How, Exactly, Did a Stupid Tiebreaker Screw Mexico out of WBC?

Some might say it was poor pitching, or a lack of timely hitting, that ended Mexico's run in the 2017 World Baseball Classic, but in the end it was math that brought 'em down. The WBC has not been short on drama or fun, and now we've got a little controversy to throw into the mix.

Mexico's team fumed after WBC officials denied a protest and eliminated them while letting Venezuela move forward to a Pool D tiebreaker game against Italy on Monday night. After Mexico hung on to beat Venezuela 11-9 on Sunday night, Mexico, Italy, and Venezuela all finished with a 1-2 record behind Puerto Rico in the pool. Mexico thought it had secured a chance to play Italy in a playoff to determine who would be the second team from the pool to advance. Venezuela thought its WBC was over, and the WBC even fired off a tweet (since deleted) saying that Mexico had survived because of an edge with a mathematical tiebreaker: team runs allowed per defensive inning. But this is where everything went haywire—the concept of a "defensive inning" was initially misunderstood; once it was corrected, Mexico actually lost the tiebreaker by a hair.

Mexico technically allowed 1.12 runs per inning, to Venezuela's 1.11, thus sending Venezuela ahead. The tiebreaker had initially been calculated based on a misapplication from a game played earlier in the tournament. Here's a crucial paragraph from MLB.com's story:

Even though Mexico gave up five runs in the ninth inning of a loss to Italy on Thursday, only eight defensive innings were counted from that game toward the calculation because an out was never recorded in the ninth.

So Mexico got tagged for the five runs, but did not get the additional inning to soften the blow. It might seem like the proper decision, if a cold one, but check out the counterargument by Mexico manager Edgar Gonzalez:

Mexico manager Edgar Gonzalez: "The rule is clear. It doesn't say outs." The tiebreaker rules says "including partial innings."
— James Wagner (@ByJamesWagner) March 13, 2017

WBC officials want you to think of it like calculating an ERA: multiply nine by the number of earned runs and divide by innings pitched, and an inning isn't technically pitched unless an out is recorded.Edgar Gonzalez wants Mexico to be given credit for playing the inning, even if no outs were recorded. Did they play the inning or didn't they? They did. He has a point. It was a bitter pill for Mexico to swallow, and it's still not going down very well.

Nos avisaron antes del juego que si ganamos por 2, pasábamos.
We were told before the game if we win by two, we play tomorrow.
— Adrián González (@Adrian_ElTitan) March 13, 2017

pic.twitter.com/NLIfgk6Vyu
— Adrián González (@Adrian_ElTitan) March 13, 2017

Mex. officials said they're lodging a protest. AGonzalez said he'll rethink his future WBC participation or tell players it's not worth it.
— James Wagner (@ByJamesWagner) March 13, 2017

The protest was denied, and A-Gon is emotional about the loss. Hey, if it's cool for the Dominican Republic to go bonkers for beating Team USA, it's OK for Mexico to lament the half-assed tiebreaker system WBC devised, and for its players to feel like the entire exercise wasn't worth it.