This is a Fanpost aimed at those of us who may not be as stat-literate as others, but want to know what the Fangraphs game graph is all about. I’ll start from the very beginning, hopefully passing along useful knowledge about run expectancy and win probability, among other things. And if you already have a good handle on the principles, hey, it’s good review. Or something.

There’s a fundamental concept in this area of baseball research called base/out states. It’s simple, really. If we’re just talking about one inning, what’s the least amount of information you absolutely have to know to understand the situation? All you really need is the number of men on base and how many outs there are. It turns out that there are eight different ways to have men on base: no one on, a guy on first, a guy on second, a guy on third, guys on first and second, first and third, second and third, and bases loaded. Furthermore, all of these can occur with zero, one, or two outs, which leads to 24 total base/out states.

Most of the data that I'll talk about in this post comes from The Book: Playing the Percentages in Baseball (Tom Tango, Mitchel Lichtman, Andrew Dolphin). In The Book, the authors created a run expectancy table. They threw all of the games played from 1999-2002 into a massive database (over 85,000 innings!) and crunched the numbers. What they primarily looked at was each base/out state, and how many runs the average team scored starting from that state until the end of the inning. For example, they were able to show that, on average, a double that starts the inning makes a team score 0.634 more runs than they would have scored before the hit. And a strikeout with the bases loaded and no outs hurts the team to the tune of -0.767 runs. Over a full season, we can add up a player’s contributions (positive and negative), and come out with a number which expresses the total amount of offense that our example player produced. Fangraphs tracks this stat under the name RE24.

To take run expectancy a step further, Tom Tango decided to expand the context. Sure run expectancy is fine for an inning, but what if we wanted to look at a full ballgame? By crunching the numbers again, Tango created a set of tables that express the win probability for both teams at any point in the game. In other words, if team A was up by four runs in the bottom of the sixth, and team B had a man on first with two outs, there’s a section of the table that gives the probability of either team pulling out a win. As you can imagine, due to including the 24 base/out states in addition to the inning number and score difference between the two teams, it’s a really large set of tables.

It’s this win probability that appears on the game graphs generated by Fangraphs. Here’s an example. Click the graph to see the full page.

via www.fangraphs.com

Yeah, I chose a good one. Ignore the bar graph at the bottom, I’ll get to that in a bit. For now, focus on the crazy line graph. Remember, in win probability, the numbers assume perfectly average teams. So at the beginning of the game, both teams have exactly a 50% chance of winning. In this game, by the top of the second, after Justin Morneau’s grand slam, the Twins had an 87.6% chance of winning the game. The score was 7-2. And by the middle of the third inning, the Twins had a 98.9% chance of winning, assuming perfectly average teams. Of course, we know what happened. Most game graphs aren’t nearly this dramatic, but that’s the beauty of the model. When the graph takes crazy dives and turns, it’s visually obvious that it was a great game to watch.

Also, much like RE24, we can tally up a player’s contributions to win probability. This stat is known as Win Probability Added (WPA). In WPA, 0.500 corresponds to one full win, as the probability of winning changed by 0.500 (50% to 100%). In the aforementioned game, Gio Gonzalez was tagged with -0.587 WPA, more than enough to singlehandedly lose the game. Thankfully, Holliday and Cust combined for a positive 0.638, enough to overcome Gio’s poor pitching. The unique thing about WPA is that, unlike other stats, it’s not context-neutral. Almost every other statistic out there (batting average, OPS, wOBA, whatever) deals with players in a theoretical vacuum. But WPA deals with actual game occurrences. Give up a solo home run when your team is up by ten? Not a big deal, and WPA shows that. Give up a bases-loaded walk in a tie game in the bottom of the ninth? That’s far worse. WPA reflects that.

As an extension to this, Tom Tango created what he called a Leverage Index (LI). Leverage Index basically explains how critical a situation is. To put it in more technical terms, Leverage Index gives a numerical representation of the biggest possible swing in win probability, where 1.0 is the average. To use my previous examples, the LI in a game situation where you’re up by ten is very low. If you give up a home run, the win probability isn’t going to change much. But the LI in the bottom of the ninth of a tie game with the bases loaded is off the charts. The high LI shows that any little mistake could be devastating. Leverage Index is always denoted in a Fangraphs game graph by the bar graph underneath the regular win probability graph. In that crazy Twins game I mentioned earlier, the LI sinks to near-zero levels when the Twins are up 12-2. And yet, when the A’s came roaring back, the LI started to rise again. The last play of the game had a huge LI, as Michael Wuertz had runners on first and second with two outs in the bottom of the ninth of a one-run game.

I admit I’ve gotten into the habit of keeping the game graph open in another tab alongside MLB Gameday (and AN, of course) during a game. It’s pretty addicting to watch the graph unfold in real-time, and wonderfully cathartic to see a crazy game in graphical form.