Monday, December 26, 2011

Christmas Day was Opening Day in the NBA this season, thanks to the owners' lockout. Among the marquee match-ups was a Chicago Bulls visit to play the L.A. Lakers. For most of the second half, Chicago's shooting showed the rust of a longer-than-usual off-season. However, the Bulls caught fire in the closing minutes to pull out a stunning 88-87 victory.

Below is a shot-sequence chart for Chicago, based on the play-by-play sheet. I haven't done one of these in a long time, but it seemed fitting for the Bulls' second half. (You may click on the graphic to enlarge it.)


For roughly the first 20 of the 24 second-half minutes, Chicago's missed shots (blue) greatly outnumbered its made baskets (red). As shown in the legend at the bottom of the chart, longer line segments indicate greater distances of shot attempts. For the stretch highlighted in pale yellow, the Bulls missed 21 of 22 field-goal attempts. However, the Bulls came back to score 18 points in just the final 4:13 of the game, which was enough to win.

Sunday, December 18, 2011

Streak-buster Sunday in the NFL

Not only did the Denver Broncos' six-game winning streak -- powered by quarterback Tim Tebow's frantic rallying of the team -- come to an end today. So did two other major streaks in the National Football League.

Denver lost 41-23 to New England. Tebow worked as feverishly as ever to bring the Broncos back, but Denver's defense allowed the Patriots to score enough to maintain comfortable leads.

The Green Bay Packers, who entered today's play with a 13-0 record, lost to Kansas City, 19-14.

Finally, at the other end of the spectrum, the previously 0-13 Indianapolis Colts got their first win of the season, with a 27-13 victory over Tennessee.

Wednesday, December 14, 2011

American football fans are abuzz with what has been termed "Tebow-mania" or "Tebow Fever." The reference is to Denver Broncos' quarterback Tim Tebow, whose unorthodox playing style, his "mixing faith with football" (in the words of one writer), and his team's winning ways have garnered him great attention.

As seen in the Broncos' game-by-game log, Denver won in Tebow's first start, October 23 at Miami, lost the next week to Detroit, and then went on a still-ongoing six-game winning streak. Amanda Rykoff, writing in an ESPN-W "roundtable discussion" captures the essence of Tebow-mania:

...I'm not going to try to explain why he's 7-1 as a starter for the Broncos this year. Or why Denver has been able to come from behind late in the fourth quarter in five of those seven victories. Or how the Broncos managed to win what seemed to be an absolutely unwinnable game on Sunday against the Bears, trailing 10-0 with two minutes left in regulation.

The blog "This Given Sunday" has a detailed summary of each Broncos/Tebow win during the stretch.

The improbable nature of many Bronco wins has led probability analysts to estimate the likelihood of Denver's comeback-heavy winning streak. The key element is the win probability in each game, based on historical data. If you click here to get to the Advanced NFL Stats website and then scroll down to the graph with all the wavy lines, you'll get an idea of win probability. First, you would select one of the lines, corresponding to how your team is doing with regard to score (e.g., leading by 7, trailing by 3). Once you have your line, then follow it along the horizontal axis corresponding to how many minutes remained in the game. For example, a team trailing by 7 entering the fourth quarter tends to win about 10% of the time.

Using a chart like the one above, analysts would then find the win probabilities for Denver in each of its victories, given the depth of Denver's dire circumstances in a given game (i.e., when it trailed the most with the least time remaining). One can then multiply the probabilities together to get an overall probability estimate of the Broncos' streak. (This is analogous to calculating the probability of rolling double-sixes with a pair of dice by multiplying 1/6, which is the probability of a six on one die, by 1/6, the probability of a six on the other die, to yield 1/36.)

Using this methodology, ESPN's Statistics and Information Blog estimates a probability of Denver winning its last six straight at "approximately one in 137,000. The odds are better that a flipped coin comes up heads 17 consecutive times."

"This Given Sunday" (the blog cited above) calculates the probability of the Broncos winning the seven games with Tebow as starter (ignoring the one loss). The verdict: "the odds of the Broncos winning all seven games from their lowest odds in each particular game situation [are] 1 in 27 million."

If you're going to use seven as the win total, you must take into account the one loss, in my view. The seven game-specific probabilities from "This Given Sunday" are as follows:

.01, .15, .58, .17, .18, .14, .01

If you throw out the high and low values, the Tebow-led Broncos typically faced around a .15 probability of winning in many of the games during the stretch. Using an online tool known as a Binomial Probability Calculator, we can ask the question: For a team that faced only a .15 probability of winning each game, what is the likelihood of that team winning seven or more out of eight games? The answer, given these assumptions, is .00001 or 1-in-100,000.

As many writers have acknowledged, Tebow obviously should not get sole credit for Denver's winning stretch. However, his contribution appears to be great. One metric is quarterback efficiency ratings, which attempt to boil down many passing statistics (e.g., completion rate, yardage gained, touchdowns, interceptions) into a single number.

ESPN's Statistics and Information Blog notes that Tebow has the highest score (96.3) on one such metric, the Total QBR, of all NFL quarterbacks this season in the final 7 minutes of the fourth quarter (using a certain minute-mark rather than, say, the fourth quarter as a whole seems a little arbitrary; would Tebow still lead if we used the final 8 minutes or 6 minutes?).

Along with Denver's defense, which has had to shut down opposing offenses, another key figure in the Broncos' recent success is kicker Matt Prater. Without his hot foot, the winning streak would be over. According to Adena Andrews's commentary in the aforementioned ESPN-W roundtable:

Prater, who was recognized as the AFC special teams player of the week after his performance against the Bears on Sunday (a 59-yard field goal to tie the game, and then a 51-yarder for the overtime victory), has hit 28 of the 29 career field goals he has attempted in the fourth quarter or overtime.

One final factor to consider is that, as unusual as the Broncos' stretch appears, maybe in the larger historical scheme it is not so unexpected. The National Football League has been around for roughly 90 years. Initially, the league had around 10 teams, and increased over the years to the teens and mid-twenties (with the NFL-AFL merger), and continued to expand to the present 32 teams. The number of games per team per season has increased from roughly 10-12 in the early years to the present 16.

Let's say that, in a given season under the modern schedule, each team would have 10 opportunities to begin a winning stretch for six games (e.g., right from the start, beginning after Week 1, beginning after Week 2, etc.). Once Week 11 had gone by, of course, it would no longer be possible to start a six-game winning streak.

As a simplification, let's say further that within each of the most recent 30 seasons, there were 300 opportunities for a six-game winning streak (roughly 30 teams X 10 opportunities); that for each of the prior 30 years, there were 200 opportunities; and for the first 30 years of the NFL, there were 100 annual opportunities. That yields roughly 18,000 opportunities. Considering the above likelihood estimate of the Broncos'  winning six straight in the comeback fashion they did (i.e., 1-in-137,000), it seems that Denver's recent feat goes beyond the ordinary course of events.

Friday, December 09, 2011

Penn State's run of consecutive NCAA women's volleyball championships, which reached four last year, is now over. The Nittany Lions were eliminated this evening in three straight games by UCLA in the Sweet 16 round.

Thursday, December 08, 2011

Today, I did my first-ever book signing, in the bookstore of my home university, Texas Tech. Several people, mainly friends and colleagues, came by. Thanks to everyone who came by to chat and/or buy the book!

Monday, December 05, 2011

Tiger Woods yesterday ended his streak of 26 golf tournaments without a win. For most of Woods's career, it seemed the only long streaks he would record would be of the winning variety. But, times have changed.

Saturday, December 03, 2011

Last night on the NHL Network's highlight show, it was pointed out that the Detroit Red Wings have been very streaky in their wins and losses thus far this season. Based on the team's ESPN.com game log, I created the following graphic of Detroit's streaks of wins (red) and losses (grey). If you want to see the little notations for games decided during a five-minute overtime (OT) period or a post-overtime shoot-out (SO), you probably need to click on the graphic to enlarge it.


As can be seen, the Red Wings won their first five games, then lost their next six, and so forth. One of the statistical methods of detecting streakiness is known as the runs test. A "run" is an uninterrupted sequence of entirely wins or entirely losses. The fewer runs a team has, the stronger the evidence of streakiness. After 24 games, Detroit has only five runs. Based on an online runs-test calculator, into which I typed a 1 for each win and a 0 for each loss, the Red Wings' number of runs was fewer than would be expected by chance (with a significance of .00082 for those of you with some statistical training).

In this type of analysis, one must be careful to check if the team's schedule contained stretches of easy or difficult opponents, which could inflate the amount of apparent streakiness. This may be the case to some extent for Detroit, but not totally. During the Wings' string of six losses, two were to Columbus and Calgary, both of which today are in last place in their respective divisions. Conversely, during its current seven-game winning streak, Detroit has beaten some of the league's better teams, such as defending Stanley Cup champion Boston, Los Angeles, and Buffalo. The November 25 win at Boston, in fact, snapped the Bruins' 10-game winning streak.