Bases loaded, no outs is one of the most tenuous points of a close baseball game. If you are rooting for the team at the plate, you feel confident your team will score here. Anything else, would be a huge disappointment. If you are rooting for the fielding team and your pitcher gets out of the jam, you are elated and praising the pitching staff for being able to handle pressure. Even though bases loaded, no outs (BLNO) seems like a sure thing, there is about a 15% chance the team DOESN’T score at all.

I’ve created this table of probability of scoring AT LEASE ONE RUN in the various base-out state situations using data from 2011-2013. The base-out states represent the 8 possible combinations of runners on base with the 3 out states that can exist [24 total]. 1- – means there’s only a runner on first, 1-3 means first and third, and 123 is bases loaded. Looking at the chart there is only an 85.18% chance that the team with BLNO scores a run. It’s one of the highest run probability situations, but there’s still a significance chance they won’t score a run.

This table considers every play that started with this base-out configuration and looks at the remainder of the inning to see if the team scored. [It uses every play in baseball from 2011-2013 including playoff games.] In general these numbers fluctuate slightly over time and between teams. This table is also context neutral, specifically batter neutral, so having Mike Trout at bat would significantly change the probability versus a player like Clint Barmes.

Looking at the table, it’s apparent to score AT LEAST one run the lead runner is the most important factor, since all the base-out states have similar probabilities between the states when the lead runner is at third or second. So having a lead-off triple is about as valuable [in the context of scoring ONLY one run] as having the bases loaded, no out.

There are different run and out possibilities that exist with each base-out state. For the lead-off triple, there is no force play on the bases, while a bases-loaded situation has a force play at every bag including home. Having bases loaded would turn a ground ball into a potential run robbing force play, while a single runner on third would require a tag. Conversely, BLNO allows for walks and hit by pitches to drive in a run. This table also looks uses the entire rest of the inning, not just the play that occurs with BLNO. So if the team got the bases loaded with no out, gets two outs, then scores a run, it still counts as a success. A double play, which is easier to get with bases loaded than just a runner on third, will dramatically reduce the run probability of the next play affecting the previous base-out state. In summary, there are trade offs that can occur effecting the overall, context-neutral probability of the base-out state.

Example — Pirates Game

*Failing to score a run in the context of this post means after loading the bases, the team does not score any runs before the end of the inning. All the probabilities are determined empirically.*

Something kind of cool happened during the Pirates game last night (8/8/2014). There were two instances that bases were loaded with no outs, and the teams weren’t able to score any runs. The not being able to score any runs with the bases loaded/no outs isn’t that uncommon. A run-probability table can tell you that ~14% of the time a team will fail to score any runs for the rest of the inning after achieving that base-out state.

*A base-out state is one of the 24 possible combinations of baserunners and number of outs. So there are 8 base states, bases empty, runner on first, etc. to bases loaded, and three different out states, 0, 1, or 2 outs. 8 x 3 = 24. *

In the control room at the Pirates game last night, we were debating how often you see two occasions in the same game where no runs are scored after the bases are loaded with no outs. It turns out it relatively rare, but it happened twice at PNC Park before 2014: May 12, 2002 and August 28, 2003.

Between 2003 and 2013, bases were loaded with no out and no runs scored 1,092 times. There were 25 games that this happened multiple times, which is 0.0923% of all games played during that time [27,094 games]. This is on par with the probability of seeing a no-hitter (0.111%) and less probable than seeing a walk-off walk to end the game (0.266%).

The probability of seeing a game with two or more non-scoring bases loaded/no outs situations is 0.0923%

Using the table below bases empty/no outs will occur in every game (this happens at the start of every inning), and all the other base-out states have varying frequencies with runners on third with low out-states being the rarest. Bases loaded/no outs is the rarest base-out state occurring in only 21.92% of all games and occurring twice in the same game only in 6.05% of all games.

Just for reference here is a chart of how often the base-out state events occur relative all events. This would represent the probability that any random event (plate appearance, at-bat, stolen base, etc.) would have that base-out state.

*All data is from retrosheet.org*