Average margin

Written July 25, 2007

Ill: 62, Duke: 72 ... Xav: 80, L'ville: 70...Sports fans' lives are inundadted with numbers like these. They stream by on tickers, refresh on browsers, and arrive in inboxes. They are ubiquitous. And yet while they do tell the most important results — who won or lost and by how much — they convey little else. I think there may be an opportunity here to convey just a little more information that better contextualizes the result.

I started thinking about this idea with the advent of second-by-second score keeping in sports. The use of such data was especially important to the derivation of player metrics, such as plus-minus ratings in basketball, that determine how well a team performs while a given player is on the court/pitch/etc. But this also had some advantages for fans, such as the graphs below that show the score progression for a series of basketball games (all copyright ESPN).

These graphs are fun to pour over when you get in front of a computer, but they aren't as useful for ticker-tape scores. What if we could instead boil this down to a single piece of data that could accompany these scores?

The most obvious statistic to try is average margin, and actually, after trying several more complicated statistics I think this ends up being the winner. I will express average margin as avgM and use the sign to indicate whether it favored the winning team (positive) or losing team (negative).

So let's look at some examples. The first two scores listed above are both 10-point margins. But as you can see from their associated graphs, in one game a team (Duke) slowly built a lead over the course of the game and therefore the average margin slightly tilts in their favor (+3.0 avgM). In the other case, though, one team (Xavier) came back after trailing most of the game and the average margin actually tilts toward the other team (-3.4 avgM). This second case is also similar to the third game, in which one team (Illinois) has a large advantage in average margin, but actually lost the game (-7.5 avgM). The next two games I threw in to show how huge leads at the end of a game can be deceiving. The final scores of these two games are similar. However, in the first case, one team (Illinois) dominated the other for the entire game and let up a little at the end (which often happens when the second or third string comes on when a game is no longer in doubt) (+17.1 avgM), while in the other case, the winning team did not put the game away until very late, which is reflected in a low average margin (+4.5 avgM).

In summary, from the final score, the first game looks like a solid win, and average margin shows that for the most part it was. The second game also looks like a solid win, but average margin shows that it was anything but. The third game looks like a tight battle, but average margin shows that the losing side controlled the game most of the way. The next game looks like a blowout that was , and the next game looks like a blowout that wasn't.

As I mentioned, I have toyed with other statistics (such as one that calculates the amount of time a team has been recently "winning" the game [using a one-minute kernel]), but I think average margin is by far the clearest metric.

It may also be interesting to automatically detect and report last second comebacks (this could be fed into "you've got to see this" SMS or email notifications). To illustrate this, I used the score graph from one of the greatest comebacks of all time in basketball — Illinois win over Arizona to make the 2005 final four (-1.3 avgM). But this also serves to illustrate that, in the end, the numbers are nowhere near a replacement for the real thing.