The Shanghai Dragons Are Bad But May Not Be *That* Bad?

I love math. I regularly post stories from FiveThirtyEight on my Facebook page, and Bill Barnwell was a frequent read back in the days of Grantland. Games and statistics are passions of mine. That’s why even though I find video game culture to be lacking, I get excited for things like e-sports, because it means a wider population can enjoy the fun and thrill of sport while being disassociated from the various stigma surrounding traditional athletics. It’s even more fun to see the concept evolve and embrace old cliches like they’re new.

I’m so glad e-sports is breaking new ground and delivering such new ideas like a reality show where everyone lives in the same house.

— Pop Ramen Comedy (@PopRamenComedy) May 19, 2018

So when I see stuff like the Shanghai Dragons of Overwatch League be so horribly bad, the wheels get turning. I had lamented that I no longer have a platform to be analytical on otaku culture, but then I realized: this is my site. I can do whatever I want. So let’s get dangerous and do the math.

Many a sports pundit will tell you that a team’s win-loss record isn’t the full story on how good (or bad) a team is, especially when a team goes 0-fer. Sports analytics has a few ways of measuring “true” quality, primarily based on the number of points one scores. After all, the object is to have the most points, so more is always better. OWL is no different; the goal is to score 3 points (aka maps) before your opponent does, so we can apply similar analytical measures to Shanghai’s prolific season.

The fancy sabermetric stat that gets trotted out is Pythagorean Expectation which is a comparison of points for and against. Over the 40-match 2018 season Shanghai won 21 maps, earned draws on 2, and lost 141. Plugging it into the formula (and giving a draw 0.5 points to both sides), we get the following:

$Wins=\frac{22^{2}}{22^{2}+142^{2}}}}\times40=0.94$

That’s pretty bad. If the expectation was significantly higher than 0, we could say that they were unlucky, losing a few matches they should have won. But an expectation of less than 1 isn’t encouraging.

We can also go through the other team’s records to see how well they played to expectation which also helps show whether this is an accurate way to model.

Shanghai wasn’t the only one who didn’t meet expectations Actual vs Pythagorean Wins, 2018
Team	2018 Map Record			Expected Wins	Actual Wins	Difference
Team	W	L	D	Expected Wins	Actual Wins	Difference
New York Excelsior	126	43	4	35.60	34	-1.60
Los Angeles Valiant	100	64	7	28.06	27	-1.06
Boston Uprising	99	77	3	26.30	26	-0.30
Los Angeles Gladiators	96	72	3	25.51	25	-0.51
London Spitfire	102	69	3	27.32	24	-3.32
Philadelphia Fusion	93	80	2	22.96	24	+1.04
Houston Outlaws	94	77	2	23.90	22	-1.90
Seoul Dynasty	91	78	2	23.00	22	-1.00
San Francisco Shock	77	84	5	18.55	17	-1.55
Dallas Fuel	58	100	7	10.44	12	+1.66
Florida Mayhem	42	125	5	4.66	7	+2.33
Shanghai Dragons	21	141	2	0.93	0	-0.93

What may surprise you is that while this may a good correlation, it’s not the best correlation. As alluded to in the wikipedia link, the best exponent isn’t always 2. In this case, the number that minimizes the amount of error is around 1.67, so let’s run this again.

Shanghai still wasn’t the only one who didn’t meet expectations Actual vs Pythagorean Wins, 2018 with factor=1.67
Team	2018 Map Record			Expected Wins	Actual Wins	Difference
Team	W	L	D	Expected Wins	Actual Wins	Difference
New York Excelsior	126	43	4	34.06	34	-0.06
Los Angeles Valiant	100	64	7	26.85	27	+0.15
Boston Uprising	99	77	3	25.32	26	+0.68
Los Angeles Gladiators	96	72	3	24.63	25	+0.37
London Spitfire	102	69	3	26.20	24	-2.20
Philadelphia Fusion	93	80	2	22.47	24	+1.53
Houston Outlaws	94	77	2	23.26	22	-1.26
Seoul Dynasty	91	78	2	22.52	22	-0.52
San Francisco Shock	77	84	5	18.79	17	-1.79
Dallas Fuel	58	100	7	11.82	12	+0.18
Florida Mayhem	42	125	5	6.23	7	+0.77
Shanghai Dragons	21	141	2	1.70	0	-1.70

It’s clear that Shanghai underperformed, but 1) all 12 teams performed 0.19 wins worse on average and 2) Shanghai wasn’t as underachieving as the London Spitfire, who fell a full 2+ wins below expectation and gave their supporters heartburn as they nearly played themselves out of the 2018 season playoffs.

A neat thing about OWL is that it occurs in 4 stages of 10 matches each. We can put the record for each stage in the formula and then extrapolate for a 40-game season.

How to Explain Your Dragons Actual vs Pythagorean by Stage, factor=1.67
Stage	W	L	D	Expected W per 40 gms
Stage 1	6	36	0	1.91
Stage 2	2	38	1	0.41
Stage 3	9	32	0	4.29
Stage 4	4	36	1	1.18

Average	5.8	35.8	0.5	1.95
Median	5.0	36.0	0.5	1.54

The average expectation across all stages was nearly wins, and if they played at their peak stage form all year, they would’ve been 4-36. This would still make them dead last but it would be a more competitive dead last.

If you view maps as a series of individual matches as opposed to points to be scored, there’s a stat for that, too. The binomial distribution helps us determine the chance of success in a series of trials when the chance of success in a trial is known and constant. To figure out that trial success we just use the map winning percentage.

How to Explain Your Dragons 2 Expected Wins via Binomial Distribution, 3+ success in of 5 trials
Stage	Map Win %	Expected Match %	Expected W per 40 gms
Stage 1	0.143	0.0233	0.93
Stage 2	0.060	0.0002	0.08
Stage 3	0.219	0.0740	2.96
Stage 4	0.110	0.0111	0.45

Overall	0.134	0.0195	0.78
Stage Mean	0.133	0.0276	1.10
Stage Median	0The re.126	0.0172	0.69

The binomial looks even less kindly on the Dragons, but let’s be honest. Even under the rosiest of lenses, this is a really bad team, you guys. They may not have been truly 0-40 bad, but their single-season and stage 2 performances were ultimate (get it? ) examples of futility in the history of pro sports.

The Dragons were bad this season… Per Game Pythagorean Expectation, Select Historically Bad Professional Sports Teams
League/Sport	Team	Year/Record	PF	PA	Factor*	Exp.
OWL E-sports	Shanghai Dragons	2018 0-40-0	22	142	1.67	0.043
NFL US Football	Tampa Bay Buccaneers	1976 0-14-0	125	412	2.37	0.056
NBA Basketball	Charlotte Bobcats	2011-12 7-59-0	5739	6657	13.91	0.113
NHL Ice Hockey	Washington Captials	1974-75 8-67-5	181	446	2.11	0.130
NFL US Football	Detroit Lions	2008 0-16-0	268	517	2.37	0.174
NBA Basketball	Philadelphia 76ers	1972-73 9-73-0	8540	9531	13.91	0.178
*-exponential factor commonly used to determine Pythagorean Expectation for given sport

…and worse in the quarter-season Per Game Expectation, Quarter-Seasons of Select Pro Teams w/ Historic Losing Streaks
League/Sport	Team	Sample	L Streak	GP	PF	PA	Factor	Exp.
NFL US Football	Tampa Bay Buccaneers	1977 Gm 8-11	28*	4	7	74	2.37	0.004
OWL E-sports	Shanghai Dragons	2018 Gm 11-20	40	10	2.5	38.5	1.67	0.010
NFL US Football	Tampa Bay Buccaneers	1976 Gm 10-13	28*	4	23	149	2.37	0.012
NHL Ice Hockey	Washington Capitals	1974-75 Gm 56-75	17	20	38	127	2.11	0.073
NBA Basketball	Philadelphia 76ers	2013-14 Gm 51-70	26	20	1857	2202	13.91	0.085
NBA Basketball	Cleveland Cavaliers	2010-11 Gm 28-47	26	20	1853	2151	13.91	0.112
NHL Ice Hockey	San Jose Sharks	1992-93 Gm 38-58	17	21	41	102	2.11	0.128
*-same losing streak

It’ll be interesting to see how the club moves on from this. Yes, they did pick up the first female in the league but there’s also evidence that women are chosen to be figureheads when disaster is imminent. That, combined with the apparent dysfunction across all levels of the team management likely makes the situation more dire than any statistic.