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Win Probability Added Graphs

by Matt Smith

As a bit of a departure, I'm going to delve into the world of sabermetrics today, focusing on “Win Probability Added Graphs”.

I've never been particularly keen on maths and complex formulas. I could find my way around algebra and such when I needed to for exams, but most of that knowledge went straight out of my brain when I finished studying the subject.

My main problem was a complete lack of interest! However, when the figures and equations relate to baseball, that problem disappears somewhat. Not that I have the inclination (or the required skills) to start getting involved in the business end of producing the stats myself. But the great thing about the internet is that there are lots of smart people who can do this for you. There seems to be two different types of people involved in this work; stat boffins and storytellers. What separates the two is how they present their information.

Whilst the raw data is undoubtedly important, its ultimate value comes from what the numbers can tell you about the game. In a lot of cases, the average fan (including myself) needs a lot more than the basic data to get anything from it. Even something as simple as a .300 batting average needs some explanation at first. Okay, you might work out that it means getting a hit 3 times out of 10. But you need an explanation, some context, to really understand what this means (i.e. that hitting .300 is the mark of a good ballplayer).

Two of my favourite baseball sites are Baseball Prospectus and the Hardball Times (see the links on the main page). Both sites allow you to access an astonishing array of stats about baseball. Baseball Prospectus in particular have developed a range of stats to provide a greater insight into the game (not least the PECOTA system which seeks to predict future performance). What I love most about these sites though are the well written articles, using the numbers as supporting evidence, which without fail either tell you something you didn't know before, or make you question the validity of what you do. And in doing so they are also able to help you gain a better understanding of (and an interest in) the raw data itself.

For some information, there's nothing better than a graph or chart to get the point across. This brings me to “Win Probability Added Graphs”. They may sound complicated (and boring!), but trust me, they're not. A guy called Dave Studeman at the Hardball Times started this craze in 2004, and his recent column about them is an excellent place for you to start (see the References link at the end). Simply put, a WPA Graph can show you how every event effects the probability of the outcome of a ball game (which in turn allows you to see what contribution, both positive and negative, each individual player made). The Fan Graphs site (http://www.fangraphs.com/) has set up a system whereby a WPA graph is published for every MLB game after it has finished and it is well worth checking out.

The reason these graphs capture my imagination is that they document something which every fan intuitively understands. Every game has key moments and crucial turning points. WPA graphs record these big plays and put them into the overall context of how they affected the result of the game.

WPA Graph - A's vs Angels 22/04/2006

Here is an example from Fan Graphs. It shows the WPA Graph for the A's game against the Angels last night. For me, the most noticeable event was the Nick Swisher grand slam. Although it changed the A's win probability considerably, the Angels still had approximately a 65 per cent chance of winning once Swish had touched home plate. From a general standpoint, you can see that for the vast majority of the game, the Angels had a better than 50 per cent chance of taking the victory.

Have a browse through the WPA graphs of recent games on the Fan Graphs site, and read through the Dave Studeman articles below for some grounding on what the system is all about. And if all this heightens your interest, download the WPA spreadsheet from Dave's Baseball Graphs website and have a go at tracking games yourself. 

I've highlighted WPA Graphs today as a good example of the difference between those storytellers and stat boffins I mentioned earlier.  Sometimes you get the feeling that some of these stat boffins are more interested in looking clever and baffling others, rather than bringing some insight into Baseball.   WPA graphs are a great example of presenting information in a way that tells the average fan something different about the game.



A recent article by Dave Studeman providing some examples of what to look for in WPA graphs, and lots of links to various resources.


The main reference article by Dave Studeman about win probability.


Here you can download a WPA spreadsheet.

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1 comment

BaseballGB » Blog Archive » Links and Fangraphs March 22, 2008 - 10:58 am

[…] posted about Fangraphs’s Win Probability Added graphs in the past, which are a great way to chart […]


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