The Optimal NFL Playoff Format: Quality vs. Quantity

An analysis of different possible NFL playoff formats, and a call for resistance against further playoff expansion.

Welcome back to my Sports Passion Project everybody, where today we’re going to be talking about playoff formats again.

The NFL has expanded their playoff format recently, to include 14 teams instead of 12. There has been much consternation about this, both on behalf of people who like this change, and on behalf of people who don’t like it, but to get one thing out of the way immediately, it must be made clear that the consequences of this change on the actual playoffs have been very minimal, to the point that there’s basically been no change to the actual playoffs.

As a result the expanded playoffs for the last five years now including the two vs seven game, we’ve seen two close games (both of which featured Buffalo trying to choke against vastly inferior opposition), and eight blowouts, the narrowest of which came when Philadelphia beat Green Bay by 12 just a few months ago. That game was never close at any point, but by the extremely low standards of the two vs seven game, it was a barn burner.

Much was said about blowout playoff games when the college football playoff tournament expanded in 2024, and there was not a single close game in the first round, but in reality, this should’ve been the expected outcome. First round blowouts are what happens when sports expand their playoff fields. In fact, I would argue that first round blowouts are the point of expanding playoff fields. If these leagues didn’t want first round blowouts, they just wouldn’t expand the tournament.

I would argue that there’s been one single time in the five years of expanded NFL playoffs that the two vs seven game has had any impact whatsoever on who wins the conference. That’s once in ten tries, and that game (Green Bay vs Dallas in 2023) had such impact that I wrote two different articles about it. This one is better.

It is true that Dallas vs Green Bay game is one of the most important games in the last several years of football, because if Dallas plays Detroit in the second round of 2023, Dallas beats Detroit in the second round of 2023, and all of a sudden Detroit has won one playoff game in two years, and the NFL world thinks of them as chokers right now. That’s a big impact on the perception of the Detroit Lions, which comes entirely as a result of this two vs seven game, but that’s still just once in ten tries. Not one of the other nine renditions of the new wild card game have had any impact on anything.

That’s a ten percent hit rate, which is such a low chance of having any impact at all that I’m willing to say that, to the playoffs, these extra playoff teams are meaningless. It’s no different than when the NBA added the 7th and 8th playoff teams in each conference in 1982. Those 7th and 8th teams were meaningless in 1982, and they’re meaningless now, in terms of determining who will win the end of season tournament.

Don’t get me wrong. The low seeded teams can mean something every now and again (i.e. Miami Heat 2023), but in the years since the NBA created the one vs eight and two vs seven series, there have been 162 of them in total, and to achieve a hit rate of even ten percent, you would need to name me 17 meaningful ones. There are a few that stand out prominently: Denver 1994, New York 1999, Golden State 2007, Chicago 2009, Miami 2023, etc., but there are not 17 meaningful examples.

As such, I believe that the main impact of expanding the playoffs is, paradoxically, felt in the regular season, because while the extra playoff teams make a real impact in the playoffs approximately ten percent of the time, the allure of being one of the extra playoff teams makes an impact in every single regular season, without fail.

If you’re a fan of an NFL team, even though the probability of being blown out in your playoff game is more than half (virtually certain if you’re not playing Buffalo), the idea of being a playoff team is just so alluring that it’s hard not to get excited about it. Believe me. I went through this first hand as recently as 2023, when my Jaguars just had to win our final game to be the seventh seed in the AFC playoffs. We would’ve gotten blown out in round one without question, but damn it. I wanted to be in the playoffs anyway.

This is what expanded playoffs are good for. The seven team playoff format made what would’ve been a meaningless game under old formats, between eight win Jacksonville and five win Tennessee, meaningful to me, because there was the promise of something to play for. Even if that something was a blowout playoff loss, being blown out in the playoffs is better than missing them altogether.

If you don’t concur with that, just tell me, would you rather be a fan of the Denver Broncos or the Indianapolis Colts right now?

So, expanded playoffs do create excitement in the middle of the standings. However, they do not do this in a cost-free way. There is a trade off. As any NBA or NHL fan can tell you, expanded playoffs have the nasty effect of creating excitement in the middle of the standings by stealing it away from the top of the standings. In a league like the NFL, where the concept of home field advantage comes much more from the field than the home, which makes seeding quite meaningless, you can see how this could become a problem.

Lots of people, when discussing expanded playoffs, elect to put themselves in the position of being a fan of the Cincinnati Bengals in 2024, or the Jacksonville Jaguars in 2023, or any team that would’ve been eliminated weeks before the end of the season under a smaller playoff format, but wasn’t eliminated until the final week under the bigger one. However, this overlooks all the teams that could’ve been playing important games under a smaller playoff format, but weren’t under the bigger one.

Back in October, I wrote an article doing just the opposite, analysing teams that would’ve played relevant games, had the playoff format been smaller, mostly focusing on the 2023 Cleveland Browns, and 2023 Kansas City Chiefs.

Both of these teams played virtually no relevant games in the 2023 regular season, but would’ve had their fans jumping up and down throughout the entire last month, had the playoff format been smaller. The Chiefs had the 2023 AFC West so locked up that even their late season losing streak did not put them in any danger at all, whereas under a smaller playoff format, they would’ve been fighting for their playoff lives at season’s end. The Cleveland Browns in real life went on a December winning streak that only served to make extra sure that nobody was going to take the five seed from them. Under a smaller playoff format, their late season winning streak would’ve been a mad dash to get back into the playoffs, which would’ve been much more exciting.

I demonstrated how the expanded playoffs in 2023 did create more relevant games for teams like 9-8 Jacksonville and 10-7 Pittsburgh, but it did so by taking away relevant games from teams like Cleveland and Kansas City.

In this article, I want to quantify that effect, in order to determine what an optimally sized playoff format would look like.

To do so, I’m going to impose a certain set of restrictions and assumptions on myself. First, I’m going to assume the NFL postseason is locked at four rounds long. This is a realism assumption, because NFL owners would never vote to go down as low as four teams per conference, eliminating an entire playoff round, and adding a fifth playoff round, with the way the current schedule is constituted, would put the Super Bowl in direct competition with the Daytona 500 NASCAR race.

I’m not insinuating that the NFL is intimidated by competition from the Daytona 500, but I am assuming that the billionaires running NASCAR would likely be able to assuage the billionaires running the NFL into not doing this, through whatever methods groups of billionaires take to manipulate each other, because the Daytona 500 being forced to compete with the Super Bowl would likely kill NASCAR outright, so, at least in my realism assumption, there would be some sort of compensation going the NFL’s way in exchange for not doing this, or them just not wanting to do it for any other reason.

Capping the playoffs at four rounds long also means restricting the number of playoff teams per conference. It can only be between five and eight. Either the five team per conference system, with three first round byes and one wild card game per conference, that the league used from 1978-1989, or the six team per conference system, with two first round byes and two wild card games per conference that the league used from 1990-2019, or the seven team per conference system that the league uses currently, or, theoretically, an eight team playoff format featuring no first round byes at all.

I’m going to grade each of these formats, under the assumption that they make no change to the actual playoffs at all, based upon the same rationale I was explaining earlier. The assumption here is that the champion under a five team playoff format will differ from the champion under an eight team playoff format less than ten percent of the time. Look at the 2024 AFC for example, where regardless of the playoff format being five, six, seven, or eight (or four, for that matter) teams, the second round matchups do not change. Therefore, the playoff format had no impact on the winner of the conference championship. None whatsoever. I assume that this is the norm, in order to disregard change within the playoffs altogether, and focus exclusively on change within the regular season.

Additionally, for the purpose of this exercise, we’re going to pretend that the NFL has a real commissioner, who acts in the best interests of the game, instead of strictly acting in the best interests of the game’s immediate cash flow. This spits in the face of any assumption of realism, but without it, nothing will ever change, so we have to go with it.

Therefore, the number of playoff games (and their associated revenues) is not a real concern in this analysis. I understand that having twelve playoff teams allows two more playoff broadcasts per season than does having ten teams in the playoffs, but perhaps the associated stalling of the NFL’s popularity growth that’s happened ever since the league expanded the playoffs the first time in 1978 will offset that. I’m discussing long term revenue through a healthy product here. I’m not discussing the NFL like an investment asset that I’m constantly looking to get rid of, in the way the league’s real owners do.

Taking into account that I don’t believe the extra playoff teams make a real impact on determining the champion, and also that the number of playoff games is not a real concern, that leaves my one real focus in this exercise.

The regular season.

More accurately, which playoff format keeps the most teams relevant long enough to produce the most possible relevant regular season games?

To answer this question, I must define what I mean by the word ‘relevant.’ For this analysis, to give as much credit to big playoffs as I can, I plan to use a very lax definition of the word. First things first, a game must only contain one team playing for anything to be classed as relevant. For instance, in week 17 of the 2024 season, the Chicago Bears played the Seattle Seahawks. Chicago was playing for nothing, but Seattle still had real playoff hopes, which drags this whole game into the relevant category, regardless of how bad the Bears were.

Operating things this way ensures that every game played before the start of December is still at least theoretically relevant. I’ll use the 2024 Cincinnati Bengals as an example. As of the start of December, the Bengals were 4-7. If they could’ve won out from here, they would’ve made the playoffs, which also makes every game they played before then relevant, by backward induction.

Because it takes only one team with anything to play for to make a whole game relevant, any game played before the beginning of December featuring at least one team with seven losses or fewer is ‘relevant,’ for the purpose of this analysis, which is basically every game in the history of the league that occurs before the beginning of December. As such, I’m going to disregard games that happen before the beginning of December, and focus only on games that occur from week 13 onwards, where the definition of relevant changes depending on what week of the season we’re in.

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In weeks 13, 14, and 15, I consider a game relevant if either of the two teams involved fits either of the following criteria:

1. Within two games of the final playoff position, either above or below. This is the deficit that I deem small enough to make up over the final five games of the season. For instance, the final team in the playoffs going into week 13 in most seasons under a playoff format with six teams or more is 6-5. This means that any week 13 game featuring any team with a 4-7, 5-6, 6-5, 7-4, or 8-3 record automatically gets put into the relevant category, because any team in this band is close enough to the playoff line to at least theoretically have the ability to get above or fall below.

   Look at how close the 2024 Cincinnati Bengals (who at one point were 4-7) came to making the playoffs. Under the seven team playoff format, their games were relevant. On the other side of the coin, the Jacksonville Jaguars were 8-3 going into week 13 in 2023, and missed the seven team tournament altogether. Their games were relevant for playoff position too.

2. Within one game of a first round bye position, above or below. This is based on the same rationale as the playoff cut-off, except teams that are in a position to score a first round bye are harder to catch. If you’re two games behind the first round bye just 11 games into the year, to me, you’re not playing relevant football as far as getting back to the top of the standings goes.

For the final two weeks of the season, the criteria change, because if you’re two games out with two games to go, you really don’t have a chance anymore, so a relevant game must contain one of the following.

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1. At least one team is within one game of the playoff line, above or below.

2. At least one team is within one game of a first round bye position, above or below.

I’ll give you two examples that indicate exactly what this system of defining relevancy is trying to do. The first is the 2024 Christmas day game between the Pittsburgh Steelers and Kansas City Chiefs. In the real life seven team playoff format, this game was not relevant, as with two games left to go, no team was within one game of Kansas City for their first round bye, and the Steelers had a three game cushion on the final playoff team. The Chiefs could’ve lost this game and still been in the driver’s seat for a first round bye. The Steelers did lose it and were still comfortably in playoff position. This game would’ve been irrelevant under an eight game playoff format also, for the same reasons.

However, if the playoff format were only five or six teams big, this game switches to being relevant, as in each case the Steelers only have a one game cushion on the final playoff position, and losing this Christmas game (which they did in real life) would’ve given them a real chance to miss the playoffs altogether.

The second example is the week 18 matchup between Pittsburgh and Cincinnati, where in either a seven or eight team playoff format, this game is relevant for Cincinnati, as they technically still had a chance to catch Denver. In a five team playoff format, this game is relevant for Pittsburgh, as the AFC North division and the conference’s third first round bye were still on the table for them, but in a six team playoff format, neither of these teams have anything to play for, since we’re saying seeding doesn’t matter here.

Pittsburgh has no chance to become one of the conference’s two first round byes, and no chance to drop out of the six team playoff field. Cincinnati has no chance to jump into the six team playoff field, so this game is entirely irrelevant. Pittsburgh’s seed could change from five to six or vice versa depending on the result of this game, but I doubt that would’ve been enough incentive to entice them to play the starters, had the six team playoff field been in effect for this game.

These two examples demonstrate the fluid nature of different playoff formats, and how they impact the importance of late-season games. There are times when the meaningfulness of a game is impacted in a monotonic way, like the Christmas game, where Pittsburgh would have something to play for, if the playoff field were smaller, and nothing if the playoff field were bigger, but there are also times when the importance of a game is non-monotonic in the number of the playoff teams. In that Pittsburgh-Cincinnati week 18 game, at least one of the teams has something to play for if the playoffs include five, seven, or eight teams, but if the playoffs include six teams, neither has anything to play for.

This is the difficulty of gauging the impact of expanded playoffs on the relevancy of the regular season, which is likely why I haven’t seen this analysis done anywhere else, but luckily for us all, I’ve decided to do it. I’ve taken every playoff format between ten and 16 teams, and graded them based upon how many relevant late-season games they produce. The result is the graph below, showcasing the amount of relevant regular season games each playoff format produces in every season since the league moved to its modern size and divisional alignment in 2002, expressed in percentage to reflect the fact that there are more post-December games than there used to be:

As I hypothesized and demonstrated above, the result is not monotonic. The amount of relevant regular season games is not strictly increasing in the number of playoff spots. In fact, the optimal playoff format by this measure changes, depending on the nature of the season it is applied to.

In terms of how often a particular playoff format produces the most relevant regular season games, counting ties as a win for both formats, the standings are as follows:

1. Seven playoff teams: 18 wins

2. Six playoff teams: 7 wins

3. Five playoff teams: 1 win

4. Eight playoff teams: 0 wins

If you’re anything like me, your eye is immediately drawn to the outlier season where the way to keep the most late season games relevant was actually to contract the playoffs to just five teams in each conference. This happens in 2005, where each conference just so happened to have five strong playoff teams, and one tag along. I’ll use the AFC as the representative example.

The 2005 AFC had 14-2 Indianapolis, 13-3 Denver, 12-4 Jacksonville, 11-5 Cincinnati, 11-5 Pittsburgh as five strong playoff teams, and had to bring along 10-6 New England for charity, whom 10-6 Kansas City couldn’t even fight with, due to the Patriots being a division winner.

That’s the Trent Green story.

This, plus the fact that 12-4 Jacksonville never had a true chance to fight for the first round bye either, due to being in the same division with Indianapolis, means there was really no fight for the first round bye, and really no fight for the final playoff position either, which means there were exceptionally few relevant games in the 2005 AFC, which is shown clearly on the above graph. You can pick out 2005 as the season with shockingly few leaguewide relevant games, under any playoff format, but in this one corner case, at least giving these AFC teams a third first round bye to fight for will counteract the false hope of teams like Kansas City and San Diego, who each never had a real chance to make the 2005 playoffs in the final three weeks anyways, and this rise in relevant games in the AFC counteracts the likely loss in the NFC enough to bring the five game playoff format to the top of the table, just this one time.

2005 is not the only outlier though. Look at the far right of the graph. It shows that there were exceptionally few relevant games played in the 2024 season also, regardless of which playoff format is chosen. In most seasons, at least 85% of the games played are relevant to at least one of the parties. In 2024, that number couldn’t even clear 75 percent.

This perhaps explains why I spent so much of my time in 2024 lashing out about the expanded playoffs. This is an indication that the lack of relevant games in 2024 was not the playoff format’s fault. It would’ve felt the same under any format. We just drew a short straw with the league environment that we were given.

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To some people, this graph would’ve been the end of the analysis. The seven team playoff format tends to create the most relevant regular season games, and therefore it’s the most optimal playoff format. However, this is my Sports Passion Project, so you just know that wasn’t going to be good enough for me. I wanted to look at the distribution.

By distribution, I mean the ways in which these playoff formats spread their relevant games out. How many relevant games are played by four win teams, desperately trying to hang on (i.e. 2024 Cincinnati), and how many relevant games are played by good teams, either trying to qualify for a sufficiently small playoff tournament, or perhaps shooting for a bye into the second round?

This is where there becomes a divergence of opinion. To some, who I would generally describe as big playoff apologists, a relevant game played between 5-7 Indianapolis and 3-9 New England, as was done in week 13 of the 2024 season, is just the same as a relevant game played between 9-2 Philadelphia and 8-4 Baltimore, also from week 13. To people who like big playoffs, the trade off of the Philadelphia and Baltimore game perhaps not meaning as much is worth it to keep the Colts’ playoff hopes alive for just that little bit longer.

I understand this perspective, as it theoretically helps to keep fans of more teams engaged for longer, but as a fan of the Jacksonville Jaguars, who is generally disengaged by the time December rolls around, even if the playoff format were to go to 24 teams, I have a hard time seeing things from this perspective. I spend a lot of my football time ignoring my own team and being a non-rooting observer, so I want my passive observation to be on games that mean something.

Even if the 5-7 Indianapolis game is still relevant to the fans in Indianapolis, is a disenchanted Jaguars fan going to watch that? I certainly didn’t. Instead, I defaulted to the Philadelphia vs Baltimore contest, and if I had my druthers, I would put as much relevance onto that game as possible.

This my issue with big playoff tournaments. It’s not as if I don’t understand that expanding the playoffs (to a point) creates more total relevant games around the league. I get that. My fundamental issue with big playoff tournaments is that not all relevance is the same. Large end of season tournaments tend to offload relevance onto the games like Indianapolis vs New England by taking it away from games like Baltimore vs Pittsburgh in week 16 last year, who because of the seven team playoff format were each playing for nothing that night.

The game nobody watched (Indianapolis vs New England) was much more relevant to the final standings than the game that lots of people watched (Pittsburgh vs Baltimore), and I consider that to be a problem. Therefore, I opted to regrade the playoff formats, this time looking only at when they created a relevant game for a team that was better than .500 at the time of the game, and the results were much different:

Looking at it this way, the seven team playoff format is not reduced to ashes, but it loses its definitive advantage. This the list of formats that created the most relevant games for the good teams:

1. Six playoff teams: 14 wins

2. Five playoff teams: 6 wins

   Seven playoff teams: 6 wins

3. Eight playoff teams: 0 wins

This is where the six team format that most of us grew up with shows its mettle. It may not create the most total relevancy across the league, but in terms of creating relevance for games that most fans will actually watch, it cannot be matched by any other format, as in fact the seven team format falls into a second place tie with the five team format, when graded on their abilities to force good teams to play relevant games.

To show how the seven team format creates so much general relevance despite losing out most years in terms of relevant games at the top of the standings, this is the graph of how many relevant games exist each year for teams that are .500 or worse at the time of the game being played. Take note of the outlier 2005 from before:

For once, we find something that is basically monotonic. The more teams a playoff format has, the more relevant games that an okay (or worse) team will be able to play. Under the eight team format, some seasons it gets over 50 percent of all NFL games played that are relevant games to bad teams. The only thing that keeps the eight team format from being a real competitor here is the NBA syndrome. Once a team gets three games clear of the playoff cut-off in the eight team format, with no first round bye to play for, their season basically ends, with nothing left to play for until playoffs roll around.

In contrast, look at the playoff format that only allows five teams per conference. There are exceptions (2006, 2015, 2017 are the clearest), all due to extreme weakness in one conference or the other, but in general, if you ever drop below .500 in a system that permits only five teams in a conference to make it, your season is over.

The six and seven team formats are more equal than most give them credit for. In general, it’s a solid bet that if you ever drop to .500 or worse in either of them, between 20 and 40 percent of games played will still be relevant.

This dichotomy between relevant games for good teams and relevant games for bad teams creates a trade off. How valuable is a relevant game to a good team, compared to a relevant game to a bad team? I don’t think it’s controversial to say that relevant games for good teams are better for the league than relevant games for bad ones, but it’s a difference of opinion how much more valuable they are.

Games that are relevant to good teams can easily triple the national TV audience of games that are not relevant at all, but when it comes to games that are relevant for good teams vs games that are relevant for bad teams, it’s difficult to find a counterfactual, because games that are relevant to bad teams often don’t even end up on the national TV schedule to begin with, unless that bad team is Dallas, New York, etc., which skews the sample.

Generally though, comparing a game with its main source of relevance being a good team playing for something, against a game that’s main source of relevance is a .500 or below team playing for something, I would say twice as much national interest is a lower bound, once we exclude drawing power of a team (Dallas, New York, KC, etc.). This is the graph generated by that hypothesis, of relevancy created by playoff formats, when a relevant game to a good team is worth twice as much as a relevant game to a bad one.

1. Seven playoff teams: 14 wins

2. Six playoff teams: 11 wins

3. Five playoff teams: 1 win

An upper bound on the importance of the game being a relevant game to a good team compared to a bad one is approximately three times, the difference between a game being relevant to a good team vs not being relevant at all. Here is a graph showcasing relevance at the upper bound:

1. Six playoff teams: 12 wins

2. Seven playoff teams: 10 wins

3. Five playoff teams: 2 wins
   

As you can see, at some point between the lower bound and the upper bound, the preference between a six team playoff format and a seven team playoff format switches. This happens at roughly k = 2.3. If your watching ratio between good team games to bad team games is 2.3 or higher, your preference is likely towards a six team playoff format. If you’re willing to stick it out and watch a lot of mediocre to bad football, you’re likely more inclined to like more mediocre teams being relevant in the seven team format.

Think of it like a football weekend. Take the one game your team plays as the bad team game. If, in addition to the game your team plays, you pay significant attention to two other games or fewer on an average weekend, seven playoff teams is likely optimal for you, due to the increased likelihood of your team being relevant. However, if in addition to the one game your team plays, you pay significant attention to three or more other games, your interest in football as a whole is sufficient so that the increased playoff relevance for good teams in general is enough to outweigh the reduction in likelihood that your team will be one of the relevant ones, so the six team format is likely optimal for you.

That brings me back to the question I set out to answer. What is the optimal playoff format?

In short, it’s not the same for everybody. It depends on your football watching preferences. If you watch a lot of football, beyond games your favourite team is playing, six teams per conference seems to be the optimal number. If you’re more of a person that strictly watches your team, seven appears to be the right format.

Any less teams than six appears to decrease the likelihood of enough teams playing enough relevant games that it’s hardly ever optimal, although in conferences that are naturally very boring, adding in a third first round bye for the top teams to fight over can spice it up a little bit. Any more teams than seven is never optimal though, because at that point you’re dealing with the NBA problem of teams both at the top and the bottom of the league having nothing to play for.

I think the NFL has reached the point of no return now, at seven teams per conference. Up until this point, there’s at least been an argument that increasing the size of the playoffs would increase the meaning of the regular season. It seems ambiguous at this point whether six or seven playoff teams per conference is optimal, but there is a credible argument for seven, if the NFL thinks its fans are more hyper-focused on their own teams than they used to be. I can buy that.

However, it is unambiguous that any more playoff teams beyond seven per conference will begin to significantly hinder the relevance of the regular season, mostly through robbing the top teams of any important games to play between November and January.

Obviously, with how much football I ingest on a weekly basis, I am more in the six team group than the seven team group. As such, playoff expansion has already gone too far for my tastes, but the important thing to take from this piece is that any further playoff expansion will begin to unilaterally harm everybody, and that we as fans need to throw our bodies in front of that ever happening.

It won’t happen in the short run. The format was just expanded, but at some point somebody will try to expand the NFL’s playoffs again, and at that point, if it goes through, the NFL regular season will never mean as much as it once did, and at that point, with a meaningless regular season, the NFL will be no different than the NBA. If you’re the 2024 KC Chiefs, with a two game lead on the whole conference, and no first round bye to look after anyways, why wouldn’t you load manage Patrick Mahomes?

People think that would never happen in the NFL, but if the playoff field ever got to eight teams or better, it would happen. Trust me. Not just in week 18 either. I’m talking midseason breaks for players. Perhaps teams would begin to just opt out of flying their top players to all these weird places that the NFL puts games these days. We saw what happened to Jordan Love, who injured his knee on some dodgy Brazilian turf in 2024. Why take the risk when you could just keep your QB home and give him a rest? After all, if you’re the Green Bay Packers, what’s the difference between playoff seeds anyways, if there’s no first round bye to fight for?

What’s the worst that can happen? You have to play your playoff game on the road, in the cold?

I have a feeling the Packers can handle that.

Just keep all this in mind, should the issue of playoff expansion in the NFL ever come up again. There must be something for the top teams to fight for. Elsewise, you get load management, and nobody wants that, so while we may be split on just how many playoff teams are the right number (some of us like six, others like seven), we can all absolutely agree that seven is the absolute maximum, unless we’re ready for load management in the NFL.

I’m not ready for that. Are you?

I didn’t think so.

Thanks so much for reading.