Stat Chug: The Five Runs Plus Outs Limit and Its Effect on the Game

Stat Chug: A specially brewed stats based draft.

The Five Runs Plus Outs Limit and Its Effect on the Game: How the Rule Limits Run Scoring and More

Of the many rules Tapey Beercone adopts by way of Piney Pinecone a very prominent statute is the Five Runs Plus Outs Limit Rule. The rule is stated thus:

Article III: Gameplay Section A: Inning
… A half inning ends when any of the following occur:
-When the third out of any inning is recorded.
-When a sum total of 5 runs and outs are reached and it is not the last inning and a Grand Salami has not been recorded in the half inning.
-When a sum total of 8 runs and out is reached and it is not the last inning.

Little known fact: It’s actually an Eight Runs plus Outs Limit… but putting aside the incredibly unlikely event of a Grand Salami the limiting number is 5. And that’s the first most obvious and self evident effect. You can’t score more than five runs. As previously documented this is a rare and impressive feat.

What may be less obvious are the simple outcomes on which the rule has no effect. This being that the rule only kicks in to limit scoring above two runs, and to hold a team to two runs or less still requires the defense record three outs. This means the rates for things such as shut out innings should be equal regardless of whether it is a last inning or not. And that’s about what we see. 31% of normal innings end in zero runs scored, and the figure is nearly equal at 27.5% for last innings. This also lends credence to the concept of a quality inning. This being any inning where the defense holds the batting team to two or fewer runs and therefore ends the innings without the assistance of the rule. Quality innings occur approximately 54% of the time, it’s no outstanding feat, but it at least shows the defense achieved average or better results.

  • Quality Inning – Any inning pitched resulting in 2 or fewer runs scored. (Requires defense to record three outs regardless of inning)

Beyond the low scoring totals for which the rule has no effect, one may wonder in what ways the rule limits high run scoring innings. By far the most common outcome is for an inning to be limited to three runs scored meaning the defense is able to record a second out before the batters score four, or visa-versa the offense gets a third runner across before the defense records the third out. This inning end state occurs in 24% of innings to date, nearly as often as the shutout inning.

Normal inning outcomes charting actual versus modeled results.

Once a team scores at least two runs in an inning, they very often find themselves in situations where both outs and runs can end an inning, once four total runs and outs are reached, be it 2 runs-2 outs, 3 runs-1 out, or four runs-no outs. The refrain is often heard shouted by one of the contestants, “Next run or out ends the inning!” Reminding the other players of the game state and the stakes of the current at bat. These situations create unique psychology for the players. It crystallizes the goal for the remainder of the inning: “Just get one out”, or “Just get that next runner home.”

An inning ending play regardless of outcome. Either “Artillery” makes it home safe for an inning ending run, or “The Wildcat”‘s throw beats him to the plate for an inning ending out!

With a definite goal in sight the inning takes on a more heightened and excited feeling. But the irony of this is that with this limit in play the leverage of the inning (the variation in run scoring outcomes) is significantly limited. For an example in a “next run/out ends the inning state” with the bases loaded the run scoring leverage is over three times less than the similar bases loaded state with no runs limit. This is because any hits in the latter state can score multiple runs and the inning continues make the recording of an out much more important.

So the rule has obvious and not so obvious effects on the innings, but what about the game as a whole? Here the effects become even more dramatic. Modeling of inning scoring based on league averages predicts about 2 runs scored per normal inning versus 3.2 runs per last inning. Without the runs/outs limit this would increase average scoring per game from around 13 runs per game up to nearly 20. Further to scores these runs would mean more runners, more batters and thus more at bats. A normal inning ends after an average of 5.7 plate appearances, but last innings average over seven. Taken over the course of a six inning game this would add on average 15 extra batters, which would add about 45 minutes to nearly an hour to the length of what is typical a three hour game.

Last inning outcomes charting actual versus modeled results

And with this we get to the crux of the issue. This being the repercussions of adding an extra hour to a game involving exorbitant beer drinking. Assuming that players’ drinking frequencies were held constant, but that games lasted on average four hours instead of three (a 33% increase), this would propel league average BPI from 1.17 all the way to 1.56, a level that nearly no player can match under the current rules. Even granting that the players would have an extra hour to work off the booze, this would still push up average end of game Inebriation from three and a half beers to over five! That’s a level that only the game’s heaviest drinkers are able to manage, and not always too well… One wonders if the average player would make it to the end of the game without the runs/out limit rule.

How many more Beerpopes would there be, if not for the Runs plus Outs Limit?…

That’s just one more interesting fact to consider as you reach into the cooler for another cold one.


Author: The Coach

#8 The Coach, founding Regent of Tapey Beercone.

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