Guest Post: E[V] of Super Bowl Boxes

A guest post from Jason Laso re: Super Bowl Boxes. The following has been lightly edited:

I guess sharp people were looking for an edge before deciding how many squares to buy or where to put them on the board. Or maybe some people were just intimidated by the idea of gambling in general (I mean who in their right mind would ever devote a significant portion of their life to something ridiculous like that). Don’t worry, I’ve got your back.

I simulated 500,000 Superbowls to come up with some brute force analytics on Superbowl Squares. Here is a graph of how likely you are to win at least one quarter based on how many squares you purchased (assuming random placement on the board):

Buying 1 square means you will win at least 1 quarter 3.3% of the time. Buying a second square increases your odds to 8.1%. To have at least a 25% chance, then you’d need to buy 7 squares. And if you’re looking for more of a coin flip than a longshot, then you’d need to buy 16 squares to have a 50/50 chance for winning at least 1 quarter.

An interesting follow up question was then posed to me: what if you just bought an entire row/column and tried to maximize your chance to win big by owning every permutation of one number (i.e. if you put your name down on every square in a row and that row that turns out to be the KC 7 row, then you’d have all of KC 7 – SF1, KC7 – SF2, KC7 – SF3, etc.).
Not so fast. Here is the expected return on investment (ROI) by which row you randomly drew:

Great news if you happen to draw the row/column with 0 (+66% ROI), 7 (55%), 3 (26%), or 4 (24%). However, the other 6 row/columns (1, 2, 5, 6, 8, 9) all show a negative expectation. The worst possible outcome would be to draw the row with 2, which would show a 50% loss. If you deliberately bought an entire row/column as outlined above, then you are expected to lose about 13% of your investment on average. If you instead bought squares and just placed them at random, then you are only expected to lose about 11%.

So all-in-all, try not to stress too hard about how many squares to buy or where you should put them on the board. In the end, the house always wins 😉

Parlays and Round Robins Can Be Good Bets - Bankroll Management

Conventional wisdom stipulates that parlays are bad bets for the typical sports bettor. Most people are sucked in by the large payouts for small investment, but if you miss 1 pick, you lose your bet.

But what if you're extremely concerned about bet limits, for example? Parlays aren't actually a bad idea, as suggested by Ed Miller, author of The Logic of Sports Betting, on Ed Feng's Football Analytics Show. But there are some major caveats that have to hold true:

1. Your win rate is profitable, obviously (> 52.38%)
2. You have extremely diligent bankroll management
3. You have very high volume - this won't work over a small number of bets
4. Your book is not adding juice on parlays - this is extremely important

Take, for example, a series of three -110 bets with a win rate of 55%. And say we try three strategies, with a base risk of $100 on each straight bet ($300 total), $100 on the parlay, or $50 on each round robin parlay ($150 total).

The math works out: you're expected to make varying degrees of gross profit, but a better ROI by using either non-straight bet strategy.

		Straight			Parlay			Round Robin
Result	Prob	Risk	Profit	ROI	Risk	Profit	ROI	Risk	Profit	ROI
WWW	16.64%	300	273	90.9%	100	600	600.0%	150	390	260.0%
WWL	13.61%	300	82	27.3%	100	-100	-100.0%	150	30	20.0%
WLL	11.14%	300	-109	-36.4%	100	-100	-100.0%	150	-150	-100.0%
WLW	13.61%	300	82	27.3%	100	-100	-100.0%	150	30	20.0%
LWL	11.14%	300	-109	-36.4%	100	-100	-100.0%	150	-150	-100.0%
LWW	13.61%	300	82	27.3%	100	-100	-100.0%	150	30	20.0%
LLW	11.14%	300	-109	-36.4%	100	-100	-100.0%	150	-150	-100.0%
LLL	9.11%	300	-300	-100.0%	100	-100	-100.0%	150	-150	-100.0%
	100.00%	E[X]	15	5.0%	E[X]	16	16.5%	E[X]	13	8.9%
		Min	-300		Min	-100		Min	-150
		Max	273		Max	600		Max	390
		Min W	82		Min W	600		Min W	30
		Min L	-109		Min L	-100		Min L	-150
		% Win	57.48%		% Win	16.64%		% Win	57.48%

NFL 1st Half Unders in Primetime

Bob Voulgaris, newly minted director of quantitative research and development for the Dallas Mavericks, is easily the most famous NBA sports bettor out there (although he's now retired from sports gambling and just stays active on NBA Twitter). One of his original profitable strategies was exploiting how sportsbooks set their NBA over/unders for each half:

It all had to do with how most bookmakers set their halftime totals, the predicted number of points scored in each half of the game. Each half, of course, is its own discrete period of play, and the fourth quarters of close games can end in elongated foul-clogged stretches of free throws, timeouts, fast play and, hence, a burst of scoring. But incredibly, bookmakers at the time didn’t account for this fact; they simply arrived at a total for the full game and cut that figure roughly down the middle, assigning some 50 percent of the points to the first half and 50 percent to the second.

Back in 2015, a former coworker came across a similar phenomenon in NFL first half over/unders, resulting in a considerable edge in specific situations. His strategy was so successful that it started 12-0 during the 2015 season, until we promptly bet it heavily on all 3 Thanksgiving Day games that year and it went 0-3.

Nonetheless, I went back and analyzed the past 3 full seasons of NFL first half totals (2015-2017) and found that the strategy still holds up remarkably well. The under has an abnormal success rate in games in which the first half over/under is >= 21 points, and is even more magnified in games that occur in primetime.

	O/U >= 21
All Games	WIN	338
	LOSS	264
	Push	19
	Total	621
	Win %	56.15%

56.15% is a very good success rate, but this market inefficiency skyrockets when the game is in "primetime":

	O/U >= 21
Primetime Only	WIN	91
	LOSS	46
	Push	5
	Total	142
	Win %	66.42%

I'm considering "primetime" to be any game that is the only game on - so Thursdays, Sunday nights, Monday nights, the London games (Sunday mornings), or the miscellaneous Saturday games late in the season. In other words, not in the afternoon on a Sunday.

Why does this edge occur in those spots? Over the years we've settled on the theory that players aren't in their normal rhythm that they experience most other Sundays, whether that's due to a shortened/extended week of practice, or just the game day pattern extending into the night. Therefore, they start slow during the game, resulting in less points in the first half. Regardless of the reason, this strategy hits at almost a 2/3 clip (66.42%).

The threshold of only betting first half O/U of 21+ results in the most profitable yield, but these effects stand up regardless of the number, just at a lower success rate:

	ALL O/U
All Games	WIN	402
	LOSS	344
	Push	22
	Total	768
	Win %	53.89%
	ALL O/U
Primetime Only	WIN	104
	LOSS	64
	Push	6
	Total	174
	Win %	61.90%

Parlaying O/U and ATS in NCAAF Relative to One Another

After my recent post on parlaying O/U and ATS depending upon the size of the spread, I received a request to look at the ratio of spreads and totals in NCAAF. So situations in which the spread is an outlandish percentage of the total, like 35%+. For example, in today's Georgia-Vanderbilt game, Georgia is favored by 25.5 with an over/under of 56. That 25.5 point spread thus represents 45.5% of the overall expected points in the game (25.5/56), which is a fairly lopsided ratio. Is there value in games where one team's score alone is supposed to make up a good portion of that game's total points?

As before, a standard 2-team payout is 13/5 (+260), and at +260, you need to hit above 27.78% of the time to turn a profit. (Note: with heavily skewed NCAAF games, most books actually don't let you parlay a side and an over/under. But this strategy can be applied to individual bets as well). So I looked at varying ratios of spreads to totals over the past 5 years of college football, and combining bets on the favorite and the over is a remarkably profitable strategy as the ratio escalates:

Ratio of Spread to Total
FAV + OVER	Actual	%	Return	ROI	% Occur
20%	414	27.62%	-9	-0.57%	42.18%
25%	339	28.70%	39	3.34%	33.23%
30%	273	30.67%	93	10.43%	25.04%
35%	215	32.33%	109	16.39%	18.71%
40%	158	32.71%	86	17.76%	13.59%
45%	114	34.03%	75	22.51%	9.43%
50%	76	33.78%	49	21.60%	6.33%
55%	58	37.66%	55	35.58%	4.33%
60%	41	37.27%	38	34.18%	3.10%
65%	24	37.50%	22	35.00%	1.80%

The more outlandish the ratio is, the more profitable it is, but of course the higher that ratio gets, the less often it occurs. If you can get any favorite that makes up 30%+ of the overall total, you're looking at a very high ROI.

I also looked at dogs + unders, in case you want to cover your risk a bit and hedge on the other extreme. There is some value in doing so, but only once you get to the sweet spot of a 45-60% ratio:

Ratio of Spread to Total
DOG + UNDER	Actual	%	Return	ROI	% Occur
20%	403	26.88%	-48	-3.22%	42.18%
25%	320	27.10%	-29	-2.46%	33.23%
30%	230	25.84%	-62	-6.97%	25.04%
35%	178	26.77%	-24	-3.64%	18.71%
40%	134	27.74%	-1	-0.12%	13.59%
45%	100	29.85%	25	7.46%	9.43%
50%	71	31.56%	31	13.60%	6.33%
55%	49	31.82%	22	14.55%	4.33%
60%	35	31.82%	16	14.55%	3.10%
65%	17	26.56%	-3	-4.38%	1.80%