You will be redirected in 30 seconds or close now.

ColdFusion Authors: Yakov Fain, Jeremy Geelan, Maureen O'Gara, Nancy Y. Nee, Tad Anderson

Related Topics: Java IoT, Microservices Expo, Adobe Flex, IoT User Interface, Apache

Java IoT: Article

Why Averages Are Inadequate, and Percentiles Are Great

Averages are ineffective because they are too simplistic and one-dimensional

Anyone who ever monitored or analyzed an application uses or has used averages. They are simple to understand and calculate. We tend to ignore just how wrong the picture is that averages paint of the world. To emphasis the point let me give you a real-world example outside of the performance space that I read recently in a newspaper.

The article was explaining that the average salary in a certain region in Europe was 1900 Euro's (to be clear this would be quite good in that region!). However when looking closer they found out that the majority, namely 9 out of 10 people, only earned around 1000 Euros and one would earn 10.000 (I over simplified this of course, but you get the idea). If you do the math you will see that the average of this is indeed 1900, but we can all agree that this does not represent the "average" salary as we would use the word in day to day live. So now let's apply this thinking to application performance.

The Average Response Time
The average response time is by far the most commonly used metric in application performance management. We assume that this represents a "normal" transaction, however this would only be true if the response time is always the same (all transaction run at equal speed) or the response time distribution is roughly bell curved.

A Bell curve represents the "normal" distribution of response times in which the average and the median are the same. It rarely ever occurs in real applications

In a Bell Curve the average (mean) and median are the same. In other words observed performance would represent the majority (half or more than half) of the transactions.

In reality most applications have few very heavy outliers; a statistician would say that the curve has a long tail. A long tail does not imply many slow transactions, but few that are magnitudes slower than the norm.

This is a typical Response Time Distribution with few but heavy outliers - it has a long tail. The average here is dragged to the right by the long tail.

We recognize that the average no longer represents the bulk of the transactions but can be a lot higher than the median.

You can now argue that this is not a problem as long as the average doesn't look better than the median. I would disagree, but let's look at another real-world scenario experienced by many of our customers:

This is another typical Response Time Distribution. Here we have quite a few very fast transactions that drag the average to the left of the actual median

In this case a considerable percentage of transactions are very, very fast (10-20 percent), while the bulk of transactions are several times slower. The median would still tell us the true story, but the average all of a sudden looks a lot faster than most of our transactions actually are. This is very typical in search engines or when caches are involved - some transactions are very fast, but the bulk are normal. Another reason for this scenario are failed transactions, more specifically transactions that failed fast. Many real-world applications have a failure rate of 1-10 percent (due to user errors or validation errors). These failed transactions are often magnitudes faster than the real ones and consequently distorted an average.

Of course performance analysts are not stupid and regularly try to compensate with higher frequency charts (compensating by looking at smaller aggregates visually) and by taking in minimum and maximum observed response times. However we can often only do this if we know the application very well, those unfamiliar with the application might easily misinterpret the charts. Because of the depth and type of knowledge required for this, it's difficult to communicate your analysis to other people - think how many arguments between IT teams have been caused by this. And that's before we even begin to think about communicating with business stakeholders!

A better metric by far are percentiles, because they allow us to understand the distribution. But before we look at percentiles, let's take a look a key feature in every production monitoring solution: Automatic Baselining and Alerting.

Automatic Baselining and Alerting
In real-world environments, performance gets attention when it is poor and has a negative impact on the business and users. But how can we identify performance issues quickly to prevent negative effects? We cannot alert on every slow transaction, since there are always some. In addition, most operations teams have to maintain a large number of applications and are not familiar with all of them, so manually setting thresholds can be inaccurate, quite painful and time-consuming.

The industry has come up with a solution called Automatic Baselining. Baselining calculates out the "normal" performance and only alerts us when an application slows down or produces more errors than usual. Most approaches rely on averages and standard deviations.

Without going into statistical details, this approach again assumes that the response times are distributed over a bell curve:

The Standard Deviation represents 33% of all transactions with the mean as the middle. 2xStandard Deviation represents 66% and thus the majority, everything outside could be considered an outlier. However most real world scenarios are not bell curved...

Typically, transactions that are outside two times standard deviation are treated as slow and captured for analysis. An alert is raised if the average moves significantly. In a bell curve this would account for the slowest 16.5 percent (and you can of course adjust that); however; if the response time distribution does not represent a bell curve, it becomes inaccurate. We either end up with a lot of false positives (transactions that are a lot slower than the average but when looking at the curve lie within the norm) or we miss a lot of problems (false negatives). In addition if the curve is not a bell curve, then the average can differ a lot from the median; applying a standard deviation to such an average can lead to quite a different result than you would expect. To work around this problem these algorithms have many tunable variables and a lot of "hacks" for specific use cases.

Why I Love Percentiles
A percentile tells me which part of the curve I am looking at and how many transactions are represented by that metric. To visualize this look at the following chart:

This chart shows the 50th and 90th percentile along with the average of the same transaction. It shows that the average is influenced far mor heavily by the 90th, thus by outliers and not by the bulk of the transactions

The green line represents the average. As you can see it is very volatile. The other two lines represent the 50th and 90th percentile. As we can see the 50th percentile (or median) is rather stable but has a couple of jumps. These jumps represent real performance degradation for the majority (50%) of the transactions. The 90th percentile (this is the start of the "tail") is a lot more volatile, which means that the outliers slowness depends on data or user behavior. What's important here is that the average is heavily influenced (dragged) by the 90th percentile, the tail, rather than the bulk of the transactions.

If the 50th percentile (median) of a response time is 500ms that means that 50% of my transactions are either as fast or faster than 500ms. If the 90th percentile of the same transaction is at 1000ms it means that 90% are as fast or faster and only 10% are slower. The average in this case could either be lower than 500ms (on a heavy front curve), a lot higher (long tail) or somewhere in between. A percentile gives me a much better sense of my real world performance, because it shows me a slice of my response time curve.

For exactly that reason percentiles are perfect for automatic baselining. If the 50th percentile moves from 500ms to 600ms I know that 50% of my transactions suffered a 20% performance degradation. You need to react to that.

In many cases we see that the 75th or 90th percentile does not change at all in such a scenario. This means the slow transactions didn't get any slower, only the normal ones did. Depending on how long your tail is the average might not have moved at all in such a scenario.!

In other cases we see the 98th percentile degrading from 1s to 1.5 seconds while the 95th is stable at 900ms. This means that your application as a whole is stable, but a few outliers got worse, nothing to worry about immediately. Percentile-based alerts do not suffer from false positives, are a lot less volatile and don't miss any important performance degradations! Consequently a baselining approach that uses percentiles does not require a lot of tuning variables to work effectively.

The screenshot below shows the Median (50th Percentile) for a particular transaction jumping from about 50ms to about 500ms and triggering an alert as it is significantly above the calculated baseline (green line). The chart labeled "Slow Response Time" on the other hand shows the 90th percentile for the same transaction. These "outliers" also show an increase in response time but not significant enough to trigger an alert.

Here we see an automatic baselining dashboard with a violation at the 50th percentile. The violation is quite clear, at the same time the 90th percentile (right upper chart) does not violate. Because the outliers are so much slower than the bulk of the transaction an average would have been influenced by them and would not have have reacted quite as dramatically as the 50th percentile. We might have missed this clear violation!

How Can We Use Percentiles for Tuning?
Percentiles are also great for tuning, and giving your optimizations a particular goal. Let's say that something within my application is too slow in general and I need to make it faster. In this case I want to focus on bringing down the 90th percentile. This would ensure sure that the overall response time of the application goes down. In other cases I have unacceptably long outliers I want to focus on bringing down response time for transactions beyond the 98th or 99th percentile (only outliers). We see a lot of applications that have perfectly acceptable performance for the 90th percentile, with the 98th percentile being magnitudes worse.

In throughput oriented applications on the other hand I would want to make the majority of my transactions very fast, while accepting that an optimization makes a few outliers slower. I might therefore make sure that the 75th percentile goes down while trying to keep the 90th percentile stable or not getting a lot worse.

I could not make the same kind of observations with averages, minimum and maximum, but with percentiles they are very easy indeed.

Averages are ineffective because they are too simplistic and one-dimensional. Percentiles are a really great and easy way of understanding the real performance characteristics of your application. They also provide a great basis for automatic baselining, behavioral learning and optimizing your application with a proper focus. In short, percentiles are great!

More Stories By Michael Kopp

Michael Kopp has over 12 years of experience as an architect and developer in the Enterprise Java space. Before coming to CompuwareAPM dynaTrace he was the Chief Architect at GoldenSource, a major player in the EDM space. In 2009 he joined dynaTrace as a technology strategist in the center of excellence. He specializes application performance management in large scale production environments with special focus on virtualized and cloud environments. His current focus is how to effectively leverage BigData Solutions and how these technologies impact and change the application landscape.

Comments (1) View Comments

Share your thoughts on this story.

Add your comment
You must be signed in to add a comment. Sign-in | Register

In accordance with our Comment Policy, we encourage comments that are on topic, relevant and to-the-point. We will remove comments that include profanity, personal attacks, racial slurs, threats of violence, or other inappropriate material that violates our Terms and Conditions, and will block users who make repeated violations. We ask all readers to expect diversity of opinion and to treat one another with dignity and respect.

Most Recent Comments
rtalexander 11/21/12 12:58:00 AM EST

Hey, could you post a reference or two that covers the theory and/or practicalities of the approach you describe?


@ThingsExpo Stories
SYS-CON Events announced today that Cloudbric, a leading website security provider, will exhibit at the 19th International Cloud Expo, which will take place on November 1–3, 2016, at the Santa Clara Convention Center in Santa Clara, CA. Cloudbric is an elite full service website protection solution specifically designed for IT novices, entrepreneurs, and small and medium businesses. First launched in 2015, Cloudbric is based on the enterprise level Web Application Firewall by Penta Security Sys...
Virgil consists of an open-source encryption library, which implements Cryptographic Message Syntax (CMS) and Elliptic Curve Integrated Encryption Scheme (ECIES) (including RSA schema), a Key Management API, and a cloud-based Key Management Service (Virgil Keys). The Virgil Keys Service consists of a public key service and a private key escrow service. 

Data is the fuel that drives the machine learning algorithmic engines and ultimately provides the business value. In his session at Cloud Expo, Ed Featherston, a director and senior enterprise architect at Collaborative Consulting, will discuss the key considerations around quality, volume, timeliness, and pedigree that must be dealt with in order to properly fuel that engine.
SYS-CON Events announced today that MathFreeOn will exhibit at the 19th International Cloud Expo, which will take place on November 1–3, 2016, at the Santa Clara Convention Center in Santa Clara, CA. MathFreeOn is Software as a Service (SaaS) used in Engineering and Math education. Write scripts and solve math problems online. MathFreeOn provides online courses for beginners or amateurs who have difficulties in writing scripts. In accordance with various mathematical topics, there are more tha...
In an era of historic innovation fueled by unprecedented access to data and technology, the low cost and risk of entering new markets has leveled the playing field for business. Today, any ambitious innovator can easily introduce a new application or product that can reinvent business models and transform the client experience. In their Day 2 Keynote at 19th Cloud Expo, Mercer Rowe, IBM Vice President of Strategic Alliances, and Raejeanne Skillern, Intel Vice President of Data Center Group and ...
The best way to leverage your Cloud Expo presence as a sponsor and exhibitor is to plan your news announcements around our events. The press covering Cloud Expo and @ThingsExpo will have access to these releases and will amplify your news announcements. More than two dozen Cloud companies either set deals at our shows or have announced their mergers and acquisitions at Cloud Expo. Product announcements during our show provide your company with the most reach through our targeted audiences.
@ThingsExpo has been named the Top 5 Most Influential Internet of Things Brand by Onalytica in the ‘The Internet of Things Landscape 2015: Top 100 Individuals and Brands.' Onalytica analyzed Twitter conversations around the #IoT debate to uncover the most influential brands and individuals driving the conversation. Onalytica captured data from 56,224 users. The PageRank based methodology they use to extract influencers on a particular topic (tweets mentioning #InternetofThings or #IoT in this ...
There is growing need for data-driven applications and the need for digital platforms to build these apps. In his session at 19th Cloud Expo, Muddu Sudhakar, VP and GM of Security & IoT at Splunk, will cover different PaaS solutions and Big Data platforms that are available to build applications. In addition, AI and machine learning are creating new requirements that developers need in the building of next-gen apps. The next-generation digital platforms have some of the past platform needs a...
"We've discovered that after shows 80% if leads that people get, 80% of the conversations end up on the show floor, meaning people forget about it, people forget who they talk to, people forget that there are actual business opportunities to be had here so we try to help out and keep the conversations going," explained Jeff Mesnik, Founder and President of ContentMX, in this SYS-CON.tv interview at 18th Cloud Expo, held June 7-9, 2016, at the Javits Center in New York City, NY.
Bert Loomis was a visionary. This general session will highlight how Bert Loomis and people like him inspire us to build great things with small inventions. In their general session at 19th Cloud Expo, Harold Hannon, Architect at IBM Bluemix, and Michael O'Neill, Strategic Business Development at Nvidia, will discuss the accelerating pace of AI development and how IBM Cloud and NVIDIA are partnering to bring AI capabilities to "every day," on-demand. They will also review two "free infrastruct...
Intelligent machines are here. Robots, self-driving cars, drones, bots and many IoT devices are becoming smarter with Machine Learning. In her session at @ThingsExpo, Sudha Jamthe, CEO of IoTDisruptions.com, will discuss the next wave of business disruption at the junction of IoT and AI, impacting many industries and set to change our lives, work and world as we know it.
More and more brands have jumped on the IoT bandwagon. We have an excess of wearables – activity trackers, smartwatches, smart glasses and sneakers, and more that track seemingly endless datapoints. However, most consumers have no idea what “IoT” means. Creating more wearables that track data shouldn't be the aim of brands; delivering meaningful, tangible relevance to their users should be. We're in a period in which the IoT pendulum is still swinging. Initially, it swung toward "smart for smar...
In past @ThingsExpo presentations, Joseph di Paolantonio has explored how various Internet of Things (IoT) and data management and analytics (DMA) solution spaces will come together as sensor analytics ecosystems. This year, in his session at @ThingsExpo, Joseph di Paolantonio from DataArchon, will be adding the numerous Transportation areas, from autonomous vehicles to “Uber for containers.” While IoT data in any one area of Transportation will have a huge impact in that area, combining sensor...
In his general session at 19th Cloud Expo, Manish Dixit, VP of Product and Engineering at Dice, will discuss how Dice leverages data insights and tools to help both tech professionals and recruiters better understand how skills relate to each other and which skills are in high demand using interactive visualizations and salary indicator tools to maximize earning potential. Manish Dixit is VP of Product and Engineering at Dice. As the leader of the Product, Engineering and Data Sciences team a...
Join IBM November 2 at 19th Cloud Expo at the Santa Clara Convention Center in Santa Clara, CA, and learn how to go beyond multi-speed it to bring agility to traditional enterprise applications. Technology innovation is the driving force behind modern business and enterprises must respond by increasing the speed and efficiency of software delivery. The challenge is that existing enterprise applications are expensive to develop and difficult to modernize. This often results in what Gartner calls...
The explosion of new web/cloud/IoT-based applications and the data they generate are transforming our world right before our eyes. In this rush to adopt these new technologies, organizations are often ignoring fundamental questions concerning who owns the data and failing to ask for permission to conduct invasive surveillance of their customers. Organizations that are not transparent about how their systems gather data telemetry without offering shared data ownership risk product rejection, regu...
Although it has gained significant traction in the consumer space, IoT is still in the early stages of adoption in enterprises environments. However, many companies are working on initiatives like Industry 4.0 that includes IoT as one of the key disruptive technologies expected to reshape businesses of tomorrow. The key challenges will be availability, robustness and reliability of networks that connect devices in a business environment. Software Defined Wide Area Network (SD-WAN) is expected to...
The Internet of Things (IoT), in all its myriad manifestations, has great potential. Much of that potential comes from the evolving data management and analytic (DMA) technologies and processes that allow us to gain insight from all of the IoT data that can be generated and gathered. This potential may never be met as those data sets are tied to specific industry verticals and single markets, with no clear way to use IoT data and sensor analytics to fulfill the hype being given the IoT today.
@ThingsExpo has been named the Top 5 Most Influential M2M Brand by Onalytica in the ‘Machine to Machine: Top 100 Influencers and Brands.' Onalytica analyzed the online debate on M2M by looking at over 85,000 tweets to provide the most influential individuals and brands that drive the discussion. According to Onalytica the "analysis showed a very engaged community with a lot of interactive tweets. The M2M discussion seems to be more fragmented and driven by some of the major brands present in the...
19th Cloud Expo, taking place November 1-3, 2016, at the Santa Clara Convention Center in Santa Clara, CA, will feature technical sessions from a rock star conference faculty and the leading industry players in the world. Cloud computing is now being embraced by a majority of enterprises of all sizes. Yesterday's debate about public vs. private has transformed into the reality of hybrid cloud: a recent survey shows that 74% of enterprises have a hybrid cloud strategy. Meanwhile, 94% of enterpri...