On a recent Effectively Wild email show, Ben and Sam explored the question of whether all 24 base-out states had ever occurred in a single game. It turned out that it had, albeit very rarely: about once every fifteen years. The question did capture the imagination of quite a few EW listeners, and Baseball Prospectus writer Jeff Long even created a Base-Out Bingo card:

This discussion got me thinking: what if you wanted to play but didn’t want to wait fifteen years to win? That, of course, also assumes you had the right game on in the first place, and as Sam pointed out, you probably wouldn’t have realised you saw the last time this happened even if you had watched the whole game at the time. (Disclaimer: if the idea of seeing if you can watch all 24 base-out states in a single day seems incredibly nerdy and not at all interesting, you probably won’t enjoy the rest of this post).

The game should be much easier if you weren’t limited to one game. What if you could switch from game to game, hunting down the various states? Stuck with a pitcher’s duel and need the bases-loaded states? No problem; just switch over to the game where the starter with poor control has already walked three in the second inning. Need to have a man on third with no outs? Flip over every time Billy Hamilton or Dee Gordon is at-bat and look for a triple.

While the game would definitely be easier, there would still be a few sticking points. Having a man on third with no outs obviously only usually happens on a triple, or perhaps a stolen base, wild pitch or passed ball following a double. Getting all of the bases-loaded states wouldn’t be so easy all at once; even a single with no outs probably scores two runners and leaves you needing a specific sequence of events to get back to bases loaded with one out.

Before suggesting that anyone should try to play, it seems prudent to answer an important question: is it even possible that you could win on any given day, assuming a full slate of games? To answer that, we need to know the frequency of each event. I used the Play Index Split Finder to get a list of every team’s plate appearances in the 2014 season, split by the various base-out states. Below is the table showing the number of plate appearances and the percentage of PA in which every base-out state occurred.

First of all, we don’t need to worry about bases empty with any number of outs, as every inning starts with that state. Just over a quarter of all plate appearances in 2014 came with the bases empty and no outs.

The same goes for 1 and 2 outs. In fact, there was only one team who managed to make it through a single game without having the bases empty with two outs: the Los Angeles Dodgers. Even picking a game with that rare occurrence, of course, wouldn’t pose a problem, as their opponents achieved that state in the same game.

As you might expect, having a man on first with any number of outs is also pretty easy to cross off. While it’s possible to watch a handful of games a year in which one of the teams doesn’t achieve one of these three states, both teams doing so is incredibly unlikely.

Moving into the states when third needs to be occupied is where it really starts to get difficult. The bases are loaded in just 2.2% of all plate appearances. Second and third occupied is even less common, at 2.16%. Just a man on third is a little simpler, but if you need it to happen with no outs, it’s really starting to get tricky. Teams only had a man on third with no outs 485 times in the entire season. Assuming that they are distributed evenly (which they won’t be, but we’ll get to that later), that’s still around three per day, so you could spend all day watching games and have a pretty good chance of not seeing that particular state.

That brings us back to our original question: is it possible to win every day of the season? Clearly each state happens often enough that there’s a reasonable chance to do so. If even the rarest possible state happened 485 times in 2014, there’s no reason why you wouldn’t see a triple with no outs, or a double and an error, on any given day; you just have to be watching the right game. There’s no guarantee you’d see it by watching two, three, or even four games, however; even the teams that achieved this state in the most games in 2014, the Giants and Diamondbacks, did so in just 22 games. If you’d watched every one of San Francisco’s games from start to finish, there was just a 13.6% chance of seeing a man on third with no outs on any given day.

There were 16 dates during the 2014 regular season on which no-one hit a no-out triple and therefore you would not have been able to complete your bingo card (I’m going to avoid dealing with any events that would move a man from second to third before the conclusion of the next PA as a full list of these specific events is much more difficult to come by). I went through them all and found that only four featured a full slate of games, and one date, July 1^st, actually had 16 with a doubleheader. Many came on a Monday or Thursday and five of the dates saw fewer than 10 games played. Interestingly, all four of the dates on which a full slate did get played were within a six-week period between the start of July and the middle of August, which raises the question of whether players triple less in the hotter months.

The good aspect of the no-out triple is you are guaranteed to have a chance at it at least 17 or 18 times a game: every time a new inning starts there is the opportunity it could happen as a result of that plate appearance, whereas many games will go by without even getting one baserunner away from having the bases loaded with no outs. In fact, if you look at the possible outcomes that can immediately follow the bases empty with no outs (a man on first, second or third, or bases empty with one out), those 485 PA with a man on third now comprise 1.04% of the total. Not a huge amount, but certainly enough to encourage the budding bingo enthusiast.

The other no-out states that happened in less 0.5% of plate appearances – bases loaded, first and third, second and third – could also be difficult to get, but all happened over 150 times more than the rarest state. Beyond that, every other state happened more than 1500 times during the season and of course, if you get those difficult ones with no outs, you then have a much better chance of getting the same state with one or two outs, as a strikeout and potentially the right kind of batted ball out will keep the baserunners where they are. Nevertheless, it is still very possible that you could watch two or three full games without getting all the states.

We don’t have to do that, of course. Being able to switch games whenever you want means you can maximise your chances of achieving the required states. How likely you are to win really depends on how successful you are at switching game at the right time and picking the right game to switch to. I have plenty more thoughts on the best ways to win, but wouldn’t that take all the fun out of it? Now that we’ve established that it isn’t ridiculous to think that we could win on any given night – even if there will be a few days a season in which it is impossible – here is my proposal for how to play Base-Out Bingo:

1. Find a group of suitable baseball fans, perhaps listeners of a particular daily podcast, to play with.
2. Pick a day with a full slate of MLB games.
3. Cross off each state as you see them live, recording the game, time and players for confirmation.
4. States must be seen live, at some point before the following plate appearance concludes, or the state changes in another way (such as a runner being picked off). States seen by skipping back an inning or watching an already completed game do not count.
5. You win when all 24 base-out states have been crossed off before the end of the night.

Join the Effectively Wild group on Facebook if you’re interested in getting involved. I’ve taken a look at the numbers from 2014 but the truth is we won’t really know how easy it is to win until people actually play.

There are more variations you could try. I have already suggested playing as a team of viewers to see how quickly all 24 can be achieved. You could play by just crossing off the states for the team you’re a fan of and keep going until you hit all 24. Be warned, though: the Orioles had just seven plate appearances with a man on third and no outs in 2014. It’s possible you could be playing for months.

Another alternative is to simply see who crossed off the most states at the end of the night, or perhaps at the conclusion of a set of games that started at the same time. This has the advantage of a finite endpoint but it’s not quite as satisfying to say you won with 21 of 24 states.

Feel free to submit your own suggestions or improvements in the comments. Base-Out Bingo is going to sweep the baseball world, so if you really want to be a trend-setter, you’d better grab your card and start playing.