Just How Big is the "Big Inning?"

Baseball fans know the feeling.  It's not a great feeling, but any regular viewer of the game will recall the sensation of frustration and futility that is nearly impossible to avoid over the course of a long season.  Perhaps your humble statistician will be able to paint a picture of the feeling: it's in the early innings, and your team's starting pitcher is holding off the other team's sluggers, all while your lineup has managed to scrape together a few runs off the opposing starter.  Then, seemingly out of nowhere, the other team kicks off a string of hits that keeps on going longer than it has any business doing.  And before you know it, your team has fallen into a hole that would take a miracle to overcome.  Your pitcher looks exhausted, your lineup looks demoralized, your skipper looks ready to throw in the towel... what to do now?  

Padres left fielder Ryan Ludwick walks past the Green Monster in Fenway Park after Boston’s 10-run seventh inning in a 2011 blowout.
Photo (c) Associated Press

Someone once told me that "half of all baseball games are won by one team scoring more runs in one inning than the other team scores the entire game."  I haven't been able to track down whether or not this is an actual quote (although I was able to find one apocryphal attribution to Earl Weaver) or just another generally accepted baseball truism, like "players perform better in contract years."  But then, maybe it's possible to answer for ourselves whether or not this hypothesis should be regarded as baseball lore or baseball fact; like all the big questions raised on this blog, the truth lies somewhere in the data.  And like Michelangelo and his slabs of marble, it will be up to us to find the figure that resides within and carve away the rest.

BURNING QUESTION

For this postulate, the premise is simple enough: Over a given period, what proportion of games ended in which the winner's single highest-scoring inning exceeded the loser's score for the game?  All recorded game across the selected period will be our data points, and we'll need to divide all of our data points into one of three categories: (1) games where the winning team's greatest single-inning run count was strictly greater than the losing team's run total for the entire game, labeled "TRUE", (2) games where the winning team's greatest single-inning run count was strictly less than the losing team's run total for the entire game, labeled "FALSE", and (3) games where the two counts were equal, labeled "PUSH" to designate an indeterminate result.

As for the range of data points, I see no reason to limit datasets to anything less than full seasons' worth of games (2430+ games for modern-day seasons), and it might even be worth comparing results across seasons.  Could there be a big discrepancy between seasons in one decade versus another?  Could the dead-ball era have experienced many more close games (i.e. greater chance for FALSE results) than the live-ball era?  How were a team's odds of winning impacted by achieving a "big inning"?  With the right dataset, it should be possible to visualize our results, and secure an answer to each of these questions in turn.

SOURCE DATA

I set out first to gather my dataset.  Starting out with the usual suspects, i.e. Baseball-Reference.com and Society for American Baseball Research, I was confounded to find that neither site appeared to have the required depth of records.  The critical yet elusive datum was the breakdown of runs scored per inning: nearly every resource has box scores and individual player contributions for each official game, but apparently none offered extended box scores that showed the number of runs recorded by inning.  I couldn't perform the research based solely on R|H|E box scores, so I was forced to continue searching.

That's when I discovered that many of these sites get their own raw source data from Retrosheet*, which describes itself as "more than an encyclopedia of the history of American baseball."  Retrosheet's game logs do indeed contain breakdowns of runs by inning, as well as other intriguing details like whether the game was part of a double-header, whether the game was played at night, and a summary of team performance statistics.  All of these features will make for excellent data mining possibilities in the future; but for now, we're only interested in the line scores, which will make this experiment possible. 

SOLUTION

Now it was time to code a script to handle all of the massive amounts of individual games I would need to sort.  The use of regular expressions ("RE") would be a must for handling the breadth of information compressed into comma-delineated lines, the storing system used in Retrosheet's voluminous .txt files.  In fact, there would prove to be enough variance across the 119 season logs covering the years from 1900 to 2018 that it proved most feasible to simply tokenize all of the 19 individual features leading up to the Home and Visitor line scores, even though they would immediately be discarded.  This doesn't require an excessive amount of computing power, so it was certainly worth the extra processing cycles to guarantee a reliable output.

With the individual game lines successfully tokenized, all that was left was some simple math to determine the label that would be applied to each data point.  I used a for loop to iterate through the individual inning run counts, finding the maximum for the winning team and the sum for the losing team.  Then a simple comparison determined the result: for a particular game, if the losing team's total was greater, mark the game "FALSE"; else if the losing team's count was less than the winning team's inning, mark the game "TRUE"; else if the two values were equal, mark the game "PUSH".  Then I wrapped this simple algorithm in an outer while loop to iterate through all of the games recorded in a given season, keeping tallies of each of the results for that season.

RESULTS

The output for the experiment was consolidated into three simple values: the percentage of data points that were labeled "TRUE", the percentage that were labeled "FALSE", and the percentage that were labeled "PUSH".  Since these were the only three possible results, every season breakdown would sum to 100%, but the results across seasons would vary.  These variances in the distribution of TRUE and FALSE results would give us the answers to two questions: What is the average percentage of TRUE results across all seasons, and do individual results vary greatly from season to season?

The experiment ultimately proved fruitful.  Not only was it possible to see the trend of TRUE results across years, there was also some noticeable correlation with known baseball eras.  The graph below shows the breakdown by season, along with the overall recorded average:

Most seasons did not reach the 50% mark for the TRUE category as predicted in the proverb, but nearly every season was near enough to the mark as to give it credence.  Especially considering the volume of PUSH results: in each of these cases, the winning team scored exactly as many runs in one inning as the losing team scored in the entire game.  Since we're operating under the assumption that every team's goal is to win as many games as possible, this category should still be regarded as a desirable result.  And since the sum of TRUE and PUSH results was always well above 50%, this suggests that achieving a big inning has a meaningful, if measured, impact on the outcome of the game.

The first outlier that jumps out is 1968: in that year, 55% of baseball games ended with the winning team scoring more runs in one inning than the losing team scored the entire game, a rate of nearly ten percentage points higher than the 69-season average.  Students of the history of the game will recall that 1968 holds a special place in baseball lore, known as the "Year of the Pitcher."  In that year, a paltry 3.42 runs per game were scored across baseball, down 14% from just two seasons prior, and a full 25% down from 1961.  In fact, from 1963 to 1968, the average count of runs per game was so low, that this likely accounts for the jump in TRUE results across that period: mathematically speaking, the odds of achieving a TRUE result in our analysis go up the lower the average runs per game is.

The opposite is also true.  Consider the valley observed across the seasons 1994 to 2000: in a time when offense was prioritized, baseball saw some of the highest runs-per-game averages in history, reaching above 5.0 runs per game for most of that stretch.  When even the losing team is scoring a little under 5 runs per game on average, it is far less likely that the winning team will have scored at least 6 runs in a particular inning, driving down the rate of TRUE results in those years.  

CONCLUSIONS

The implications of our research are intriguing:  the proverb that was the catalyst for our curiosity proved to be almost true, and certainly close enough to permit veteran bench coaches to repeat it without fear of reproach.  In this case, the baseball wisdom holds up.  And in the end, we were indeed able to find answers to our questions:

• What percentage of games does the statement hold true? 
  In a little less than half of MLB games, the winning team scored more runs in one inning than the losing team scored the entire game.
  
• Are there noticeable variances across greater spans of time?
  Yes.  Specifically, in periods with less scoring, the odds of this kind of result occurring is greater than in periods with greater scoring, owing to the fact that it is far more likely for low-scoring games to have the winning team's runs concentrated in a single inning than it is for high-scoring games.  In other words, a 1-0 scoreline will result in a TRUE result 100% of the time, while a 10-9 scoreline will result in a TRUE result about 0.001% of the time.
  
• How much does achieving a "big inning" impact a team's odds of winning?
  Measurably, although it's certainly not a guarantee.  For data point examples drawn from the small-ball '60s, a big inning in one of those games could more than double a team's chances of winning (+130% in 1968).  But in the homer-happy '90s, a big inning wasn't enough to guarantee victory - in fact, it only improved your chances by about 18% in 1998.  All in all, it still came down to how well your defense held the other team from catching back up in the late innings.

So, it would turn out that the pitcher has more of an impact on the outcome of the game than even the offense's ability to achieve a "big inning" across the course of a game.  And in light of our definition of a big inning, this makes sense: essentially, our definition of a "big inning" changes depending on how easily the opponent is able to score.  In a game where only three runs are scored, a 2-run inning is a big inning.  But no doubt our dataset includes  teams that earned 3 runs, all in one inning, yet ultimately lost to teams that scored 4 runs in an inning (TRUE result) or lost to teams that scored 1 run each over four innings (FALSE result).

The upshot of this analysis is that the strategy for a team that gives up a big inning to its opponent changes in virtually no material way.  Sure, that team can afford to be more aggressive in situations that warrant a judgment call, like stealing second base with 1 out.  But overall, runs come in either small bits or big chunks, and either approach will be needed to pull your team out of the fresh new hole it has just dug itself.

*The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at www.retrosheet.org.