Category Archives: data visualization

Arizona COVID Cases on Slow Uptrend in Summer 2021

It has been nearly two months since we focused on Arizona's experience during the coronavirus pandemic. When we last checked, it appeared Arizona's level of COVID cases following the surge of uncontrolled immigrant crossings into the state was stabilizing.

That pattern held through the end of May 2021. However, beginning in the first week of June 2021, Arizona has experienced a slow upward trend in cases. That new trend can be seen in the following chart tracking the 7-day moving averages of the state's COVID cases and new hospital admissions. Presented in logarithmic scale, the figures for each data series has been aligned with respect to the approximate date of initial exposure to the SARS-CoV-2 coronavirus variants infecting those who have tested positive for COVID-19.

Arizona's Experience During the Coronavirus Pandemic, 15 March 2020 - 14 July 2021

At this time, the data for COVID deaths is as yet too incomplete to confirm the change in trend across all three data series.

The change in trend appears to roughly coincide with the Phoenix Suns' first trip to the NBA playoffs in more than a decade, which prompted large crowd gatherings and celebrations after the team beat the Los Angeles Lakers in the first round of the playoffs in the first week of June 2021. The team has continued its success, beating both the Denver Nuggets and the Los Angeles Clippers, and is now playing the Milwaukee Bucks for the championship in the NBA finals.

The situation parallels the change in trend we observed in California after the Los Angeles Dodgers won the World Series. The main difference is that Arizona's current upward trend is rising at a much slower rate. We think that difference is attributable to the Operation Warp Speed coronavirus vaccines, which have been successfully deployed to half the state's population, especially the state's senior population, which has reduced the incidence of COVID-related hospitalizations and deaths.

The state is also seeing an uptrend in COVID ICU cases that has really picked up in late June 2021.

Arizona's Experience During the Coronavirus Pandemic, 15 March 2020 - 14 July 2021

The timing of the increase in COVID ICU bed usage is delayed about two weeks behind what we would expect for a major change in the rate of incidence beginning in the first week of June 2021. We think this delay may be similar to what Arizona experienced following the Black Lives Matter protests and riots in late May and early June 2020 because of the age demographics of the participants. Then as now, younger individuals less likely to require hospitalization were infected in relatively larger numbers, which then spread to the older individuals they came in contact with following the event. The older individuals were the ones who drove up hospital admissions and ICU bed usage after they became sick, roughly two weeks afterward.

Exit question: Will any enterprising attorneys make the connection and hold the NBA accountable? They don't seem to have figured out the BLM protest connection in Arizona's May-June 2020 surge in COVID cases....

Previously on Political Calculations

Here is our previous coverage of Arizona's experience with the coronavirus pandemic, presented in reverse chronological order.


We've continued following Arizona's experience during the coronavirus pandemic because the state's Department of Health Services makes detailed, high quality time series data available, which makes it easy to apply the back calculation method to identify the timing and events that caused changes in the state's COVID-19 trends. This section links that that resource and many of the others we've found useful throughout the coronavirus pandemic.

Arizona Department of Health Services. COVID-19 Data Dashboard: Vaccine Administration. [Online Database]. Accessed 25 April 2021.

Stephen A. Lauer, Kyra H. Grantz, Qifang Bi, Forrest K. Jones, Qulu Zheng, Hannah R. Meredith, Andrew S. Azman, Nicholas G. Reich, Justin Lessler. The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application. Annals of Internal Medicine, 5 May 2020.

U.S. Centers for Disease Control and Prevention. COVID-19 Pandemic Planning Scenarios. [PDF Document]. Updated 10 September 2020.

More or Less: Behind the Stats. Ethnic minority deaths, climate change and lockdown. Interview with Kit Yates discussing back calculation. BBC Radio 4. [Podcast: 8:18 to 14:07]. 29 April 2020.

Fewer and Deeper Long Losing Streaks for S&P 500

Compared to the period from 1950 through 1980, the S&P 500 (Index: SPX) of the last four decades experiences notably fewer long losing streaks. But during the last twenty years, those losing streaks have become substantially deeper.

We've calculated the smallest, largest, median and mean declines the S&P 500 experience during its longest losing streaks of six trading days or longer in duration beginning in the periods of 1950 through 1980, 1981 through 2000, and 2001 through this point of 2021. That information is visualized in the following chart:

Magnitude of Declines in the S&P 500 During Its Longest Losing Streaks, 3 January 1950 - 2 July 2021

The median and mean decline of the index' value is roughly similar in the periods for 1950-1980 and 1981-2000, although the number of losing streaks declined. But since 2000, while the number of long losing streaks has continued to fall, the magnitude of the associated decline of stock prices has become much larger when they have occurred.

Previously on Political Calculations

Visualizing Long Winning and Losing Streaks for the S&P 500

With the S&P 500 (Index: SPX) having ended its latest prolonged winning streak of 7 days earlier this week, we wondered how frequently such long streaks for the index happen.

We're defining a long streak as lasting six or more trading days. Since 3 January 1950, the index has experienced 321 long streaks. 208 of those have been winning streaks and 113 have been losing streaks. The longest winning streak of 14 days began on 26 March 1971. The longest losing streak began on 22 April 1966 and lasted 12 trading days.

We've generated the following barcode chart to visualize each of the S&P 500's long streaks since 3 January 1950:

Long Streaks (6 Trading Days or Longer) in the S&P 500, 3 January 1950 - 7 July 2021

In the chart, we're using the horizontal axis as a timeline, with the vertical bars marking the date each long streak began. The duration of the streak is shown by the length of the bars - these are shown as positive values if they were winning streaks and negative values if they were losing streaks. Periods where streaks occurred more frequently appear as thicker bars, while periods where long streaks were sparse appear as empty or blank space.

Overall, the combination of the relative frequency of the long streaks and the scale of the chart produces a visualization that looks a bit like a UPC barcode.

The visualization does reveal a number of interesting patterns.

  • Long streaks were much more common in the first three decades of this period than they have been in the most recent four decades.
  • Long winning streaks are more common than long losing streaks.
  • Long losing streaks have become more rare since 2000.

Here is some data to quantify these observations.

From 3 January 1950 through 31 December 1980, there were 120 winning streaks and 72 losing streaks, a W/L ratio 1.7-to-1. From 2 January 1981 through 2 July 2021, when the S&P 500's most recent long streak began, there have been 88 winning streaks and 41 losing streaks, a 2.1-to-1 W/L ratio.

Splitting this latter period roughly in half, from 2 January 1981 through 31 December 1999, there were 44 winning streaks and 26 losing streaks, a 1.7-to-1 W/L ratio, similar to what was seen from 1950 through 1980. Since 3 January 2000 however, there have been 44 winning streaks and 15 losing streaks, nearly a 3-to-1 W/L ratio.

What changed in the last 20 years to produce that outcome? Is it a statistical anomaly where we'll eventually have a period characterized by clusters of long losing streaks as the trend reverts to the mean? Or has something else changed to stop losing streaks in the S&P 500 from becoming long losing streaks during this period?

We don't know the answers to these questions. As far as we know, we're also the first to report these observations, but if we learn others have noticed and reported it, we'll add that information to the end of this post. For now though, we're very happy to find ourselves back at the cutting edge of discovery!


Yahoo! Finance. S&P 500 Historical Data. [Online Database]. Accessed 7 July 2021.

Previously on Political Calculations

U.S. Teens Lead Coronavirus Recession Job Recovery by Age Group

U.S. teens have become the first demographic group to fully recover their pre-coronavirus pandemic recession job levels as measured by percentage of the population employed.

That surprising result is visible in the following chart, we've tracked the non-seasonally adjusted employment-to-population ratio the various 5-year age group cohorts whose employment status is tracked through the Current Population Survey. The chart covers the period from January 2017 through May 2021, where February 2020 represents the last month before existing trends were broken by the negative employment impact of the coronavirus pandemic arriving in the United States.

Percentage of U.S. Population Employed by Age Group, January 2017 - May 2021

In the next chart, we're showing three separate snapshots in time, for February 2020 (before), April 2020 (the bottom), and May 2021 (the latest data at this writing). The chart makes it very easy to see that the employed share of the teen population has surpassed its pre-coronavirus level, unlike every other age demographic group.

Post-Coronavirus Recession Employment to Population Ratio Job Recovery by Age Group, Snapshots on February 2020, April 2020, and May 2021

With respect to all other age groups, teens are the least educated, least skilled, and least experienced segment of the U.S. labor force. And yet, this demographic group has the first to recover to its pre-coronavirus recession level of employment. We'll explore the possible reasons for that in an upcoming post.


U.S. Bureau of Labor Statistics. Labor Force Statistics from the Current Population Survey. Employed persons and employment-population ratios by age. [Online Database]. Accessed 14 June 2021.

COVID Cases, Hospitalizations, and Deaths Traced to Date of Exposure

Six. Twelve. Nineteen.

For those who have had COVID-19, those are the median number of days you would need to subtract from the date they...

  • experienced symptoms and went to be tested, or
  • became sick enough to be admitted to hospital, or
  • passed away if they became especially sick,

... in order to determine approximately when they first became infected by the SARS-CoV-2 coronavirus.

We're going to drive home the significance of those numbers using Arizona's detailed data for COVID cases, hospital admissions, and deaths, where we should see the peaks in the data for each these outcomes synchronize. Here's the graphical result of the math:

Arizona's Coronavirus Pandemic Experience, Daily Rolling 7-Day Averages for Cases, Hospital Admissions, and Deaths Indexed to Approximate Date of Exposure to SARS-CoV-2 Coronavirus (Linear Scale)

In this visualization, the relative scale of cases, hospitalizations, and deaths make it tough to see the pattern in the data. In the following chart, we're showing the exact same data, but using a logarithmic scale to better illustrate the synchronized pattern.

Arizona's Coronavirus Pandemic Experience, Daily Rolling 7-Day Averages for Cases, Hospital Admissions, and Deaths Indexed to Approximate Date of Exposure to SARS-CoV-2 Coronavirus (Logarithmic Scale)

Using the logarithmic scale lets us compare data that differs by orders of magnitude. For COVID-19, the daily number of those testing positive in Arizona often ranged in the thousands, while the number of those admitted to hospital peaked in the hundreds, and the number of deaths could be counted by tens.

Taking noise in the data into account, the synchronization pattern is fairly strong between all three sets of data when indexed to date of initial viral exposure.

There is an interesting pattern when comparing the timing of troughs for deaths when compared to the other two howver, where the the trend for deaths continue downward for a short period after the trends for cases and hospitalizations have reversed and begun tracking upward. We think this characteristic might be attributable to the age demographics of those being exposed to COVID-19, with older individuals more at risk of dying from COVID lagging in initial exposure behind younger individuals.

We also think the data for deaths is subject to considerably greater noise at low levels than the other datasets, especially when its daily numbers drop down toward single digits. This characteristic can been seen in the short-term trough coinciding with 15 September 2020 and a short-term spike in deaths occurring in late March 2021.

We're featuring this data visualization exercise today because we haven't seen anyone else present COVID data this way anywhere else, and because it will be helpful in answering a different question we have, which we'll feature in upcoming weeks!