December 27, 2009
Pittsburgh, PA
The Pittsburgh Steelers beat the Baltimore Ravens 23-20 in a game in which the star running backs were future elevator assault perpetrator Ray Rice and future racial instigator Rashard Mendenhall, and the quarterbacks were future team non-supporter Ben Roethlisberger and CURRENT Cleveland Browns starter Joe Flacco. This game is notable because the spread closed Steelers -3 and the total closed 43, the only game in my database (regular seasons 2007-2021) in which both the spread and the total landed exactly on the number. For my final article of 2023 I’m going to take the tired old trope “Vegas knows”, add a question mark and turn it into a bet. Do you want to bet on “Vegas”? Or against them?
We can think of the outcome of an NFL game as a point on a two-dimensional graph, with the score margin on one axis and the total points on the other. Starting from the spread of Steelers -3, move 7 points in either direction to form a range that’s 14 points wide (Steelers win by 10 to Ravens win by 4). Starting from the total of 43, move 7 points in either direction to form a range that’s 14 points wide (36 total points to 50 total points). Overlap those two ranges to get a 14 x 14 square that we’ll call “the box”.
Final scores such as Pit 23 Bal 20 / Pit 26 Bal 21 / Bal 24 Pit 22 would be inside the box.
Final scores such as Pit 45 Bal 0 / Bal 21 Pit 3 / Pit 27 Bal 26 would be outside the box.
Final scores such as Pit 30 Bal 20 / Pit 26 Bal 16 / Bal 26 Pit 24 would be on the border of the box.
Let’s discuss a bet on whether a particular game would fall inside or outside this 14 x 14 point box, with anything on the border being a push.
This would be a unique kind of bet because you’re not betting on a particular side or total; rather, you’re betting on how predictable (by “Vegas”, if you must) or unpredictable the outcome will be. You can think of this bet as a distant cousin of the volatility derivative, something that’s gained a ton of popularity over the last couple decades in the big casino called Wall Street.
Why 14 x 14? No particular reason, other than that a 7 point move in either direction is big enough to include a good mix of key and non-key numbers no matter where you’re centered. But you could make the box any size you want.
Okay, time for the fun part. How can we price this bet? We can start by looking at 15 years of historical data.
Mathematically, the inside the box / outside the box bet is equivalent to an over/under on this quantity, which we’ll call “distance to center”:
distance to center = max [ abs( V team points – H team points + V spread ), abs( V team points + H team points – total)]
where abs is the absolute value function, a.k.a. that thing where you chop off the negative sign if there is one.
With a box that’s +/- 7 points in size, an “inside” bet is a bet on distance to center under 7, and an “outside” bet is a bet on distance to center over 7, with both bets pushing on a distance to center of exactly 7.
Here is the distribution of distance to center for 15 years of NFL regular season games:
Our 7 point box has an inside win frequency of 16.2% and a push frequency of 2.5%, for fair odds of -501 outside / +501 inside. To get to something approximating equality between inside and outside, we’re gonna need a bigger box. Much bigger. You’d need to go +/- 13.5 from your center, giving you an enormous 27 x 27 box.
I have to admit that this result surprised me so much that I went back and double checked my data, then triple checked it. And I’m not the only one – when I asked my Twitter followers, who I’d like to think skew sharper than average, their guesses were mostly as wrong as mine.
Why does our intuition steer us so wrong here? I’m no cognitive psychologist, but if I had to guess I’d say it’s a combination of two familiar themes: underestimation of variance, and confusion between unbiasedness and precision when it comes to market efficiency. NFL closing lines are among the most efficient in the sports betting world, but efficiency only requires unbiasedness, not precision. Meaning, a total of 43 is efficient if there’s an equal probability of landing over 43 and under 43, even if it never lands exactly 43 (or even if it never lands anywhere close to 43). Applying a market efficiency argument to this inside/outside bet is like using an electric-type attack on a ground-type Pokémon: it has no effect. (Sorry, this is what happens when you live with a 10 year old.)
If any of my dear readers happen to operate a sports book, this is where your eyes should be lighting up because your whole business model is built around taking cognitive defects and turning them into cash. Offer +400 odds on an inside the box prop, and I would guess that the public will be pushing kids and grandmothers out of the way to get to the window.
Next, we need to try to tame this monster that we’ve created. How can we handicap this crazy thing?
Using my intuition even though it’s already let me down once, I would expect a strong predictive relationship between higher inside the box frequency and lower spreads and/or lower totals. Right? Wrong (again). The correlations are weak to nonexistent.
What about that old Wong teaser classic, counting the number of 3s and 7s that are inside the box?
There’s something there…sort of. The head scratcher is the high inside frequency where there are no 3s or 7s in the box, corresponding to spreads of 14 or more. Why? I’m not quite sure. I guessed that it had something to do with no zeros in the box, but that doesn’t seem to be it. Leave your theories in the comments!
How about by month? Surely you’d have more outside the box in September and more inside in Dec-Jan as we know more about the teams, right?
Eh…sort of…
So we’ve tortured this data and really found very little in the way of predictive power for this inside/outside bet…which is an interesting phenomenon because outside of novelty stuff like coin flip props, there isn’t much in the sports betting universe that truly defies analysis.
BUT…let’s conclude 2023 on an unanswered question. Perhaps even an unanswerable one.
Does it really defy analysis? Or are we just doing the analysis wrong? Let’s return to one of my favourite themes: Total variance = process variance + parameter variance. This is a bet on variance, after all. Perhaps all we’ve shown so far is that there’s not much we can do to predict the process variance. But what the data doesn’t show is which games had key players out, or playing hurt, or bad weather, or a visiting team that arrived late because of a delayed flight. Some of these things may be quantifiable with a detailed enough data set. Some may not…in which case we might have to rely on judgment. Is it possible that we’ve accidentally discovered data-nerd kryptonite, a problem that can only be properly solved with good old-fashioned human handicapping???
And on that note, I’d like to wish all of my readers a happy holiday season and all the best as we ring in the new year. If there are any enterprising Ontario-licensed operators out there who would like to try their hand at the inside/outside the box prop (Super Bowl??), you’ll get a bet from me…even if this data nerd can’t crack it on a spreadsheet.
See you in 2024.
Matt
Plus EV Analytics 
I would chalk the 14+ thing up to teams letting up when up 2 or 3 tds. When you look at average cover for a 2.5-5.5 fav is 7.5-8pts, but a 14.5+ fav has a cover margin closer to 6-6.5pts.
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