Freelance Friday: Setting The Record Straight On Basketball Betting

Flickr | Joel Kramer

Freelance Friday is a project that lets us share our platform with the multitude of talented writers and basketball analysts who aren’t part of our regular staff of contributors. As part of that series we’re proud to present this guest post from William Guo. This post is a response to a Freelance Friday post from a weeks ago (by different contributors) about the challenges of betting on basketball. You can follow William on twitter @wmguo.

How are NBA lines made?

Linesmakers typically have a top down method and a bottom up method. In a hypothetical matchup between the Clippers and the Bulls, using very rough numbers:

Top down:

1. Power rate both teams in the preseason. (Let’s say +6 for both teams – 55 to 60 win range)
2. Look at current SRS-like metric. (+6 for LAC, +2 for CHI)
3. Combine the two, factoring in injuries, for current power rating. Rough estimate would yield about +7 for LAC, +4 for CHI, imply LAC to be a 3 point fav on neutral ground.
4. Pretend this game is in Chicago, and CHI has an extra day of rest. Roughly CHI-1 then would be the spread.
5. Sense check with moneyline: a 1 point spread would mean CHI has roughly a 53% chance to win. Sounds reasonable.

Bottom up:

1. Rate every player. Chris Paul we projected at the preseason +7 and he’s played basically to expectation. He’s played about 73% of minutes eligible, but since this is a close and big game, let’s say he’s going to play 80% of minutes.
2. Project a rotation, and sum-product for each team. I get something like LAC is a +11 team, while CHI is a +6. Both teams are a lot higher than in a top-down method, because I am not factoring in minutes for end of the bench guys. So LAC should be about a 5 point fav on neutral ground, which sounds decent, as LAC’s bench is much weaker.
3. Adjust for rest/HCA. Something like LAC-1 would be the spread.
4. Sense check again with moneyline. This would imply LAC is 53% to win. Again, sounds reasonable.

Then the linesmaker will combine the two methods, think about specific match-ups and coaching, and factor in how much people have bet on the two teams in the past. How does PK sound? (PK means the spread is 0.) It’s not that scientific of a process, but it doesn’t matter if the lines is off, as gamblers will very quickly hammer out the line.

How do NBA lines move?

Typically BetCRIS is the first book to open a line, opening the day before the game is to be played. Pinnacle and The Greek open shortly afterwards, then most other sports books don’t even try to make a line and instead just follow the leaders. The limits are typically very small, $2,000 maximum. Most books are within half a point of the market average, and almost always all are within a full point. There’s three likely scenarios on why a book is off market:

1. The bookmaker screwed up. The guy that was supposed to be on top of the sport went to the bathroom, the market moved, and they are now going to get a flood of money on a side they don’t want.
2. The bookmaker needs a side to balance the book. For whatever reason if they are heavy on CHI, they would be willing to give up an extra point of value in order to attract LAC money.
3. The bookmaker has specific information, usually injury related, that it believes the market does not have. This requires a very confident and experienced linesmaker to be able to swing the line out of sync with the market.

Books are forced to take a side, as it’s impossible to have exactly the same dollar amount of both sides of a bet. They would like to be heavy the “right” side — the side they feel is better, although it’s questionable whether books know which side is the right side. Books also need to ensure they are not unnecessarily exposed on a single game — even if a bookmaker is confident on a side, risk management dictates the book is loathe to take a 90%-10% split in money wagered on a game, even if they are holding the “right” side. Hence, books move the lines in order to attract money on the other side.

Within minutes of a line opening, there will be line movement. These are guys who have thought about the game and have made a number, created a way to be alerted when the lines open, and bet on numbers they think are even half a point off — obviously professionals. Sometimes, there are fakes, in that gamblers will bet one side in hope of moving the line, and then will come back on the other side when limits increase. Only after the bookmaker has seen sufficient action on both sides will the betting limits be increased. Less than a quarter of NBA game spreads open and close at the same number.

Citing opening lines on a game is pointless. Many smaller books will rush out a line and send it to the media for publicity, but only after the limits raise is the line actually meaningful. Once the game closes and all money is on the game, then the spread is probably the single best indicator to predict a game’s results. (Note: For reference, Pinnacle’s standard max bet for an NBA game side is $20,000, although even that number will be increased for marquee games.)

How good is the market?

Very. The below charts are from my database of CRIS closing spread for the 1995-1996 to 2013-2014 seasons (Note: I apologize for any data errors, but there shouldn’t be many.). The line of best fit on the following graph is Observed Win% = 50% + 0.033461 x (Spread), or that by every additional point a team is favored, the team is about 3.3% more likely to win the game. The R^2 is .9939, which means more than 99% of the variation in likelihood to win the game is found within the spread.

That the spread predicts likelihood of a winner is a happy coincidence — that’s the job of the money line. The actual purpose of the spread is to predict the margin of victory, and it does so well, with an R2 of .9885, which means slightly less than 99% of the Margin of Victory is explained by the spread. The line of best fit for the below graph is Margin of Victory = 0.967968 x Spread, or that for every point a team is favored, they typically win by .97 points. (Note: Spreads above 10 run into small sample size issues and hence are not included, although the relationship continues to hold very well — R^2 is still above .98 in both equations.)

Despite being a social science with so many variables, predicting the winner of NBA games is a solved problem.

So can people beat the spread?

Yes.

But it is hard.

Elihu Feustel, in his book Conquering Risk, estimates 98% are recreational bettors who are guaranteed to lose in the long run, <2% are sharp, and “tiny fractions” of 1% are syndicates, “a group of talented individuals who put their skills together like a business to generate profits from sports betting.”

The Wall Street Journal, citing Bwin (a recreational sportsbook, one that does not cater to professionals) data used for studies on gambling addiction, cites past gambling data showing about 11% of gamblers win. However, of the 10% who gamble the most, only 5.4% win.

I spoke to seven bookmakers, and heard a range between 3% to 10% of accounts win. Note that percent of accounts is not the same as percent of people — as winners get banned, they create new accounts, so the percentage of accounts that win overestimates the number of winning bettors. From these data points, I feel the consensus estimate that I always hear, 5%, probably skews high.

How do winning gamblers make money?

Generally speaking, there are two types of bettors:

1. Value bettors, who typically have a firm estimate of what they think the number should be, which comes in part from a model. Very few people blindly bet a model result, and these people are typically not successful. The trader understands what the model does and does not include, and will adjust accordingly.
2. Situational handicappers, who typically don’t know what the number should be, but still think that the market number is not appropriate.

I won’t get into how to build a model, but I will go into three common cases of situational handicapping.

An overrated player being injured

Despite all the plaudits about his play, I felt Brandon Knight to be overrated by the common consensus, and wrote an article saying so. There was a nice situation for a situational handicap on February 2, 2015, when the Bucks opened as a seven-point underdogs, but were bet down to a 5.5 point underdog. At around 6pm Eastern time of game day, Brandon Knight was a late scratch with a sore right quadriceps and the spread moved immediately, probably on air, (i.e., not because of bets, but in anticipation of bets) to MIL+6.

Ideally, one would be able to value the Bucks without Brandon Knight, and project how their performance would be against the Raptors with a model. The situational handicapper would have no idea whether the injury to Brandon Knight is worth the 0.5 point move, but would reason that because Knight is overvalued by the market, the Bucks would be a good bet. This is obviously very noisy, and hard to quantify the edge that MIL+6 would have, but is a good example of a situational handicap.

Team trends

Instead of betting spreads (who will win, given a handicap) and the money line (who will win), one can also bet totals — how many combined points will be scored by the two teams. Projecting a total  has two key elements — how many points each team will score per possession and the number of possessions the teams will have.

The below chart is a list of over-under results for the Orlando Magic in January 2015. The streak of seven overs in a row between 12 January 2015 and 25 January 2015 would be the equivalent of flipping a fair coin and having it land heads seven times in a row, which has less than a 1% probability. However, when flipping a coin 82 times, there is a ~26% chance of observing 7 heads in a row at some point, so this is an unremarkable result. However, the pace also noticeably spiked in January, coinciding with this streak of overs.

After the game on January 10, 2015, some quotes suggested there was a change in the approach the Magic play.

Nikola Vucevic: “We talked about it throughout the whole year: that we want to play at a faster pace. We weren’t doing it for some reason, and I think the guards just one game decided, Vic and Elfrid, to as soon as they get the ball just run. We just followed them, and everything kind of came into place.”

Victor Oladipo: “Pace. Changing the way we play. Realizing how we’re effective and what we have to do in order to win. We’ve just got to continue to keep doing it.”

Even opponents recognized it. Dwight Howard: “I just think it started with their point guard, the guy with the crazy hair, he’s the one that started everything. On the offensive end, he just pushed the pace and he made things happen.”

Zach Lowe noticed too, mentioning in his column posted on January 14, 2015: “The Magic are trying to be a fast-paced spread pick-and-roll team, with three shooters spotting up around (mostly) Payton/Vucevic pick-and-rolls.”

The Orlando Pinstriped Post agreed in a January 15, 2015 article: “As the players put it, they and coach Jacque Vaughn chose to pick up the pace and find more efficient, quicker ways to score. Since laying that egg against the Lakers, the Magic have looked fresh and energized, thanks in large part to their young starting backcourt of Elfrid Payton and Victor Oladipo.”

With more possessions in a game due to the increased pace of the game, the total points scored was always going to be higher. It didn’t require magic, or even careful observation of the Magic: the scouting and the stats both asserted that the Magic were a different team in January, and the market was a bit slow to adjust, leaving a profit opportunity for astute gamblers. Again, this is probably sub-optimal, as one would like a model result to benchmark against rather than blindly betting the overs, but this is another example of a situational handicap.

Wisdom of Crowds

The concept of the wisdom of crowds is well known but commonly mis-interpreted. On August 22, 2014, ESPN had an NBA Summer Forecast in which 224 experts tried to predict the number of wins of every NBA team in the upcoming season. The panel included famous statheads like Daniel Myers, Jeremias Englemann, Kevin Pelton, Dean Oliver, journalists like J. A. Adande and Chris Broussard, ex- players like Antonio Davis and Tim Legler, and team-specific bloggers from the likes of Roundball Mining Co. That’s a diverse, large, and well differentiated crowd, meeting all the requirements for the wisdom of crowds. Handily, we can test the wisdom of this crowd because win totals are something that can be bet on, albeit on a fairly small market. The LVH Westgate has the largest limits (max bet $1000) and opened on September 30, 2015.

Betting every team’s projected season win totals from the Summer Forecast against the LVH opener would have had a handicap of one less month of information, but still would have yielded a record of 18-12. (Note: Basketball-Reference projections for season wins were used to project profit or loss for teams which have not already cashed.) But one doesn’t need to bet every team — how about betting only games where there’s at least a one-game difference between the betting line and the expectation? 15-5. Two-game difference? 9-3. Three-game difference? 3-0. (Note: Increasing confidence leading to a greater win percentage is a fabulous sign for a model’s robustness. Data current as of April 1, 2015.)

Contrast this with the ESPN NFL panel. 13 panelists is a much smaller sample size, and the diversity is much less — nine ex-players, three journalists, and only one quant guy. This ESPN Panel predicts the result of every NFL game, and @AnonymousGamblr on a recent podcast contended one should blindly bet the other team against the spread when the panel is unanimous in predicting a winner. The thinking is that this crowd is not one that is particular adept at picking games, but has disproportionate market influence due to their status.

This approach didn’t work that particular game — the Falcons won 56-14 and easily covered the 5.5 point spread, but over the course of the season, fading this panel would have gone 45-39-3 against the close. That 53.5% may not sound like much, but being profitable in a liquid and deep market of America’s most popular sport to bet on a method that requires no knowledge is very impressive.

What’s the difference? The ESPN NBA panel is wiser than the NFL one (and the NFL game market is wiser than the NBA season win totals). Understanding the psychology of the market is a great way to profit on investing and in sports gambling. I wouldn’t recommend betting the NBA Summer Forecast or against the ESPN NFL Panel blindly next year, but these are useful to consider as examples of situational handicaps.

Levers of Gambling Profitability

In investing, the DuPont equation is well known for understanding how much return an equity investment yields. In a similar analysis, gambling can be broken down into three levers: vig paid, line value, and ability to hit on coin flips.

Reducing Vig

Vig is short for vigorish – typically, one must risk $11 to win $10 (also known as -110 lines), hence requiring a 11/21 ≈ 52.4% win ratio. If one can lower it by betting into -105 lines, found at certain sports books such as Pinnacle Sports, then that required win ratio would be lowered to 10.5/20.5 ≈ 51.2%.

Bookmaker, the US division of BetCRIS, is currently giving a 50% welcome sports bonus, up to $300. (Note: All bonuses will have restrictions before withdraw.) Right now Bookmaker gives back to its Platinum customers about ~0.8% of the total amount risked via their BetPoints loyalty program. (Note: Winning too much will lose one’s ability to participate in loyalty programs.) There is also debt forgiveness, whether through the kindness of the book, or by running away from debts. These would lower the costs associated with gambling.

On the other hand, certain books charge vig on bets that push. Both that and buying a tout’s picks will increase the cost of gambling, and be seen as paying higher than normal vig.

Line Value

From Elihu Feustel’s excellent book Conquering Risk: “Closing lines are the best predictor of the fair line because of market terror or market efficiency, depending on your perspective. In the stock market, if there is an efficient market and perfect information, any stock’s price will be properly priced (neither too high nor too low). Curiously, market efficiency works better in sports setting than in stock betting because, although the sports market is less efficient than the stock market due to higher transaction costs, the information is more readily available, and teams more transparent than most publicly traded companies.”

The theory behind line value is akin to the efficient markets hypothesis in finance. Say in the earlier example, the Clippers closed as a two-point favorite at -110 vig against the Bulls. Earlier bets are honored at the line when they are placed, so it’s possible to have a ticket on Clippers -1 -110. This is a more favorable price than the market — this ticket would push instead of lose if the Clippers win by exactly 1, and would win instead of push if the Clippers win by exactly 2.

One can calculate exactly how much more favorable it is one of two ways:

1. Look at what it would cost to buy onto the -1. If the current market price is Clippers -2 -110, at many books one can pay more vig to bet an the alternate line, say, Clippers -1 -125. That would imply the LAC -1 bet has an Expected Value (EV) of about 3%.
2. Look at historical push charts to determine how often a two-point favorite wins by two-points and by one-point. The exact math may be tricky because of differing approaches used to counteract the small sample size, but historically a one-point boost at -2 is about 3 to 4% in EV.

From summing up one’s bets by their line value, an expected win percentage can be derived. This is an excellent predictor for one’s future win percentage, much better than past win percentage in the same vein that margin of victory predicts future win-loss record better than past win-loss record. If we can continue to place bets as favorable as this example, we would expect to win about 53% of our bets. Books profile players based on their line value. Within 25 or 50 bets, a book will have a good idea of whether the player will be a profitable or unprofitable bettor.

A word of caution: line value is not useful as a metric in other sports where the market is not nearly as efficient. It is also self-perpetuating for some gamblers, as when they bet they move the line, and hence create line value for themselves.

Another way to get line value is to pick off obviously wrong lines. Last year, I saw the Oklahoma Thunder at +1200 (i.e., risking $100 would pay $1200, implying about a 7.5% probability) to be winning at halftime and full-time against the Philadelphia 76ers — a typo, as the line should have been -1200, not +1200. I’ve also seen lines like DAL -3 +1050 when the market was DAL -3 +105, another typo. I would advise not betting these, as betting them will likely lead to being banned by the sportsbook, or being freerolled (the book will not pay on a winning bet, but will keep the money on a loss) on the bet, or even losing the entire balance deposited at the book. If these types of bets are accepted and honored, then it is a EV goldmine.

Lastly, there are arbitrage opportunities. Imagine one book offers SAS-300/PHI+270, and another book offered SAS-350/PHI+310. Betting on SAS-300 at one book and PHI+310 at the other would guarantee a profit. This situation is extremely rare, but can be interpreted as line value, as at least one of the lines is out of sync with the market.

Coin flips

By efficient markets theory, betting into the closing spread in a large market should be a 50-50 proposition, or like flipping a coin. In practice, because of well-known biases, gamblers instead average 48.8% against the closing spread in a database I have access to.

The conventional wisdom is that very sharp players can bet at the closing spread at better than 50-50, but not enough to cover standard -110 vig (i.e., their winning percentage is greater than 50%, but less than 52.4%.) In practice, I have seen gamblers hit as high as 54% with no line value, but it is hard to determine whether this is small sample size, a function of them betting so late that the line did not have a chance to move, or truly sustainable. As a general rule, I would say that coin flipping as a value driver is not sustainable for most bettors.

Conclusion

Sports betting has changed a great deal with the advent of Big Data, with increased awareness of statistics and its applications making spreads tighter, but certain gamblers have managed to stay ahead of the market by trying to make as many +EV bets as possible, constantly analyzing and quantifying the game while managing their risk. Like in most industries, a profitable living is hard, but certainly not impossible. The odds are against you, good luck!

I hope this is an insight into the world of sports betting. Please contact me or leave comments with any corrections or additions.