Click here to close now.

Welcome!

GovIT Authors: Liz McMillan, Pat Romanski, Bart Copeland, Brad Thies, Kevin Jackson

Related Topics: Java, SOA & WOA, Adobe Flex, AJAX & REA, Apache

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We recognize that the average no longer represents the bulk of the transactions but can be a lot higher than the median.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

Conclusion
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?

Thanks!

@ThingsExpo Stories
One of the biggest impacts of the Internet of Things is and will continue to be on data; specifically data volume, management and usage. Companies are scrambling to adapt to this new and unpredictable data reality with legacy infrastructure that cannot handle the speed and volume of data. In his session at @ThingsExpo, Don DeLoach, CEO and president of Infobright, will discuss how companies need to rethink their data infrastructure to participate in the IoT, including: Data storage: Understanding the kinds of data: structured, unstructured, big/small? Analytics: What kinds and how responsiv...
Since 2008 and for the first time in history, more than half of humans live in urban areas, urging cities to become “smart.” Today, cities can leverage the wide availability of smartphones combined with new technologies such as Beacons or NFC to connect their urban furniture and environment to create citizen-first services that improve transportation, way-finding and information delivery. In her session at @ThingsExpo, Laetitia Gazel-Anthoine, CEO of Connecthings, will focus on successful use cases.
The Workspace-as-a-Service (WaaS) market will grow to $6.4B by 2018. In his session at 16th Cloud Expo, Seth Bostock, CEO of IndependenceIT, will begin by walking the audience through the evolution of Workspace as-a-Service, where it is now vs. where it going. To look beyond the desktop we must understand exactly what WaaS is, who the users are, and where it is going in the future. IT departments, ISVs and service providers must look to workflow and automation capabilities to adapt to growing demand and the rapidly changing workspace model.
Sensor-enabled things are becoming more commonplace, precursors to a larger and more complex framework that most consider the ultimate promise of the IoT: things connecting, interacting, sharing, storing, and over time perhaps learning and predicting based on habits, behaviors, location, preferences, purchases and more. In his session at @ThingsExpo, Tom Wesselman, Director of Communications Ecosystem Architecture at Plantronics, will examine the still nascent IoT as it is coalescing, including what it is today, what it might ultimately be, the role of wearable tech, and technology gaps stil...
Almost everyone sees the potential of Internet of Things but how can businesses truly unlock that potential. The key will be in the ability to discover business insight in the midst of an ocean of Big Data generated from billions of embedded devices via Systems of Discover. Businesses will also need to ensure that they can sustain that insight by leveraging the cloud for global reach, scale and elasticity.
The Internet of Things (IoT) promises to evolve the way the world does business; however, understanding how to apply it to your company can be a mystery. Most people struggle with understanding the potential business uses or tend to get caught up in the technology, resulting in solutions that fail to meet even minimum business goals. In his session at @ThingsExpo, Jesse Shiah, CEO / President / Co-Founder of AgilePoint Inc., showed what is needed to leverage the IoT to transform your business. He discussed opportunities and challenges ahead for the IoT from a market and technical point of vie...
IoT is still a vague buzzword for many people. In his session at @ThingsExpo, Mike Kavis, Vice President & Principal Cloud Architect at Cloud Technology Partners, discussed the business value of IoT that goes far beyond the general public's perception that IoT is all about wearables and home consumer services. He also discussed how IoT is perceived by investors and how venture capitalist access this space. Other topics discussed were barriers to success, what is new, what is old, and what the future may hold. Mike Kavis is Vice President & Principal Cloud Architect at Cloud Technology Pa...
Hadoop as a Service (as offered by handful of niche vendors now) is a cloud computing solution that makes medium and large-scale data processing accessible, easy, fast and inexpensive. In his session at Big Data Expo, Kumar Ramamurthy, Vice President and Chief Technologist, EIM & Big Data, at Virtusa, will discuss how this is achieved by eliminating the operational challenges of running Hadoop, so one can focus on business growth. The fragmented Hadoop distribution world and various PaaS solutions that provide a Hadoop flavor either make choices for customers very flexible in the name of opti...
The true value of the Internet of Things (IoT) lies not just in the data, but through the services that protect the data, perform the analysis and present findings in a usable way. With many IoT elements rooted in traditional IT components, Big Data and IoT isn’t just a play for enterprise. In fact, the IoT presents SMBs with the prospect of launching entirely new activities and exploring innovative areas. CompTIA research identifies several areas where IoT is expected to have the greatest impact.
Advanced Persistent Threats (APTs) are increasing at an unprecedented rate. The threat landscape of today is drastically different than just a few years ago. Attacks are much more organized and sophisticated. They are harder to detect and even harder to anticipate. In the foreseeable future it's going to get a whole lot harder. Everything you know today will change. Keeping up with this changing landscape is already a daunting task. Your organization needs to use the latest tools, methods and expertise to guard against those threats. But will that be enough? In the foreseeable future attacks w...
Disruptive macro trends in technology are impacting and dramatically changing the "art of the possible" relative to supply chain management practices through the innovative use of IoT, cloud, machine learning and Big Data to enable connected ecosystems of engagement. Enterprise informatics can now move beyond point solutions that merely monitor the past and implement integrated enterprise fabrics that enable end-to-end supply chain visibility to improve customer service delivery and optimize supplier management. Learn about enterprise architecture strategies for designing connected systems tha...
Dale Kim is the Director of Industry Solutions at MapR. His background includes a variety of technical and management roles at information technology companies. While his experience includes work with relational databases, much of his career pertains to non-relational data in the areas of search, content management, and NoSQL, and includes senior roles in technical marketing, sales engineering, and support engineering. Dale holds an MBA from Santa Clara University, and a BA in Computer Science from the University of California, Berkeley.
Wearable devices have come of age. The primary applications of wearables so far have been "the Quantified Self" or the tracking of one's fitness and health status. We propose the evolution of wearables into social and emotional communication devices. Our BE(tm) sensor uses light to visualize the skin conductance response. Our sensors are very inexpensive and can be massively distributed to audiences or groups of any size, in order to gauge reactions to performances, video, or any kind of presentation. In her session at @ThingsExpo, Jocelyn Scheirer, CEO & Founder of Bionolux, will discuss ho...
The cloud is now a fact of life but generating recurring revenues that are driven by solutions and services on a consumption model have been hard to implement, until now. In their session at 16th Cloud Expo, Ermanno Bonifazi, CEO & Founder of Solgenia, and Ian Khan, Global Strategic Positioning & Brand Manager at Solgenia, will discuss how a top European telco has leveraged the innovative recurring revenue generating capability of the consumption cloud to enable a unique cloud monetization model to drive results.
As organizations shift toward IT-as-a-service models, the need for managing and protecting data residing across physical, virtual, and now cloud environments grows with it. CommVault can ensure protection &E-Discovery of your data – whether in a private cloud, a Service Provider delivered public cloud, or a hybrid cloud environment – across the heterogeneous enterprise. In his session at 16th Cloud Expo, Randy De Meno, Chief Technologist - Windows Products and Microsoft Partnerships, will discuss how to cut costs, scale easily, and unleash insight with CommVault Simpana software, the only si...
Analytics is the foundation of smart data and now, with the ability to run Hadoop directly on smart storage systems like Cloudian HyperStore, enterprises will gain huge business advantages in terms of scalability, efficiency and cost savings as they move closer to realizing the potential of the Internet of Things. In his session at 16th Cloud Expo, Paul Turner, technology evangelist and CMO at Cloudian, Inc., will discuss the revolutionary notion that the storage world is transitioning from mere Big Data to smart data. He will argue that today’s hybrid cloud storage solutions, with commodity...
Every innovation or invention was originally a daydream. You like to imagine a “what-if” scenario. And with all the attention being paid to the so-called Internet of Things (IoT) you don’t have to stretch the imagination too much to see how this may impact commercial and homeowners insurance. We’re beyond the point of accepting this as a leap of faith. The groundwork is laid. Now it’s just a matter of time. We can thank the inventors of smart thermostats for developing a practical business application that everyone can relate to. Gone are the salad days of smart home apps, the early chalkb...
Cloud data governance was previously an avoided function when cloud deployments were relatively small. With the rapid adoption in public cloud – both rogue and sanctioned, it’s not uncommon to find regulated data dumped into public cloud and unprotected. This is why enterprises and cloud providers alike need to embrace a cloud data governance function and map policies, processes and technology controls accordingly. In her session at 15th Cloud Expo, Evelyn de Souza, Data Privacy and Compliance Strategy Leader at Cisco Systems, will focus on how to set up a cloud data governance program and s...
Roberto Medrano, Executive Vice President at SOA Software, had reached 30,000 page views on his home page - http://RobertoMedrano.SYS-CON.com/ - on the SYS-CON family of online magazines, which includes Cloud Computing Journal, Internet of Things Journal, Big Data Journal, and SOA World Magazine. He is a recognized executive in the information technology fields of SOA, internet security, governance, and compliance. He has extensive experience with both start-ups and large companies, having been involved at the beginning of four IT industries: EDA, Open Systems, Computer Security and now SOA.
The industrial software market has treated data with the mentality of “collect everything now, worry about how to use it later.” We now find ourselves buried in data, with the pervasive connectivity of the (Industrial) Internet of Things only piling on more numbers. There’s too much data and not enough information. In his session at @ThingsExpo, Bob Gates, Global Marketing Director, GE’s Intelligent Platforms business, to discuss how realizing the power of IoT, software developers are now focused on understanding how industrial data can create intelligence for industrial operations. Imagine ...