We might be beating a dead horse, but qualifying for the World Cup out of CONCACAF is an entirely different beast.

Looking at the Hexagonal matches for CONCACAF qualifying during the past three World Cup cycles in comparison to UEFA group-stage qualifying, you see an incredibly staggering advantage for home teams in North America.

Here is a percentile breakdown of results for CONCACAF:

RESULT PERCENT Away Win 21% Tie 18% Home Win 61%

Here is the same breakdown for UEFA:

RESULT PERCENT Away Win 24% Tie 33% Home Win 43%

The bias is clear, but there are many theories as to why this is the case. Longer travel and more uncertain playing conditions are leading candidates, and the cultural fortresses of the Estadios Azteca and Saprissa (in Mexico and Costa Rica, respectively) certainly play a role as well.

Let's break it down. There are 41 percent more home victories and 45 percent fewer draws in the Hex than in UEFA group-stage qualifying. Also, North American World Cup hopefuls earn an average of 2.01 points per match at home.

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The European equivalent only earns 1.62. Over a 10-game group stage, this is incredibly significant and entirely changes how we should be approaching our analysis. By comparison, this bias creates an increasing amount of pressure to perform at home – and makes the road-victory scalp significantly more valuable.

Controlling for home-field biases seen in the Hex, I've created a model that projects the likelihood of qualification by means of a Monte Carlo simulation. Assuming that all CONCACAF teams are equal (though they are most certainly not), below are the qualification chances for each squad. For teams that are stronger than the average, consider these baseline numbers. For teams that are weaker than average, consider these numbers their best-case scenario.

TEAM AUTO FOURTH USA 88.57% 7.77% Costa Rica 73.11% 15.26% Mexico 50.60% 24.1% Honduras 48.85% 23.55% Panama 36.80% 24.14% Jamaica 2.08% 5.19%

Mexico's measly 50 percent chance of automatic qualification is certainly low-balling, but it really does speak to the hole that Mexico have dug for themselves. With the Hex's clear emphasis on home results, namely wins, Mexico's three draws in three matches at Azteca have caused them to drop a handful of points that they would have otherwise been expected to claim (about three – so far).

Scoring above their expected points on the road has certainly kept them afloat, as El Tri have about two more points than previously expected.

While I'm not one to count my chickens before they've hatched, I'm now at least estimating the size of the USA's basket. The USMNT is really in a strong position, having earned above their expected point totals both on the road and at home.

CHECK OUT THE CURRENT CONCACAF HEXAGONAL STANDINGS

Even an average squad would expect to automatically qualify 89 percent of the time with the current state of the Hex table – and I think it's fair to claim that the United States have gone far enough to prove they aren't a middle-of-the-road CONCACAF team this cycle.

The real question becomes how many points the United States will likely need to clinch qualification.

If this simulation was perfect, we could say that the United States has a 97 percent chance of qualifying for Brazil with a mere six points in their final five matches. This is unlikely, since Mexico are likely to outperform the average CONCACAF team for the remainder of their matches.

USA POINT TOTAL WIN HEX TOP THREE FOURTH 25 100% 100% 0% 23 100% 100% 0% 22 99.3% 100% 0% 21 98.82% 100% 0% 20 90.9% 100% 0% 19 79.41% 100% 0% 18 68% 100% 0% 17 30.88% 99.87% 2.18% 16 10.69% 97.82% 2.18% 15 1.68% 88.21% 11.65% 14 0% 45.47% 49.02% 13 0% 14.31% 58.4% 12 0% 2.36% 34.78% 11 0% 0% 9.94% 10 0% 0% 0%

But across hundreds of thousands of simulations of this model, the United States never failed to automatically qualify with at least 18 points. Only when this level was reached would I be comfortable punching some non-refundable tickets.