Similarly, the win expectancy with 2-run lead in the 8th with none out (0.870) is higher than the win expectancy with 1-run lead in the 9th with none out (0.842). The win expectancy with 2-run lead in the 7th with none out is 0.824, which is much larger compared to the win expectancy with 1-run lead in the 8th with none out (0.753). But there's much bigger benefit when one can have a bigger lead going into late game situation. Granted, 0.026 over 162 games is a bit over 4 wins, so that's nothing to sneeze at. So the threat of a shutdown bullpen is largely overblown, since even the best three-headed monster won't do much better over the standard win expectancy table.
Even with three Wade Davis's, the win expectancy after 7th inning would only be 0.726 as opposed to 0.700. Based on this list, one would have to clone two more Wade Davis's to hold onto a 1-run lead in 7th inning above the standard win expectancy probability. So if the Yankees are trying to hold onto a 1-run lead from the 7th inning, there's still a 44% chance that they will lose if they don't score any run afterwards. As an example, the trio of Chapman, Miller, and Betances have allowed runs in 16.9%, 18.3%, and 17.6% of their appearances in 2015.
The % of appearances with runs allowed does not necessarily reflect true talent level since we don't account for the context of each appearance, but the overall message should be clear: it's very difficult, if not impossible, to construct a bullpen that can hold down a 1 run lead in 7-9th inning. Here, I counted their appearances with any runs allowed (not limited to earned runs) and checked the % of appearances with at least some runs allowed. Let's take a look at the top 10 relievers by ERA with at least 60IP in 2015. This means that if we need three reliable relievers to "close the game", we would need three relievers who individually allow a run to score in less than 11.2% of their appearances. Finally, the win expectancy at the top of the 7th, up by 1 run, with 0 outs is 0.700. The fact that two pitchers will have to handle two innings actually means that two pitchers that allow a run to score in less than 13.2% of their individual appearances. So we need two pitchers to collectively put up a zero with greater than this probability. The win expectancy at the top of the 8th, up by 1 run, with 0 outs is 0.753.
By similar logic, we can look at the qualification of a set-up man plus the closer. The win expectancy at the top of 9th, up by 1 run, with 0 outs is 0.842, so we would need a pitcher who allows a run to score in less than 15.8% of his appearance. So let's think about what the job qualification would be for an ideal "closer", who handles the 9th inning. Once the opponent scores a run, our imaginary team will lose for sure. What are the characteristics that we would want for the bullpen? The objective here is to minimize the probability that any run would score in each inning. It will be entirely up to the bullpen to put the game away. Now let's do a thought experiment: imagine a team that will always lead by exactly 1 run at the top of the 7th (as a home team) but will not score any runs after that. I will use the simplest definition, which is that the leading team wins the game without letting the opponent score. Let's begin by thinking about the act of "shutting down an opponent". The numbers and data used in this post are taken from the 2010-2015 Win Expectancy matrix () and Fangraphs. I will use Win Expectancy to make this argument. In this post, however, I will show that while there can be a shutdown closer, the concept of a shutdown bullpen that can end games early by closing out the 7-9th inning is largely a myth. Critics of the Blue Jays might point to the three-headed monsters in New York or Boston and claim that the front office has failed in creating a reliable bullpen that can end games early. Bullpen is also a big topic across the league right now, with a large amount of the Royals' success credited to its bullpen and many teams moving to imitate the Royals. With the Blue Jays bullpen leading the league in loss at 0-7 with 5 blown saves in just 21 games, naturally there is an increasing scrutiny on individual reliever performance and bullpen construction.