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As I was watching the FOX pre-game show before the Eagles-Giants game on Saturday night, there was a conversation among the panelists on how hard it is to beat a team for the third time in the same season. We’ve all probably heard a form of this argument across sports (beating a team again in the CFB playoff that you played in the regular season is a common one), and sometimes it even comes up after just one previous game played.
The common arguments presented for this side generally revolve around the following:
“It is just hard to beat another team three straight times.”
“The [losing team] learns more about what they did wrong and makes adjustments.“
The [losing team] can change up what they do/their strategy in the third game, but the [winning team] will continue to play how they did before.
At a quick glance, some of these arguments should sound odd to you.
“It is just hard to beat another team three straight times.”
This is a good one to start with. At the time we are having this conversation, the [winning team] has already beaten the [losing team] twice in a row. At the beginning of the season, there is definitely a lower probability of three wins against one team happening. But once we know one team has already beaten the other twice? Well to beat them three times in a row they only have to win…one more time. The fact that they already beat them twice should increase a naïve estimate of their win probability in the third game, not decrease it.
“The [losing team] learns more about what they did wrong and makes adjustments.“
Always a fun one. Assumes a) winning teams don’t learn from those games and b) winning teams do not make adjustments after wins.
The [losing team] can change up what they do/their strategy in the third game, but the [winning team] will continue to play how they did before.
Similar to the last point, there’s a pretty frequent assumption that the winning team is stagnant while the losing team has a thick backup plan that they couldn’t make work in the first two attempts, but will find success in the third.
But we are not just hear for a quick glance, so I also looked at some numbers to back up my thoughts.
First, some other relevant work. This article from Football Perspective gives a good basis for this problem, and the conclusion from looking at 1970-2020 data (sample size of 21 games) was that a team that won the first two matchups in a season and then played a team again in the playoffs won ~66% of the third games. That alone gives us some strong evidence that the losing teams don’t seem to be miraculously better the third time around.
To expand on this, I looked at betting data to see if the teams that lost the first two times around are outperforming expectations in the third game, even if they don’t win outright. I only have betting data going back to 2006, which leaves us with eight valid cases, but does round out our data through Saturday’s Eagles-Giants game. Not the world’s largest sample size, but this is a newsletter not a research paper.
In those eight games, the team that won the first two games went on to win the third game 62.5% of the time, pretty much in line with our Football Perspective number.
Based on pre-game betting odds, the team that won the first two games would be expected to win 5.4/8 games, and the real number was 5/8 games. This could be evidence of slight overperformance by the two-time losers, but with only eight games to look at I would not expect that difference to be statistically significant. Also if we account for a ~2% vig by the sports book, it’s really about 5.2/8 games.
Looking at the spread, the team that won the first two games covered the spread 62.5% of the time, so again, not much evidence that the two-time losers are outperforming in the third game.
I will add the obligatory disclaimer that it is possible that bettors are already pricing in their “idea” that it is hard to beat a team a third time, and that is why it is not showing up in the numbers. I don’t think this is really a concern, but a non-market based evaluation metric (Elo ratings, another power ranking) would be a good second pass at this problem to see if adjusting for those changed any results.
Of teams who played three games against each other in one season, a team only won both of the first two games ~30% of the time. That 30% then have a win probability of 62.5% in the third game — meaning that (given we know two teams played each other three times in a season), winning the second game (if you have won the first) is actually less likely than winning the third game once you have already won the first two.
To me, this is sufficient evidence to say that we do not have sufficient evidence to make a case that beating a team for a third time in a season is somehow harder than it sounds. Historically the team that won the first two games wins the third more often than not, and they also seem to not be underperforming relative to the money line or the spread.
Two closing thoughts:
If a team beat another team 100 times in a row and was playing again, would commentators still talk about how hard it is to beat a team 101 times in a row? I hope not, but that would go against the reasoning they use to justify why beating another team three times in a season is hard.
When it came time to actually make picks, everyone except Strahan from the FOX team went with the Eagles, all with the Eagles to cover the spread too. Guess they didn’t think it was that hard for the Eagles to beat the Giants for a third time after all?