Monday, March 19, 2007

As can be seen in my earlier entries below, I have spent the past four days following streak-related phenomena in the opening rounds of the men's (and to a lesser extent, women's) NCAA basketball tournaments. In many cases, I provided simple mathematical calculations for how likely a given streak was, given the prior (baseline) performance level of the player. Statistics, and numbers more generally, are not the only way to characterize streaks, however.

There is a growing trend toward representing statistical phenomena in a visual/graphical format. If you've read any game articles on, you'll see an example of such a graphical presentation, what ESPN calls a "Game Flow" graph (shown to the right of an article, midway down the page).

These Game Flow graphs contain two differently colored lines (or curves), one representing each team in a game. The horizontal axis depicts elapsed time and the vertical axis, each team's total score at a given point in time. The vertical distance between the two teams' curves at any instant represents the magnitude of lead for the team that's ahead.

If you don't want to figure out each team's score by comparing the height of the curve to the score labels on the vertical axis, you can click directly on the graph. Then, you can move the cursor left and right and see the actual score displayed for any point in time (this only works on the actual ESPN Game Flow graphs, and not on my examples below).

It is quite easy to detect team scoring runs and droughts from the ESPN Game Flow graphs. Shown below are two examples I created. In the top graph, the grey trianges depict scoring runs, as one team's point total is staying flat (a scoring drought), while the other team's total is rising concurrently (such triangles do not exist in the actual ESPN graphs, just in my examples). Such a run can help a team either pull away from its opponent or wipe out a deficit.

UCLA's first-round men's victory over Weber State, which featured Bruin spurts of 12-0, 9-0, and 14-0, provides sequences from an actual game that resemble my first example (link to article and Game Flow graph). If you have any difficulty picking out the three runs on the ESPN page, just look for the three flat line segments for Weber State (dark blue), located late in the first half and early and late in the second half.

My lower example presents an oversimplified situation in which no team scoring runs occur. Rather, one team gradually expands its lead over the other team, by accumulating small momentary scoring advantages. Team A might make a three-pointer, Team B might get a two, Team A might also then get a two, and Team B might not score on its next possession. Team A might then hit another three, followed by Team B making one free-throw out of two. Under this scenario, both teams' point totals increase in a relatively linear fashion, albeit with one team's score advancing with a sharper slope. The first-round men's game between Tennessee and Cal State Long Beach matches this latter scenario (link to article and Game Flow graph).

By coincidence, my Texas Tech faculty colleague Peter Westfall (who is in the Rawls College of Business Administration) published an early version of a Game Flow graph in 1990 in the American Statistician ("Graphical Presentation of a Basketball Game," Vol. 44, pp. 305-307). Instead of plotting two overlapping curves to represent the teams in a game and inviting readers to figure out the point difference at any moment, Westfall opted to plot only the difference score between the two teams (i.e., Team A's score minus Team B's) across time. He provides his reasoning for this choice in the article.

1 comment:

Anonymous said...

Alan, very informative blog. I am new to your postings but I too have
noticed a growing trend towards using statistical analysis to determine a
game's momentum. I am currently tracking "Hoops Predictor", a proprietary
algorithm that was developed by a former Stock Exchange trader. This
indicator uses intragame data to project which team is currently holding the momentum. If the tool calculates a team as having strong enough momentum, their research projects it to ultimately win the game.

But where I feel it excels far above the "Game Flow" tool is that it will continue to project and show the percentage odds of a team to win the game, even though
it may currently be losing in points. The website uses graphics like histogram and pie charts that update dynamically. Game Flow just shows you which team is currently ahead in score whereas Hoops Predictor dynamically gives you a team's win/loss percentage, according to the algorithm,
regardless of the score. They say on their website that the formula is over 80% correct and so far, by my experience, it's held up to be true. The tool is marketed as a game but I'm sure (as you may be aware) that it can be used for other purposes as well.

The best thing about it is that it's free. Keep up the good work.