As you can see, Columbus shot less frequently when in the lead. This is a pretty typical trend.
Using logistic regression, we can evaluate the effect of shots and shot quality on a leading team's chances of conceding the next goal. The model I've built, like Garry's, breaks down a game into a sequence of game states. The game begins at 0-0, and each time a goal is scored, a new game state segment begins. My model takes as inputs the number of shots the leading team takes, and the average quality of those shots (using the site's expected goals model) during a segment. It then outputs the probability of that team conceding the next goal.
In general, teams that shoot more are less likely to concede the next goal in a game. Teams that take better shots are also less likely to concede the next goal. If we include only situations where a team is up by one goal, the same results hold. However, if we only look at time frames towards the end of games and where teams are up by one goal- situations where parking the bus would be appropriate- things change.
To examine the problem this way, I've built separate models using data filtered by when each segment begins. I've filtered the data this way since I'm hoping to answer the question of when a team should start to go into a defensive shell. Using the start time of the segment, I think, is a good though not perfect proxy for this. For example, then, to see whether parking the bus is a good tactic up a goal after 70 minutes, the model is built using data from game segments which begin on or after the 70 minute mark. Note that as a point of interest I've also included whether the leading team is home or away as a variable in the model.
The chart below shows the minute mark I've filtered by, and whether each of the three variables for the leading team- shots, shot quality, and venue (home or away)- has a statistically significant effect on whether that team concedes a goal.