The cornerstone of the Book of Romans is Romans 1:17, which quotes Habakkuk 2:4 (NASB) -
Behold, as for the proud one,
His soul is not right within him;
But the righteous will live by his faith.
Righteousness is only through faith. When Jesus said that "you no longer see me" in John 16:10, he was referring to trusting in him by faith. We have never seen Jesus (nor can we see him at the moment), but we trust in him. This faith results in righteousness, which is the crux of the Book of Romans. The Spirit of God convicts us that the only means of righteousness is through faith on Jesus Christ.
Thus we can also understand why the Spirit also convicts the world of sin (John 16:9). This sin not only includes our transgressions against God but also our very state of spiritual death (separation from God). This spiritual death is removed, or washed away, by faith in Jesus Christ, when the believer is "born again." Thus the Holy Spirit convicts the world of sin, "because they do not believe in me." That is, belief in Jesus removes the condemnation of sin, which is spiritual death.
Last but not least, the reference to the devil for conviction of judgment (John 16:11) is the certitude that in as much as the devil is condemned to eternal fire, so also will be the destiny of those who remain in a state of spiritual death.
The issue is not whether or not you are a good or bad sinner, but whether you have the righteousness of God through faith.