We're really starting this newsletter off strong by having the second ever edition be a day late. It really wasn't my intention, but I got super busy over the last couple days and ran out of time to put the newsletter together. Better late than never, I guess...

Anyway, thanks for sticking with me, forgiving my tardiness, and subscribing! The reaction to this has been awesome and I'm really thankful for you all. On to the news:

The Rundown

(in no particular order)

  1. 1.

    A brief follow-up to last week's penalty discussion: Jesse Davis posted the findings of Lotte Branson's PhD thesis that attempted to incorporate goalkeeper-dependent penalty taking principles into an optimal strategy for penalty-saving. Branson suggests using real-world goalkeeper data — such as early-diving reach, late-diving reach, and average correct corner guess rate when diving late — to inform a model that provides save probabilities for various diving policies based on the specific goalkeeper's actual archetype. She also finds that aligning off center increases expected save percentage and that diving late is beneficial if the kick is expected to be within reach (i.e. if the keeper has a higher diving reach length).

  2. 2.

    Over at xG Football Club, Alex to summarized a paper suggesting a new method of predicting defensive value similar to VAEP but using a different outcome variable. The researchers estimated the probability that the defending team would regain possession and that the attacking team would create an "effective attack" — enter the box or take a shot — within the next five actions. They also trained the model on both tracking and event data, where VAEP is a strictly event-based framework. By using these more common "success" definitions, the researchers found a positive recovery case in 36% of event states and a positive attacking case in 14% of event states versus positive scoring and conceding cases in 0.7% and 0.2% of cases, respectively. I'm not fully sold on the definitions they used for positive and negative outcomes because they are inherently different (and not all shots are created equally, etc etc), but I do like the creative thinking and alternative approach to an existing EPV framework — especially with an emphasis on defensive value.

  3. 3.

    The numbers are in and the World Cup final between Spain and Argentina ranked as the most-watched soccer telecast in US history with over 61.5 million viewers across FOX and Telemundo/Peacock. Peak on FOX was 51.7 million.

  4. 4.

    If you haven't yet read the Where Goals Come From series by Jamon Moore and Carlon Carpenter that they wrote for ASA in 2021, what are you doing with your life? Jk. But if you're unfamiliar, the good news is, Jamon summarized the key findings and dusted off the ol' pen to add a new entry into the canon, this time using StatsBomb data on past World Cups. Jamon found that prior to the final, the 2026 World Cup's 3.04 goals per game is highest goal per game rate since 1958. Additionally, Jamon found that elite teams at the World Cup are finding ways to create shots from progressive passes — the most valuable pass type — at rates significantly higher than lower performing teams. That being said, there has been real change for the smaller sides since 2018: "The evolution we're documenting is real. Weaker World Cup teams have demonstrably shed the pure survival strategy of parking the bus and winning penalties. Modern soccer has rewarded progressiveness and bravery. They're getting into organized attacking positions more consistently than they were in 2018." However, "once they're there, they still lack the quality to execute the final combination, relying on something going wrong for the defense — a loose ball, a scramble, a mistake. They arrived as a team, but they're finishing alone." It's a great piece that I highly recommend reading in its entirety.

  5. 5.

    Ian Fleming created a Shiny app that lets anyone go back and simulate the outcome of past NWSL matches based on the shots each team created in that match. For example, I ran it on the Reign's 2-0 win against the Thorns a couple weeks ago and found that the final scoreline only had a 14.35% chance of occurring (the most likely outcome was a draw, with a 23.99% chance of occurring). Here's the original post. It's a good illustration of how to apply xG at a single-game level, since creating more xG doesn't always mean a team "deserved to win." If you're less familiar with the math behind xG or how it's useful, I recommend playing around in the sandbox tab of Ian's app.

  6. 6.

    The third place match between France and England hit Scorigami, since a 6-4 scoreline has never before occurred in World Cup history (thanks, Jude).

The Post-Match Report

A weekly newsletter that collates soccer analytics happenings from across the internet. Stay up to date on new research, blog posts, projects, bluesky conversations, and more, plus a few analytical deep-dives here and there.

A closer look: momentum

Let's do it. Let's talk about momentum.

I was admittedly the perpetrator of a public crashout on Bluesky1 a few weeks ago over an article that essentially boiled down to the author not really knowing what FIFA's momentum graphic meant. I'll do my best to distill my thoughts on the matter, provide some historical momentum context, and answer the question of "What is momentum?" since I definitely think it's a question worth asking.

Let's start with the most recent example of momentum discourse and work our way backwards. Momentum was heavily featured at the World Cup, appearing on seemingly every game broadcast in a bottom right corner popup that showed an axisless chart depicting a squiggly line and some colors. And you know what? Yeah, what even is this?

A screenshot of a fifa broadcast showing a "Match Momentum" popup between England and Croatia.

At a glance, the graphic shows you a few different things. First, when goals occurred. Second, presumably, which team had more "momentum" in each segment of the match. The major context that's missing, though, is how the momentum is defined and what the magnitude of these momentum swings are. FIFA, conveniently, has yet to publish any information regarding how, exactly, their proprietary momentum model works, but we can infer some information from how momentum is usually calculated.

The modern version of momentum is almost always calculated by using possession value, which is a model-based measure that estimates the probability of the in-possession team scoring and conceding in the next five to ten seconds2. Any given on-ball action will impact these probabilities either positively or negatively. So, instead of looking at a more simple stat like possession, we can actually measure how much danger each team was creating based on the total possession value of their actions. Usually, for a chart like this, those values will be subtracted, meaning that if England generated 0.4 possession value and Croatia generated 0.2 possession value, the net momentum would be 0.2 in favor of England. That net momentum is usually smoothed to create a chart similar to the one you see above.

There are, however, different ways of displaying momentum. Many charts use this smoothed "swing" method, but others choose to display more information by providing both the total possession value for each team and the net momentum in the same chart. This is what futi does:

Momentum chart on futi showing greyed out bars and lighter bars within them instead of a line.

The greyed out bars indicate each team's possession value generated in that two-minute bin, while the lighter bars are the net difference. This strategy is useful mainly because it helps differentiate between two different scenarios that are treated similarly in the line-based momentum chart. First, consider a two-minute bin where each team is attacking a lot, the game is very transitional, and lots of things are happening very quickly. The data would show that both teams created a lot of possession value, but the net outcome could be near zero if the teams were evenly matched. Now, consider a scenario where neither team is creating anything, the game is dull and stagnant, and all you want to do is pick up your phone to scroll TikTok. In this case, the net momentum will again be near zero. The line-based momentum chart has no way of telling a viewer whether a near zero net momentum falls into the first or second category, it just tells you that the teams were even. Hence, the bar-based momentum chart can be more useful for making this distinction.

The history of momentum and how it came to be is a complicated one, mainly because no one knows who did it first. This week we got a little bit of a history lesson in momentum from Joris Bekkers and Nils Mackay, who discussed the lineage of the chart on Bluesky and LinkedIn. According to Mackay, Andy Kirk was creating momentum charts — or something similar — for Arsene Wenger at Arsenal in 2016, but the first public example likely came in 2017 when Tom Decroos, alongside Vladimir Dzyuba, Jan Van Haaren, and Jesse Davis, published a paper titled "Predicting Soccer Highlights From Spatio-Temporal Match Event Streams"3 that contained this chart:

Chart showing predicted goal probability on y-axis, time in minutes on x-axis, and Team A and Team B lines with various peaks.

In the Fall of 2018, Eliot McKinley published GameFlow, which was ASA's version of the momentum chart and perhaps the first version to use the bar method — though it was inspired by SofaScore's bar-based momentum graphic. GameFlow still exists as a bot on Bluesky in case you want to see these for every MLS, USL, and NWSL match.

Bekkers and Mackay also came to their own versions of momentum around that time, which is a pretty cool reminder of how different people in entirely different places can all converge on similar concepts at similar times.

Then, of course, there's the reminder that all of this had been invented a hundred years ago by Hungarians.

Overall, I think it's fair to be confused by momentum. When faced with a chart without axis labels, a natural response is "what the hell am I looking at?" There is a use in it though, as evidenced by how many leading soccer analysts all separately decided that momentum was something worth defining in the late 2010s. Momentum describes a match better than a box score can. It tells a chronological story that goes beyond the result and shows the viewer what it felt like to watch the match. It can be a good way of identifying trends. And, as I've hopefully shown, there are different ways to display it, each with pros and cons.

It may be confusing at first, but once you understand momentum and what goes into it, you're one step closer to understanding the game itself.