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14 Dec 2007
Outside Foxborough: Toeing The Betting Line
Note: Due to some technical difficulties on the Patriots Daily site, we're running Outside Foxborough on FO this week.
A significant portion of the talk surrounding this week's upcoming Jets-Patriots game has revolved around the betting line for the game, and how dramatic it is in light of both the Patriots' historic offensive attack and a perceived desire for retribution following the Week 1 "Cameragate" incident.
For those of you unfamiliar with a betting line, allow me to provide you with an example.
DALLAS (-7.0) (-$120)
WASHINGTON (+7.0) (+$105)
In this example, Dallas is the home game, as their team name is capitalized. They are favored by seven points over Washington. These seven points constitute what is known as "the spread". What that means is simple: For a bet on Dallas to be successful, Dallas must beat Washington by more than seven points in order for them to "cover" the spread. If Dallas wins by exactly seven points, the bet is a push and the bettor's money is returned. For a bet on Washington to be successful, they need to win, tie, or lose by less than seven points.
The second part of the line, to the right, contains what you'll need to gamble to make $100 on your bet. In Dallas' case, the negative sign in front of the $120 indicates that the odds are such that a casino will pay you $100 if you gamble $120 on Dallas, which would return a total of $220 to the bettor. In Washington's case, the positive sign means that if you bet $100 on Washington, you'll receive $105 in winnings, for a total of $205 in return. In short, if the sign is negative, it refers to how much you'll need to gamble to win $100; if it's positive, it refers to how much you can win for gambling $100.
Now that the explanations are out of the way, let's take a look at the Jets-Patriots line. In this game, the spread has been at or around 24 points all week. That's right at the accepted record for history's largest line, which was a 1976 encounter between the Pittsburgh Steelers and the Tampa Bay Buccaneers, who were an expansion team. The Steelers won, 42-0, and covered. If the line gets to 24.5, it would be a new record.
What all that in the hopper, can we make any sort of prediction about whether the Patriots are likely to cover this gargantuan line? Of course, that's where the data comes in.
Intrepid FO intern Matt Accornero went and found the betting lines in all games that occurred from 2001 through 2006. For many, he found both the opening and closing lines, although some opening lines are missing. This provides us with 1594 games to analyze, which isn't an irrefutable sample, but is certainly a sample that should reveal some trends, if there are any. For the purposes of this study, we'll be looking at the closing lines.
Of course, where the sample becomes a larger issue at the margins, which is where we are with the Patriots this year. Simply put, not many teams get to go into games with a 20+ point margin; in fact, not a single team in our dataset had a 20+ point spread. The closest were the 2002 Eagles, who played the Texans at home giving -19.5 points, in a game where they did not cover, only beating the Texans by 18.
First, I checked to see whether the lines change depending upon the time of the season -- namely, does Vegas feel more confident about teams later in the year, and respond to that by setting more robust lines?
| Avg Spread | Avg Outcome | Diff | |
| Weeks 1-4 | 2.32 | 2.56 | 0.24 |
| Weeks 5-8 | 2.41 | 3.21 | 0.80 |
| Weeks 9-12 | 2.45 | 1.61 | -0.84 |
| Weeks 13-17 | 2.67 | 2.59 | -0.08 |
In that table, the Avg. Spread being 2.32 means that the home team was favored, on average, by 2.32 points. (All spreads in the article are relative to the home team.) They won by 2.56 points, or .24 points more than the expectations of the line. As you can see, the line does rise slightly as the season goes along, but not so much to be a significant difference. Furthermore, the average outcome doesn't seem to be particularly affected, so it's hard to say that familiarity really affects the spread.
Next, of course, I wanted to see if there were any trends that existed in teams beating the spread. First, I checked point differentials in games and compared them to the pre-game spreads, to see if there were any differences. I marked games where the difference between the expected outcome (the spread) and the outcome itself was more than three points. I also ignored spreads that didn't have at least ten games of results to draw from.
| Line | Diff |
| -7.5 | 3.9 |
| -7 | 0.9 |
| -6.5 | 0.6 |
| -6 | -1.0 |
| -5.5 | -2.6 |
| -5 | |
| -4.5 | -5.5 |
| -4 | -1.7 |
| -3.5 | 1.9 |
| -3 | -0.9 |
| -2.5 | 1.8 |
| -2 | -3.1 |
| -1.5 | 1.1 |
| -1 | 3.1 |
| 0 | 1.1 |
| 1 | -4.7 |
| 1.5 | 0.2 |
| 2 | 0.5 |
| 2.5 | -2.0 |
| 3 | -0.6 |
| 3.5 | 2.8 |
| 4 | 0.1 |
| 4.5 | 0.9 |
| 5 | 1.9 |
| 5.5 | 0.3 |
| 6 | -0.5 |
| 6.5 | 0.3 |
| 7 | 0.7 |
| 7.5 | 3.5 |
| 8 | 0.9 |
| 8.5 | -0.7 |
| 9 | -2.3 |
| 9.5 | 2.6 |
| 10 | 1.8 |
| 10.5 | -0.9 |
| 11 | -2.1 |
| 11.5 | 3.9 |
| 12 | -5.1 |
| 12.5 | |
| 13 | -0.4 |
| 13.5 | -6.2 |
When the line of a game was -7.5 points, or in other words, when the road team in a game was favored by 7.5 points, the average score saw the road team win by 3.6 points, or the home team lose by 3.6. That results in a difference of +3.9 points from the expected margin.
As you can see, the ends of the spectrum saw much more dramatic differences from the expected scoreline than the middle. Unfortunately, it doesn't mean much, because the differences were strewn in opposite directions. Take a look at the 11.5 and 12-point spreads; in games where the spread saw the home team favored by 11.5 points, the home team won, on average, by 15.4 points; in games where the spread was 12 points, the home team only won by 6.9 points. In other words, there's no real indicator of what a big line does beyond the fact that it's more likely to see variance than a small spread.
A natural followup: Are favored teams more likely to cover in certain types of games than others?
| Spread | Favorite | Underdog |
| -7.5 | 25% | 75% |
| -7 | 35% | 56% |
| -6.5 | 33% | 67% |
| -6 | 50% | 50% |
| -5.5 | 65% | 35% |
| -5 | 56% | 33% |
| -4.5 | 70% | 30% |
| -4 | 50% | 46% |
| -3.5 | 41% | 59% |
| -3 | 46% | 46% |
| -2.5 | 49% | 51% |
| -2 | 60% | 33% |
| -1.5 | 46% | 54% |
| -1 | 43% | 57% |
| 0 | 55% | 45% |
| 1 | 42% | 58% |
| 1.5 | 53% | 47% |
| 2 | 55% | 45% |
| 2.5 | 39% | 61% |
| 3 | 43% | 48% |
| 3.5 | 58% | 42% |
| 4 | 45% | 53% |
| 4.5 | 51% | 49% |
| 5 | 59% | 41% |
| 5.5 | 53% | 48% |
| 6 | 45% | 53% |
| 6.5 | 50% | 50% |
| 7 | 49% | 49% |
| 7.5 | 58% | 42% |
| 8 | 44% | 52% |
| 8.5 | 50% | 50% |
| 9 | 39% | 61% |
| 9.5 | 54% | 46% |
| 10 | 50% | 42% |
| 10.5 | 43% | 57% |
| 11 | 31% | 69% |
| 11.5 | 57% | 43% |
| 12 | 40% | 60% |
| 12.5 | 38% | 63% |
| 13 | 46% | 54% |
| Avg. | 48% | 51% |
Basically, no. The only thing that's even remotely worth noticing and looks the slightest bit consistent is that heavy road favorites (here, -6.5 to -7.5 points for the home team) aren't likely to cover. Of course, the Patriots have been favored by way more than 7.5 points on the road at points this year.
What about that magical item in our bag of holding known as DVOA? Well, it may be able to offer us some assistance. The difference between two teams' seasonal DVOA has a very strong (+.54) correlation with the difference in points between them in that game. The difference between the Jets and the Patriots' DVOA, through thirteen games, is 79.7% -- large, but not the largest in our dataset. If we note the scores of all games with a difference of 75% more between the overall DVOA of the two competitors, the average margin of victory in said games is…23.7 points. Not bad.
Finally, is DVOA smarter than Vegas? Well, realistically, no. If it was, Vegas would have snatched us up, and you wouldn't be reading this column. Is it helpful? Sure. There are 34 games in which the line of the game was six points or more, while there was a difference in DVOA of ten percentage points or more in the other direction. For example, when Green Bay took on Detroit in Week 3 of the 2006 season, Green Bay (2006 season DVOA: -1.4%) was a 6.5 point underdog heading to Ford Field, whose Lions' 2006 DVOA was -19.5%. The result? A seven-point Packers win, which would be a credit to DVOA as opposed to the Vegas line. In those 34 games, DVOA went 23-11. In all fairness, the DVOA metric we're looking at has a whole season's results in it, while Vegas can only see what's been played so far. If we only look at games played in Week 9 and later, though, DVOA remains successful (8-6) against the spread.
Unfortunately, our look into the numbers didn't reveal too much into being able to make an informed decision about whether to bet on the Patriots or the Jets on Sunday. I'm personally inclined to take the Jets for several reasons, primarily because of their pacing. The Jets have been one of the slowest teams in the league over the past few years, using a slow, ball-control offense while playing defense against teams that gashed them on the ground, using up more plays and time in the process. Furthermore, while we haven't done the research into this topic, I would imagine the swirling winds and blustery weather predicted limiting both teams some offensively. All in all, I obviously would predict a Patriots victory, but it might only end up being by a couple of scores instead of four or five.
23 comments, Last at 21 Dec 2007, 5:56pm by Fred Farmer
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Comments
One has to be careful with these stats, and shouldn't use any one number to draw conclusions. However, it does look like big home dogs (6 points or more) cover and big home favorites (12 points or more) cover. Absent weather, the Pats look interesting!
psst ... both team names (DALLAS and WASHINGTON are in caps in your example)
It would have been useful to have had a column indicating how many data points existed for each Line value.
When you have tables of data like the ones here, you absolutely must include the number of data points as well. Otherwise it's very hard to interpret the information.
And for the DVOA v. Vegas comparison, as you say, using season ending DVOA isn't a useful comparison. So don't do it! In addition to cheating by using info Vegas doesn't have from games that aven't been played yet, you're using the results of the game you're predicting in the DVOA score. That's really not useful.
#2, That's because they're both home, playing remotely via the Internet on Madden, xbox, what have you. Cuts down on injuries.
"Of course, where the sample becomes a larger issue at the margins, which is where we are with the Patriots this year. Simply put, not many teams get to go into games with a 20+ point margin; in fact, not a single team in our dataset had a 20+ point spread. The closest were the 2002 Eagles, who played the Texans at home giving -19.5 points, in a game where they did not cover, only beating the Texans by 18.
First, I checked to see whether the lines change depending upon the time of the season — namely, does Vegas feel more confident about teams later in the year, and respond to that by setting more robust lines?
Avg Spread Avg Outcome Diff
Weeks 1-4 2.32 2.56 0.24
Weeks 5-8 2.41 3.21 0.80
Weeks 9-12 2.45 1.61 -0.84
Weeks 13-17 2.67 2.59 -0.08
In that table, the Avg. Spread being 2.32 means that the home team was favored, on average, by 2.32 points. (All spreads in the article are relative to the home team.) They won by 2.56 points, or .24 points more than the expectations of the line. As you can see, the line does rise slightly as the season goes along, but not so much to be a significant difference. Furthermore, the average outcome doesn’t seem to be particularly affected, so it’s hard to say that familiarity really affects the spread. "
Hm. Either I am not understanding the study/presentation here, or the study/presentation is flawed. I don't see how that chart could be showing effects of familiarity on the spread, even if the numbers were different than they are. I think that chart is showing nothing more, and nothing less, than Vegas thinks the average home field advantage is about 2.5, and possibly that home field advantage is bigger later in the year (probably due to weather effects for outdoor teams).
Let me give an example. Imagine a good team who has two perfectly average teams in division, who they play twice each. Let's further say that in the first few weeks they play each team once, one at home, one away. How good is the good team for the example? Let's make it so that on a neutral field, they would beat a perfectly average team by 7 points in the estimation of Vegas.
The spreads for those two games might look like this:
Good team (GT) -4.5 at Avg Tm 1.
Avg Tm. 2 +9.5 at GT.
The average spread relative to the home team is (9.5-4.5)/2=5.2=2.5.
Now lets say that later in the year, Vegas has determined through familiarity that the average teams are, in fact, average, but GT is VGT and probably would beat an average team by 10 points on a neutral field. The spreads for the remaining two games between these teams would be:
VGT -7.5 at Avg Tm. 2
Avg Tm. 1 +12.5 at VGT.
The average spread relative to the home team is (12.5-7.5)/2=5.0/2=2.5.
Wouldn't the way to see if familiarity is affecting the spreads be to factor out the home field advantage from the spread, and then take the average of the absolute values of the spreads?
Or maybe the way to see effects on familiarity would be to take the average of the spreads relative to the favored team. That should do the trick-- in my example above, the average of the earlier/non-familiar spreads would be 7 relative to the favorite. The average of the later/familiar spreads would be 10 relative to the favorite.
"Finally, is DVOA smarter than Vegas? Well, realistically, no. If it was, Vegas would have snatched us up, and you wouldn’t be reading this column."
I combine team's offensive and defensive DVOA to produce a spread which I then compare to the betting line for that week. If I had bet every game over the past two seasons where the DVOA spread differed from the Vegas line by at least 3.5 points, this would have produced a record of 103-68, or 60%. And that's just betting blindly. Not too bad I think.
Also, if you had backed the teams in each division which DVOA said would have the best record, you'd be on Tampa Bay at about 9/1 and Green Bay at 6/1 (roughly best prices available in the UK) to win their divisions and both at about 100/1 to win the Super Bowl.
For those interested, I think DVOA has a lot to offer for punting purposes.
The weather forecast for tomorrow at Foxboro:
A wintry mix early. Precipitation will change to a mixture of rain and freezing rain for the afternoon. High 37F. Winds ENE at 20 to 30 mph. Snowfall around one inch.
Take it as you will.
"Finally, is DVOA smarter than Vegas?"
Vegas isn't interested in picking the actual outcomes of games; Vegas wants to set a point spread such that an equal amount of money is bet on either side of the line. For the most part, Vegas is very good at setting betting lines, and the closing line in particular will be very accurate (because by the time the betting closes, they've seen what actual bettors are willing to bet).
So the notion of "being smarter than Vegas" is misguided; what you want to do is be smarter than the mass of OTHER BETTORS. For that, you'd want to look at not only "what is the likeliest outcome of a game" (based on DAVE or DVOA) but also which factors influence bettors (e.g. does the average bettor overestimate the effect of "revenge", or underestimate the effect of weather?) and what factors influence the NUMBER of bettors (e.g. in a game between teams playing for populous New York and low-population Green Bay, do the homers for New York sway the line?).
But I'm surprised to see the mis-statement about the nature of Vegas point spreads, in an article to which they are so central.
#10 beat me to it. It is a thing that is missed by many who aren't serious gamblers. When it comes to the spread you are tyring to be smarter than aggregate gambler's opinions, not the bookies.
Also, one of the problems with betting the spread is that it does not align the goals of the teams with the goals of the gambler. If you bet Dallas -7 and they are on the Washington 10 yard line with 8 seconds to go in a tied game. They kick a field goal to win the game. You need a touchdown to save you from losing. Your objectives aren't synced up. Same thing occurs during garbage time -- underdogs can sneak back in and cover large spreads because there is no downside to the winning team.
I am convinced DVOA could be used to profitably work the straight money line bets (which do align the goals of the gambler and the team), I'm just not sure how.
Although it is a common belief that the bookie is trying to equalize bets, Levitt has shown using bets-placed data that bookies generally do take positions on games, and on average make money doing so.
Happy Fun Paul - therein is the thing; there is wisdom in the masses. For example, I am in a weighted football pool, with about sixty people, where you pick games with no spread, and weight them according who is more likely to win, starting at 16 points for the game you're most confident in, down to 1 or 3 points depending how many games are being played.
The accumulated average pick in this pool is in second place. I, of course, am dominating in first place, having chosen some 8-9 more games correctly than anyone else, but, year after year, the combined picks of the masses outperform almost every single individual, year after year (I'm usually in contention for the top spot out of the people, last year was the only exception :I)
"I combine team’s offensive and defensive DVOA to produce a spread which I then compare to the betting line for that week. If I had bet every game over the past two seasons where the DVOA spread differed from the Vegas line by at least 3.5 points, this would have produced a record of 103-68, or 60%. And that’s just betting blindly. Not too bad I think.
Also, if you had backed the teams in each division which DVOA said would have the best record, you’d be on Tampa Bay at about 9/1 and Green Bay at 6/1 (roughly best prices available in the UK) to win their divisions and both at about 100/1 to win the Super Bowl.
For those interested, I think DVOA has a lot to offer for punting purposes."
It is easy to spot trends in historical data. What is not so easy is determining if those trends were mere coincidence, or if they are likely to repeat themselves. For instance, NE has beat the spread every week that I have worn my Miami hat, and failed to cover every time I have neglected to wear it. If I had bet based on this, I would be 13-0. Of course, this is simply coincidence, and so placing future bets based on whether or not I am going to wear my hat would be foolish. I realize it is a somewhat silly example, but my point is that just because there is a correlation between event A and event B, does not necessarily mean there is a causation, and if there is no causation, there is no reason to think that the correlation will continue. I believe this is why this site exists, in fact.
Also, if you had backed the teams in each division which DVOA said would have the best record, you would have GB and TB, but you would also have Philly and SF instead of Dallas and Seattle, which you would have had if you had gone with Vegas. You would have better odds with GB and TB, but that is equaled out with 2 things. One, TB was only favored by 1/10 of a win, and two, your AFC lineup would look like this:
NE, BAL, JAC, and SD, while if you took the general consensus, it would be the same except with INDY instead of JAC.
Further, if you were to take the DVOA (or Dave earlier in the year) favorite in every game Vs a person who took the Vegas favorite in every game (moneyline this is), your win % would be virtually identical. At least this year it would be, I don't know about previous years. This isn't a knock on DVOA, being able to match Vegas is a pretty good feat all on its own, but let's not pretend that it is surpassing Vegas when it isn't.
"I combine team’s offensive and defensive DVOA to produce a spread which I then compare to the betting line for that week. If I had bet every game over the past two seasons where the DVOA spread differed from the Vegas line by at least 3.5 points, this would have produced a record of 103-68, or 60%. And that’s just betting blindly. Not too bad I think."
I use a similar system. Difference in DVOA, +.14 for the home team. Then multiplied by 3. This is a remarkably accurate representation of the Spread in most cases, and in the cases where it differs by more than 5 points, I jump on the opportunity (Baring major injuries).
honestabe, what system do you use?
^^
I forgot to add, I use the difference in DVOA (+.14) and multiply it my 21.
The .14 comes directly from FO as the home field advantage. And 21 points is roughly the average score per team in an NFL game. This means 2 teams with a difference of 100 DVOA will have a 21 point spread.
I'm MORE than happy with this system, and I think you'd find it's great for Point Spread leagues.
WIS has also shown some great use in predications against the Money Lines...
re: 15. I have a kinda complicated system which is roughly:
Team Pts =
((1 + Off DVOA) x (1 + Opp Def DVOA))^1.2 x 6/7 x Avg Team Pts
+((1 + S-T DVOA) x (1 - Opp S-T DVOA))^1.2 x 1/7 x Avg Team Pts
I added the constant so that whatever the match-up (eg two evenly matched teams cf. NE v MIA) I would produce a realistic point-spread.
And then I add and subtract pts for home advantage (differs for each team and week of the season).
The only bet which it has shown for this week is KC +4 (it was available in a few places in the UK), as my calculations had TEN as a 0.5 pt favourite.
re. 14:
"It is easy to spot trends in historical data. What is not so easy is determining if those trends were mere coincidence, or if they are likely to repeat themselves."
I might be wrong, but I thought that you can use Excel and the binomial distribtion to find the likelihood that over a sample of 171 games, a 50% punter would achieve a record of 103-68 or better.
This is the system I have used all season, so it's not like I have adjusted my method to find the one that comes up with the best winning percentage retrospectively.
And now that there's been a move for the Giants, my method would suggest that WAS +5.5 is a bet, as I have NYG as only 2-pt faves.
Re: 10, 11, 12
Andrew is correct. Bookies do not necessarily want to equalize the betting. They do take positions, and usually win. See the link for 2 examples this week: not moving the line for Seattle or Indianapolis, despite overwhelming money on one side of the bets. Guess who came out winner for both?
19: Or not, click my name for link. I suppose it is possible they are lying, but according to their own admission, they do in fact set the line in such a way as to attract equal money on both sides of the ball. While sports betting is not really my thing, in my experience, Vegas avoids gambling like the plague.
Re: 20
I think we're both right. Generally, Vegas wants to equalize the money. The cases I pointed out were exceptions. But it would be wrong to assume that by laying money, you are betting against the views of the conventional public. There are clearly games where bookies do take positions. More often than not, they are correct.
In fact, I see this as another reason why NOT to gamble on football. If Vegas really didn't know what they were doing, Aaron would now have a different sports car to drive for every day of the week.
I think people can talk themselves into gambling more easily if they think they are betting against millions of those fans who take off their shirts in snowy stadiums... it's still a bet against the house, and the house always wins.
That I agree with.
A readable article but slightly lacking in rigour.
If you're going to use DVOA to predict game outcomes you absolutely must test your conclusion on out of sample games.
Also using season ending DVOAS to predicted games played within that season is as meaningless as using the actual scorelines.You surely have to use the DVOA values each team had going into that game.
If you're trying to test DVOA against the Vegas line to be fair to Vegas you have to compare the dvoa prediction against EVERY Vegas prediction over a representative timescale.
Just picking out the games where you think Vegas is out of line doesn't hack it.If Vegas arbitrarily chose to add 20 points to the "correct" line of every Monday night game virtually any rating system would pick those games out as having incorrect lines.You'd probably go 17-0 ats,but that wouldn't make every rating system better than Vegas overall.
I've followed this link http://www.punters-paradise.com/forums/showthread.php?t=8278&page=2 posted in reply 158 in the Week three DVOA ratings thread where someone's used DVOA to rate every game since week 5 and they're beating Vegas 99-63 against the spread since then.
Maybe DVOA's better than you think.
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