One of my favorite sabermetric baseball articles of all time was written by Sky Andrecheck in 2010 — part as a meditation on the purpose/meaning of playoffs, and part as a solution for some of the thorny logical concerns that arise from said mediation.
The basic conundrum for Andrecheck revolved around the very existence of a postseason tournament, since — logically speaking — such a thing should really only be invoked to resolve confusion over who the best team was during the regular season. To use a baseball example, if the Yankees win 114 games and no other AL team wins more than 92, we can say with near 100% certainty that the Yankees were the AL’s best team. There were 162 games’ worth of evidence; why make them then play the Rangers and Indians on top of that in order to confirm them as the AL’s representative in the World Series?
Andrecheck’s solution to this issue was to set each team’s pre-series odds equal to the difference in implied true talent between the teams from their regular-season records. If the Yankees have, say, a 98.6% probability of being better than the Indians from their respective regular-season records, then the ALCS should be structured such that New York has a 98.6% probability of winning the series — or at least close to it (spot the Yankees a 3-0 series lead and every home game from that point onward, and they have a 98.2% probability of winning, which is close enough).
This style of setup may seem strange (and, admittedly, the 1998 Yankees are an extreme example), but it preserves the integrity of the regular season by tying the odds of postseason success quite directly to performance during the 6 months leading up to the playoffs. And despite the long odds, there’s still an opportunity for the underdog to turn the tables and advance. It would take an incredibly improbable sequence of events, but that’s what a team should have to accomplish in order to undo 162 games worth of evidence in the opposite direction.
As for football, the NFL obviously doesn’t play series, but the same concept can still be applied; instead of spotting games in a series, we can spot a team the lead in points before kickoff. In the NFL, Chase & I once found that a team’s “true” talent can be estimated by adding eleven games of .500 ball to its regular-season record. Using that, we can calculate the probability of either team’s true talent level being higher in a given matchup, and add points until the pregame win expectancy matches said probability.
Take tomorrow’s Bengals-Chargers tilt. Cincinnati went 11-5 (true talent: .611), while San Diego went 9-7 (.537); both of those talent estimates come with a standard deviation of .096. Based on their records, the probability of the Bengals’ true talent being higher than San Diego’s is 70.7% (this is derived from the means/standard deviations listed above and the mathematical proofs laid out here). In order for the pregame win probability to be 70.7%, we must spot the Bengals about 7.3 points to begin the game — however, the game is also in Cincinnati, and we know this typically means they will start with a built-in 2.5-point advantage, so we’d only need to add about 5 points (spotting them a 5-0 lead to begin the game) in order to bump their win probability up to the level deserved by their regular-season record relative to San Diego’s.
Here are the number of points we’d have to add, rounded to the nearest integer, for all of this weekend’s games:
| game_id | game_date | round | home_tm | mean | stdev | road_tm | mean | stdev | p(better) | pregame_lead |
|---|---|---|---|---|---|---|---|---|---|---|
| 201401040clt | 2014-01-04 | w | clt | .611 | .096 | kan | .611 | .096 | 50.0% | kan 3, clt 0 |
| 201401040phi | 2014-01-04 | w | phi | .574 | .096 | nor | .611 | .096 | 39.3% | nor 6, phi 0 |
| 201401050gnb | 2014-01-05 | w | gnb | .518 | .096 | sfo | .648 | .096 | 17.1% | sfo 15, gnb 0 |
| 201401050cin | 2014-01-05 | w | cin | .611 | .096 | sdg | .537 | .096 | 70.7% | cin 5, sdg 0 |
Note that this also addresses the seeming inequity of having 8-7-1 Green Bay host the 12-4 49ers; the Packers can be at home, but we’ll spot San Francisco a 15-0 lead to start the game — 12.8 for the pure difference in regular-season records and 2.5 more because they’re having to play on the road. Likewise, the Saints (11-5) would get an automatic 6-0 lead to start their game with the 10-6 Eagles since the game is in Philly, and the Chiefs would start out leading 3-0 against Indy because they’re having to play on the road despite both teams posting identical 11-5 records during the season.
Another benefit of this setup is that every regular-season game matters. No longer would teams have nothing to play for and rest their starters in week 17, when an extra win could very easily make the difference between winning and losing a playoff game.
Finally, if we dislike that the NFL playoffs seem to be getting more random in recent seasons, this process will nip that trend right in the bud. For instance, good luck to the 10-6 Giants going into the Super Bowl against the 16-0 Patriots, facing an instant 22-0 deficit — which is what this system would produce by dint of the biggest disparity in records of any playoff game since 2002. (The difference between the 2011 Giants and Packers’ records was equally large, but Green Bay would only start that game with a 19-0 lead under this system because they were at home).
Of course, maybe such unpredictability isn’t a bad thing — the NFL’s popularity has never been greater than during this period of wacky playoff outcomes — but if the goal is purely to make the playoffs fairer and give regular-season games more meaning, a handicapping system like this would reduce the role of randomness and ensure that the best team is rewarded more often with postseason success.