure 11, the scatter plot matrix sets fixed values for prediction accuracy and payout percentage (\(p=0.65,\ r=0.65\)). The matrix also analyzes the impact of other factors, namely investment proportion (\(z=0.05,\ldots,\ 0.95\)) on its \(y\)-axis, the multiplier for withdrawal (\(w=1,\ldots,\ 2\)) on its \(x\)-axis, and the proportion withdrawn (\(v=0.1,\ldots,\ 0.9\)) on the \(x\)-axis of each plot, on (average of median) _roiC_ for Strategy C. This impact is shown on the \(y\)-axis of each plot and denoted by color. To facilitate the observation of insights, one of five different background colors is applied for each plot. Starting from low investment proportion \(z\) values and going upwards:  
* Pink background denotes scenarios in which _roiC_ decreases.
* Gray background denotes scenarios in which _roiC_ stays mostly constant.
* Light green background denotes scenarios in which _roiC_ increases slightly.
* Darker green background denotes scenarios in which _roiC_ increases considerably, with the increasing values of the proportion withdrawn v. Meanwhile, a white background denotes scenarios in which no consistent patterns exist.
* The following observations are made from Figure 11.  
* Pink plots: Not making any withdrawals at all (\(v=0\)) is typically more profitable (higher _roiC_) when the investment proportion has low values, less than \(z<0.40\);
* Gray plots: For certain \((w,z)\) value ranges, _roiC_ is insensitive to changes in \(v\);
* Green plots: The return _roiC_ typically increases as the values of the proportion withdrawn \(v\) increase when the investment proportion is \(z\geq 0.40\), and the multiplier for withdrawal is \(w\geq 1.20\). In other words, higher values of \(v\) are preferred for higher _roiC_ with higher values of \(w\) and \(z\).  
After observing these patterns for Strategy C, similar to the analysis for Strategy B, two further research questions were identified: \"Can (near-)optimal values \((w^{*},z^{*},v^{*})\) for the three decision variables \((w,z,v)\) be derived? Are there any patterns in these (near-)optimal values?\". Again, because the data generated in the experiments are for discrete points in continuous space, the derived values could only be near-optimal rather than optimal. To this end, for each \((p,r)\) value pair, database queries were used to search within the experimental results for the values of \((w,z,v)\) that yield the highest _roiC_ for that pair. Although all near-optimal values were obtained, no pattern was directly discovered from the results. The near-optimal values for the decision variables \((z^{*},w^{*},v^{*})\) of strategy C, for each \((p,r)\) pair, are provided in full in Supplementary File S8.  
Figure 11 is only an illustrative example of the types of insights that can be obtained through visual analytics when analyzing the experimental results. Naturally, different insights would be gained for different combinations of factors and responses and different constant values of \((p,r)\) assumed. Analysts can select the factors, responses, constant values, and parameter ranges that are most suitable for their investment settings and analysis needs, and subsequently, they can analyze the results to discover fresh insights and new knowledge that they can apply to reach better investment decisions.