There is an ongoing debate between historians as to whether Stalin’s rise to power was a result of Trotsky’s mistakes or other factors such as Stalin’s individual successes and/or individual genius. It is likely that Stalin came to power due to both of these factors.
One major factor in Stalin coming to power, that wasn’t a Trotsky mistake, is the fact that Stalin held the position of secretary for the Bolshevik party. This gave him, to some extent, control over party business. Stalin could control what was discussed at party meetings as he drew up the agendas. This helped him come to power because it made sure that the party talked about topics which were important for him to be able to take power – it allowed him to ‘lay the foundations’ for his campaign to become leader. As well as being party secretary, Stalin later had control of the party organisation. Stalin could choose which party delegates were sent to the annual party congress, so could pack the congress with his supporters. This meant that he could capitalise fully on the mistakes of his opponents (like Trotsky) and out-vote them on key issues, thus destroying their chances of challenging Stalin for the party leadership. Stalin then had control over party membership so he could expel the more radical elements of the party (students and soldiers) who were likely to support Trotsky – this helped Stalin come to power as it allowed to him to only allow people who were likely to support him into the party.
Another factor that allowed Stalin to come to power due to his individual genius was that he very rarely sided with particular members of the party - he stayed in the background (‘grey blur’) and pretended to be a moderate peacemaker. Because of this, the other party members seriously underestimated Stalin; while he appeared to be a peacemaker, he was manipulating his opponents