"What are the odds?" The SF & SJ Giants Have Identical Games, Inning-by-Inning

On Tuesday, May 19, 2015, the San Francisco Giants beat the Los Angeles Dodgers by a score of 2-0. That same day, the San Jose Giants, Class A Advanced Affiliate of the San Francisco Giants, also happened to be playing at home, and beat the Modesto Nuts by the same score, 2-0. But look at the box scores side-by-side:

Source: mlb.com

Source: milb.com

As pointed out by my co-worker with the San Jose Giants, inning-by-inning they're identical: each Giants team scored the same runs in the same inning. So just how unlikely is this?

Competitive Balance Throughout NBA History

In my previous post, I asked whether competitive balance in the NBA had decreased in recent years, after determining that this year's group of teams that trailed 2-3 in a 7-game series (after being tied 2-2) were actually less evenly matched than the historical series comeback rate of 18% indicated.

To compare season-to-season competitive balance, I used the Noll-Scully Measure (NSM), which is the ratio of the actual standard deviation in each to season to the "ideal" standard deviation for that season. The lower the NSM, the greater competitive balance (CB) there is in the league. A perfectly balanced league would have a ratio of 1; if the ratio is less than 1, than the teams are even closer in wins than we would expect (which does happen, although rarely).

The NBA was formally created in 1950, and there have been many changes to its playoff structure (remember the original purpose of this research looked into 7-game series), but at least one round of the playoffs has always been a 7-game series. Thus, I calculated the NSM for each season for the entire history of the NBA since 1950:

There's a good deal of variation in the league's competitive balance, but there doesn't appear to be a significant trend to indicate less balance recently (although the ratio did drop below 1 for a brief period of time way back in the 1950's). Even so, this year's NSM is 2.92, which is above the average of 2.58 (and thus indicates below average CB for this season). In fact, the NSM has been above this average in 7 of the last 8 seasons:

Year	NSM
2015	2.922779391
2014	2.805581752
2013	2.763560925
2012	2.494208925
2011	2.86081387
2010	2.901691628
2009	3.064976463
2008	3.004894569

This isn't definitive, but maybe CB actually has decreased in recent seasons.

Effects of Competitive Balance on Demand in American and European Sports Leagues

For my semester research project in my last economics course at UNC, ECON 445 (Industrial Organization), I analyzed the effects of competitive balance on attendance (and thus demand) by "comparing (competitive balance) to each league’s attendance figures, and then additionally comparing these results to the home-field advantage in each league related to the “Uncertainty of Outcome” hypothesis."

The report can be found here.

Winner of Game 5 in 2-2 NBA Series

How important is Game 5 in a 2-2 series? Winner of the game advances 82 percent of the time in NBA: http://t.co/NASoXmgSbI

— RealGM (@RealGM) May 13, 2015

The above stat has been brought up a lot in this year's NBA Playoffs, since 3 of the 4 current series were tied 2-2. Per the above Real GM article (and every ESPN infographic on Sportscenter for the past week), "In NBA history, the winner of Game 5 is 147-33 to go on to win the entire series."



But how likely is it that the winner of Game 5 wins the series 82% of the time? The team up 3-2 has to lose 2 in a row to lose the series. As before, I'm using the Log5's from this year's three 2-2 series to approximate the average chance the trailing team has to come back and win 4-3:

3	2	Game 6	Game 7	Prob Win Series
GS	MEM	38.77%	21.61%	8.38%
ATL	WSH	40.92%	23.28%	9.53%
CLE	CHI	51.12%	31.85%	16.28%
				11.40%

So in fact (based on this year's predictions), it's actually even more unlikely that a team comes back in win 4-3. The most "balanced" series, CLE-CHI, is still short of the 18% threshold that we've seen in the 180 instances that have occurred so far (and by the time that I wrote this, CLE already finished the series and won 4-2). The z-score for the difference between the actual 18% comeback rate and the predicted 11% is 2.40, which results in a p-value of 0.992.

So why have teams historically won at a higher clip? Firstly, the three series from this year are likely not representative of all of the 7-game NBA series that were tied 2-2. Secondly, it raises a different question: has competitive balance decreased in recent years? I.E. Were NBA teams more balanced historically? That's a question for another time.

Teams Down 3-0 in the NBA Playoffs

In NBA history, teams with a 3-0 lead in a playoff series have gone on to win the series 100 percent of the time (110-0)
— GSWStats (@gswstats) April 24, 2015

There are 5 teams this year with a 3-0 lead in the first round of the NBA Playoffs, and as illustrated above, it's extremely unlikely any of them will blow their respective leads. But just how unlikely is it that a team down 0-3 has never come back to win the series? 

Usually the better team/higher seed will be up 3-0, but not always: this year the Wizards (East 5-seed) are up 3-0 on the Raptors (East 4-seed). Thus, I used the Log5's from this year's five 3-0 series to approximate the average chance the trailing team has at coming back and winning 4-3:

3	0	Game 4	Game 5	Game 6	Game 7	Prob Win Series
GS	NO	29.87%	15.19%	29.87%	15.19%	0.21%
WSH	TOR	48.27%	67.60%	48.27%	67.60%	10.65%
CLE	BOS	38.26%	21.23%	38.26%	21.23%	0.66%
CHI	MIL	47.77%	28.92%	47.77%	28.92%	1.91%
HOU	DAL	59.40%	39.66%	59.40%	39.66%	5.55%
						3.79%

The Raptors have the best chance to be the first team to do it, about 1 in 10. Overall, 3.79% is low, but not entirely impossible (it's equivalent to about 1 in 26). But more unlikely than a team coming back from 3-0 is the fact that no team has done it in 110 tries. Using this year's 3.79% as a proxy, (1-3.79%)^110 = 1.42%. Just like a 16-seed beating a 1-seed in the NCAA tournament, a team coming back from 0-3 is bound to happen eventually. Just ask the 2004 Red Sox.