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Do throws to first do anything?

Yes they do.

Based on actual data from 2002-09 the stolen base percentage of a runner decreases if at least one throw is made over to first by the pitcher:

Stolen Base
Percentage
No Throw Made 75%
At Least One Throw Made 64%

In fact, it even makes a difference if he makes more than one throw:

Stolen Base
Percentage
One Throw Made 66%
Two Throws Made 65%
Three or More 64%

Both of these conclusions match what we found last time. If it's your pitcher making the throws, cheer him on. But if it's the opposing pitcher, it's your job as a fan to let him know that you don't appreciate all those throws!

So the more throws, the worse chance the baserunner has of stealing second.