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.

NBA Playoffs Picks

Once again, I'm using the Pyth component of my MDS Model to pick the NBA Playoffs bracket:

Some notes (all rankings reflect Pyth):

• The entire West should be incredible. #2 LAC vs #3 SA, #8 HOU vs #9 DAL, #4 POR vs #6 MEM all in the first round. And then the potential #1 vs #2, GS vs LAC in the Western Conference Finals. Just the first round will outshine any round from the East.

• Speaking of the East dumpster fire known as the East, the Nets are in the playoffs. The Nets are #23 in my model. There are 30 teams in the NBA. They are 23 out of 30.
• There are 3 teams (MIL, BOS, BKN) with .500 or worse records in the playoffs (all from the East).
• The 11th best team (Utah) from the West would have made the playoffs in the East. And per my model, they would've been favored over every Eastern playoff opponent except for CLE and ATL.
• CLE is ranked 5th in Pyth, ATL 7th overall.

• Personally I think it should be a contractual obligation for the Hawks to play the Pacers in the first round and for it to be on NBA TV. We were this close to that happening again, but the Nets had to pull it out against the Magic last night.

The Curse of the Chicago Cubs

The Cubs last won the World Series in 1908, 107 years ago. The Curse of the Billy Goat could be to a blame, bad management could be responsible, or the club has just consistently gotten unlucky (which could be interpreted as being caused by the curse, that's up to you/Cubs fans). However, it's really hard to win a World Series - so is 107 consecutive years an extremely unexpected drought?

It would make sense to approximate a team's chances at winning it all in a given season by simply giving them a 1 in n chance, with n being the number of teams in the league. This isn't all that straight-forward of a calculation, since MLB has expanded multiple times in the past century (so it's not just (1/30)^107). Since there used to be fewer teams (and thus 1 in n was higher), the resulting figure is very low that the Cubs would go that long without winning the title: 0.41%.

However, there's an even more unlikely event that's occurred during that time span: the Cubs not winning the National League. In this case, the last time they won the pennant was 1945, 70 years ago. There is only a 0.17% chance that they would never win the NL in that span. Of course, the infamous Bartman incident in 2003 contributed to this, and those probabilities are so low... maybe the Cubs really are cursed.

Analyzing Tokoto's NBA Draft Decision From a Financial Perspective

UNC junior SF J.P. Tokoto announced Wednesday that he's entering this year's NBA Draft, which came as a surprise to many, including myself. He's ranked 69th on Chad Ford's Big Board, and is projected to be a Second Round pick at best, or to go undrafted.

Aside from UNC's lofty expectations for next season, the question surrounding Tokoto's draft decision is whether declaring for this year's draft was the right choice financially. This year's draft is loaded, and Tokoto was projected 26th in 2016's draft, which would have made him a late first rounder. However, that assumes that he wouldn't have lost significant playing time or gotten injured in his senior season at UNC.

The NBA Draft switched to 2 rounds in 1989, and since then, 70.25% of second round picks have ended up playing in the NBA. So right off the bat we can discount his expected first-year NBA earnings by that rate, since almost 3 in 10 second round picks don't ever end up playing in the NBA. Meanwhile, 98.80% of first round picks have played in the NBA: but that doesn't even matter, because first round contracts are guaranteed. As a projected 26th pick in 2016, Tokoto would have received his money regardless of whether he ever played an NBA game (which, of course, would also be more than that of a second round contract). Additionally, a late first round rookie contract is generally guaranteed for 2 years, with a team option for 2 additional years.

Then there's the possibility he goes undrafted, with the best-case scenario probably being the D-League, followed by hopefully a chance as a bench player with an NBA team (i.e. the path James Michael McAdoo took to playing for the Golden State Warriors). Alternatively, he could play in Europe, which would pay more than the D-League (although recently the Euro has greatly weakened relative to the US Dollar; I doubt this factored into his decision at all). However, it's hard to find contract information for European leagues to compare to the other possible scenarios, so here are the NBA/D-League possibilities:

Contract	Guaranteed Money	Expected Money	Discounted Value
Late 1st Round	$2,350,000	$2,350,000	$2,350,000
Late 2nd Round	$0	$500,000	$350,000
Undrafted	$0	$150,000	??? (< $150k)

The discounted value takes into account the possibility of getting drafted and not making an NBA roster. Figures are taken from similar players in each contract situation (all data gathered from Basketball-Reference, and much of the analysis contained in this post is credited to my roommate).

Clearly the first round possibility is the best one, so it's likely Tokoto didn't see that staying for his senior season would cause his draft stock to improve. And the clear financial alternative not yet discussed is for this scenario: staying to play in the NCAA for another year would result in a salary of absolutely nothing. So even the "worst case" of < $150k is clearly greater than 0. And this exact case is working out for McAdoo (who also surprised Carolina fans last year by leaving for the NBA), since the Warriors are one of the favorites to win it all. It's quite possible he wins a ring in his first year in the league.

Competitive Balance in College Basketball, Based on the Final Four

A few days ago, I calculated competitive balance (CB) in NCAAB based on the champions of the NIT, looking at the marginally good teams right off of the cut line of the NCAA tournament.

A more accurate representation of overall CB in college basketball is obviously the finalists of the NCAA tournament, so I've updated the Herfindahl–Hirschman Index (HHI), which measures CB. In this case, it is the sum of the squares of the number of Final Four appearances by team i (f_i) during the designated period, over the number of possible Final Four finalists during the period (I'll be using the past 10 years). To account for the fact that there are 4 teams in the Final Four each year, we include a multiplier of 4 in the summation.

The closer HHI is to 1, the less CB there is in the league. Complete CB (4 different teams every single year) would be 0.1.

There have been 22 different Final Four finalists in the past decade (out of a possible 40), which indicates some saturation, far from complete CB. The HHI = 0.225, which supports this notion. The following teams (10 of them) account for 26 Final Fours in the past 10 years:

Team	Count
Kentucky	4
Florida	3
UCLA	3
Michigan State	3
Connecticut	3
North Carolina	2
Duke	2
Butler	2
Ohio State	2
Kansas	2
Sum	26

Competitive Balance in College Basketball... Per the NIT

A standard measure of competitive balance in economics is the Herfindahl–Hirschman Index (HHI), which, in this case, is the sum of the squares of the number of championships by team i (c_i) during the designated period, over the number of champions during the period. By doing this for the NIT, we can gauge the competitive balance of the bubble teams: the fringe teams just outside the NCAA tournament field. I'm using the past 10 years, so n = 10 in the following equation:

The closer the HHI is to 1, the less competitive balance there is in the league. So if the same team wins the champion every year, HHI = 1 (10 years, 1 champion). For example, women's basketball's HHI is very high, as there have only been 3 different champions in the past 6 years (Connecticut has won it 4 times). If a different team wins the title each year, HHI = 1/10 (1/n, complete balance).

The NIT champions from the past 10 years are as follows:

There has only been one repeat champion, Stanford, so the HHI = (2/10)^2 + 8 * (1/10)^2 = 0.12. Complete balance would be 0.1, so the competitive balance in the NIT is very high.

Play-by-Play Simulator for College Basketball

All season I've been planning on writing a play-by-play simulator for college basketball, and finally have it done for the final game: the national championship. 

Using KenPom's team and player data, I wrote a simulator in Python that aims to reflect the actual flow of a game, including taking into account the following factors:

Factors Considered
Turnover rate (at the team level)
If turnover, whether the defending team had a steal (StealRate). If so, which defensive player stole the ball
If no turnover, which offensive player took the shot (% Shots), and what type (3PA/FGA)
If a foul was committed (FTRate), points scored off free throws (Free Throw %)
Regardless of foul, if shot was made (2PT FG % or 3PT FG %)
If made, whether the shot was assisted (AssistRate) and which offensive player had the assist
If miss, whether the defending team had a block (BlockRate). If so, which defensive player blocked the shot
If miss, whether the miss was rebounded by the offensive team (Off Reb %). Which offensive or defensive player rebounded the miss
If offensive rebound, possession resets

The opening tip is determined by a formula taking into account each team's effective height. An explanation of all of these stats can be found here, by KenPom.

There are still some complexities that I need to add to the simulator:

Qualifiers
If <= 6-point game with less than 90 seconds remaining, the defending team should foul
If 3-point game with less than 35 seconds left, the offensive team should shoot a three
If a player has 3+ fouls in the first half, they should sit until the start of the second
If a player has 4+ fouls, they should sit until <= 4 minutes left in regulation
If a player has 5 fouls, they're removed from the lineup

However, this rough draft should still represent the flow of an actual college basketball game fairly accurately.

Finally, after 10,000 simulations, here are the results for predicting tonight's game:

Final Score: Wisconsin 69.372, Duke 67.170
Wisconsin: 56.03%, Duke: 43.97%
Total: 136.542

Predicted Box Score:

Wisconsin	Points	Rebounds	Assists
Kaminsky	19.639	6.961	3.144
Hayes	11.965	3.776	2.053
Dekker	14.075	3.651	1.400
Jackson	0.5705	0.092	0.176
Koenig	9.2386	1.359	2.636
Dukan	4.2493	1.487	0.542
Showalter	2.0977	0.659	0.427
Gasser	7.5346	2.965	2.071
Duke	Points	Rebounds	Assists
Okafor	13.986	4.962	1.409
Winslow	11.594	5.163	2.154
Allen	2.5854	0.487	0.218
Cook	14.391	2.997	2.571
T Jones	12.241	3.281	5.785
Jefferson	3.7338	2.186	0.507
M Jones	7.091	1.820	1.230
Plumlee	1.5455	0.527	0.312

For what it's worth, KenPom's prediction is Wisconsin 70-69, 55%