When sports decide which teams make the playoffs, there are often tiebreakers used to sort-out teams with identical records. One of the most common tiebreakers is the “head-to-head” record.
Head-to-head record is a poor tiebreaker, especially compared with, say, strength of schedule.
Let’s NCAA basketball as an example. Suppose Wake Forest (my alma mater) and Western Carolina (the school where I teach) both go 29-1 in the regular season. Suppose Western Carolina’s only loss was to Mars Hill, and Wake Forest’s only loss was to Western Carolina.
The diehard “head-to-head” people would say “Western Carolina should be ranked higher! They won the head-to-head matchup!” But I say: what about the other 29 games? Wake Forest plays in the ACC, and has multiple games against Duke, UNC, Miami, NC State…you get the picture. Western Carolina has a much weaker schedule against the likes of Wofford, the Citadel, VMI, Chattanooga. Sure, Wake Forest lost to Western Carolina, but in turn, Western Carolina lost to Mars Hill! Which loss looks worse, hmm?
The problem with head-to-head is that it’s only one data point. Any team can lose a single game. Maybe Wake Forest was missing their starting 5 due to the flu for that one game against Western Carolina. (Clemson’s loss in football to Syracuse, earlier this year, was partially due to their starting quarterback being out). A tie-breaker should be as broad as possible, and take the entire year into consideration. This is especially true in basketball or baseball, when the long seasons make head-to-head records well-nigh meaningless.
I’m thinking about this now because college football is nearing its end for the year, and some arcane committee will have to decide who gets into the college football playoff and who stays out. There are those who have complained that an undefeated Wisconsin team (currently #3) should be ranked higher. But the Badgers have played an easy schedule, compared to, say, Auburn, who has faced the toughest road possible. (Look at strength-of-schedule rankings here.) In fact, I personally rank Auburn (10-2) higher than Wisconsin (12-0) for that very reason. We only have 24 total data points here, but if Auburn and Wisconsin swapped schedules, then Auburn would be 12-0 easily and Wisconsin would be, at best, 7-5.
I can’t say it enough. Head-to-head is a garbage tiebreaker. It’s only one data point. Strength-of-schedule incorporates literally dozens of data points and should always take precedence.
Many Worlds Theory 
Yes, but it was a 6-month journey to Mars and the gravity there is only 38% that of the Earth, so it wasn’t such a bad loss for WCU. They should have driven to the hoop more and laid off the 3s, as they didn’t have enough time to adjust their shooting mechanics to the road conditions.
Which every way you look at it, it is never fair to compare two teams who has different schedules. However, for two teams play in the same league/competition, head-to-head record should be a better tiebreaker than strength of schedule, as teams which have already qualified for the playoffs (strong teams) and teams which have already missed the playoffs (weak teams) often choose to give their reserve or young players a run in the last few games before the end of the regular season, which makes those games very unfair.
A classical example would be that Team A beat Team B with a 3-1 head-to-head record, but Team B won a couple of meaningless garbage games by big score near the end of the season, then suddenly Team B is ranked ahead of Team A.