A question I've heard often is: Is it correct, in Scrum methodology, to track an individual's performance? This question has only one answer: No. Tracking and measuring the productivity of a single member of an Agile team is against the spirit of Scrum. The real question should be: If you were able to calculate such a metric, what would you do with the data? I suspect the answer is that you would use it to reward or punish on the basis of productivity, and this is something you don't want happening within a Scrum environment.
The Scrum framework doesn't prevent you from measuring whatever you want to measure. However, you'd be missing the spirit of Scrum if you measured the work of a single team member. Productivity metrics for knowledge workers are generally flawed, studies show, so you'd likely end up playing with incorrect data. The fundamental point is that if a Scrum team member is not able to contribute, then this points to a team problem. The Scrum spirit means that everyone jumps in to help; ideally, all team members work together on all of the stories. Different skill levels or types contribute to the best of their abilities. To create metrics for individuals, besides being inaccurate, would probably cause competition and division within the team. Individuals should work as a unit, be tracked as a unit, and succeed or fail as a unit.
It's unfortunate that Scrum tools have an "assigned to" field. Members should volunteer for stories and tasks; they should not be assigned work. It's better to think of this field as merely naming the primary person working on a task or story. I strongly feel that any team member who only does his own stories or tasks and doesn't help others in the team is a poor Scrum team member. Such behavior should not be rewarded, especially not in some kind of performance review. The best teammates are helpful and collaborative, and you can't measure their personal contribution to the team's velocity. You can only measure the entire team's velocity.
My conclusion is that tracking an individual's performance constitutes crime in the Scrum world. The fundamental idea of Scrum is team collaboration, and team members "volunteer" for tasks rather than having them assigned. One of the core values of Scrum is courage, and it's not a bad practice to announce at the daily stand-up, "I missed my task timeline today." If that's the case, the Scrum team collaboratively aligns itself to meet the sprint backlog, at least enough to result in a shippable product when the sprint ends. It's certainly possible that not all tasks in the sprint backlog get completed at the end of the sprint, but the Scrum team should be smart enough to plan the next sprint in a way that avoids a similar pitfall.
The keys, then, are accurate sprint planning and a "must-do" sprint retrospective. Most important, don't wreck the Scrum by measuring an individual's work items.