Be honest with me for one second. Have you ever watched the Reds struggle to score runs (first 9 games of the year), go on an offensive tear for a game or two (21 runs scored vs the Marlins), and then think that they “used up” all their offense and are destined to go back into a slump? I have, and that is why I did some research into the idea that the Reds offensive production for a game tomorrow may be influenced by how they performed in a game today. In terms of my theory, the numbers do not support it at all. However, there was one takeaway that could somewhat be applied to the current state of the Reds offense.

Looking at the past 1500 Reds games (dating back to September 2009), I calculated the average number of runs scored in a game that immediately followed a prior game. I factored out off-days, All-Star breaks, and off-seasons to ensure I only captured games where “momentum” was immediate and could be a real factor.

The average number of runs scored over the time frame was 4.3. Based on a formula that creates four groups based on standard deviation from the mean, the data fell into the following quartiles:

Quartile 1: 6 or more runs

Quartile 2: 4 or 5 runs

Quartile 3: 2 or 3 runs

Quartile 4: 0 or 1 run

The first connection I checked was if there were more low scoring games immediately following a high scoring game. The table below shows that is not the case, and over the last ten years, was less likely to happen to the Reds.

If you do not like reading tables with numbers as much as I do, here is a summary:

- When the Reds scored 6 or more runs (31% of the time):
- 29% of the time they scored 6 or more runs the next day
- 28% of the time they scored 4 or 5 runs the next day
- 27% of the time they scored 2 or 3 runs the next day
- 16% of the time they scored 0 or 1 run the next day

Stopping here for a minute, we can see that the Reds actually had a higher likelihood of posting another high score and scored 3 or less runs only 43% of the time.

- When the Reds scored 4 or 5 runs (25% of the time):
- 33% of the time they scored 6 or more runs the next day
- 25% of the time they scored 4 or 5 runs the next day
- 27% of the time they scored 2 or 3 runs the next day
- 15% of the time they scored 0 or 1 run the next day

The red highlighted cells show that when the Reds scored 4 or more runs, it was less likely that they would score 1 or less runs the next game. The much more common and equally realistic occurrence was anywhere between 2 and 8 runs.

- When the Reds scored 2 or 3 runs (27% of the time):
- 30% of the time they scored 6 or more runs the next day
- 25% of the time they scored 4 or 5 runs the next day
- 25% of the time they scored 2 or 3 runs the next day
- 20% of the time they scored 0 or 1 run the next day

Also similar to the first two quartiles but with a higher chance of scoring 0 or 1 run. On to the last one.

- When the Reds scored 0 or 1 run (17% of the time):
- 28% of the time they scored 6 or more runs the next day
- 22% of the time they scored 4 or 5 runs the next day
- 28% of the time they scored 2 or 3 runs the next day
- 22% of the time they scored 0 or 1 run the next day

Here is where we see the biggest change in pattern by far, as the percent of occurrences of less than 3 runs jumps all the way up 50%. It is not huge, but it definitely does not fall in line with the other groups. The other interesting data point is the average runs scored in the next game. Quartiles 1 to 3 range from 4.3 to 4.5, while Quartile 4 sits at 4.08. Again, not a huge difference, but enough of a variance from the other groups that it seems to point to something.

To follow up on this idea that poor offense could be “contagious” from day to day, I looked at each number of runs scored per game and the average runs scored on the following day.

Factoring out some of the outliers at the top (only 6.5% of games had 10 or more runs), there are a few numbers that stick out here. When either 4 or 6 runs were scored, the average runs scored the following day was 9% higher than average. That falls somewhat inline withe the previous chart, but also seems to be a bit random. If the team played well offensively, there really is no data suggesting they would play well again or totally forget how to hit. However, the number that stands out the most to me is when the Reds were shutout the previous day.

Based on this data set, the game after a shutout was 12% below average for run scoring. Looking at the first week of games this year, the Reds were shutout in three consecutive games. The average runs they scored in the following games was 1.67, which obviously checks out below the mean. This is an extreme example but the larger data set shows a slight historical trend. Playing poorly one game translated to a worse than average game the next day. Scoring less than two runs in a game means that almost everyone on the team struggled, which could take a day or two, maybe even a week to work through. Or in the case of the Reds this year, the better part of a month.

Slumping is contagious.

Fascinating post. I wasn’t expecting to see much of a drop-off in runs scored the game after a shutout. Figured that was just a “when it rains, it pours” feeling without any statistical backing. Interesting that there’s at least some relationship. I’d be interested to see if this still applies across all MLB teams.

I was thinking the same. I wonder if this applies across the board with other teams. This was great work with the data.

Thanks. It was a bit manual getting the data, I have yet to get into more advanced tools that would make this easier but if I get really bored one night then maybe I will give it a go for the entire league ha

Scoring can be fickle. I would be more curious of the relationship between OBP from game to game. You can reach base ten times and still get shut out, or score six on four hits due to errors, etc.

Interesting thought. By that logic, I would think OPS would probably be better as a measure for how the team was hitting as well as getting on base.

Good point!

First glance looks like there is actually less of a trend for OPS:

Average runs scored following a Q1 – Q3 game: 4.40

Average runs scored following a Q4 game : 4.08 (7% lower)

Average OPS following a Q1 – Q3 game: 0.718

Average OPS following a Q4 game: 0.695 (3% lower)

Thank you thank you thank you! This is fascinating even with all the charts

I hope you follow through on this for the rest of the year And after the World Series, too. That way we could all use our own selection bias to explain why it happened on certain days. If nothing else of course we can blame Jose Peraza.

Seriously though, I’m amazed that I’ve never seen this type of investigation, before. I look forward to the comments

Thanks again

Appreciate the interest. It does seem like something to dive into more but I will need to work on my data mining skills!

One theory for the low scoring could be fatigue as it would generally hit players somewhat equally since they’re on the same travel/sleep schedules.

Offensive momentum is inversely proportional to the ability of the next day’s starting pitcher.

I figured that 1500 games would be a decent starting point for factoring out a lot of variables. Most pitching staffs will have good and bad pitchers and pitching matchups are very random for the most part. I think it would be more valuable to look at the entire league rather than just the Reds

Interesting stuff, thank you for looking at the data. Curious to know if you did any statistical analysis to see the likelihood of getting these results through random variance (which is not to say that team scoring is random in the aggregate, but rather that team fluctuations, themselves dependent on individual player fluctuations, generally contain a lot of different variables that all vary this way and that over the course of a season).

I took a quick look at the counts of games in each quartile plus the quartiles for their follow-up games and input them into a chi-square table. The result is that you could get this same assortment of games and scoring results 47% of the time without there being a genuine connection between the different data points.

You didn’t present the raw data (for obvious reasons) but I would be curious to see what would happen if you compared the mean runs scored in each quartile to see the odds that they would vary due to random variance vs a real change. The avg. runs scored in Q1, Q2 and Q3 are all so close to each other that I’m not sure we can conclude that they represent true fluctuations in underlying team performance (as opposed to variance caused by randomness, pitcher matchups, ballparks played in, injured players, etc.).

The avg. runs scored for Q4 are low enough though that it would be cool to see if that tests out as being significantly out of whack with the other quartiles, especially since that is the one group of games for which the odds of continuing to score at a below-average clip outpace the odds of reversing that trend.

It’s also possible that team-wide slumps are more likely to show in the data when we examine 4 or 5 game stretches as opposed to just the game immediately following. Of course, that’s also less interesting because everyone knows at that point that the team is slumping.

In any case, those were just some varied thoughts I had while reading your piece; thanks again for doing the work to look at this information.