Peak data and the 'fouls won' test

In the past week, two types of 'peak' measurement have been in the news: both are bad, both are understandable, only one of them feels worth keeping around.

England's win over Mexico in the men's World Cup was watched by a peak audience of 9.1 million people, according to the BBC. For context: that's insane. Over a tenth of the nation was sleep-deprived on Monday, July 6th.

For extra context: it kicked off 2am local time. The biggest live TV draw of 2025 was the Celebrity Traitors finale -- in prime-time, of course -- which hit just over 12 million viewers.

Days later came news of the latest heatwave. The headline here was that the 'wave could hit 34 degrees celsius. The heat will, as usual, be focused around the south-east, and so about a tenth of the nation will be fried, etc etc.

But we don't actually know whether a tenth of the nation was truly sleep-deprived or heat-struck. In fact, TV audiences and extreme weather forecasts might be the only times that we use 'maximum value' as a statistic. Usually we use averages, and some fancy-dans will be sure to use the median average instead of the mean, to avoid being skewed by weird outliers. So, why do we still use peak audience and peak temperature?

In both cases, part of the problem is the 'shape' of the data, which messes with averages. In TV, the length of a programme will affect the average viewership, as will the amount of 'dead time' (like pre- and post-match coverage). And for weather, well, what do you do about night-time?

The issue is not just that the data within each match or day is up-and-down. It's that the way that this looks is different from TV programme to TV programmes, or from day to day, as well.

If you were comparing football matches against football matches, which all had the same amount of pre- and post-game coverage, maybe that'd be fine. But you're comparing it to Eastenders and The Traitors and Royal Weddings and random events in the Olympics. All of these programmes last for different lengths of time, with different expectations around whether viewers would watch the whole thing.

And with temperature, here in the UK the sun rises and sets at different times not just throughout the year, but within the season of summer.

That all said, to be totally honest, it's not difficult to come up with better metrics in either case.

You could take a 'day-time average temperature' between, say, 7am and 10pm, while taking the average of the most-watched 5 minutes of a TV show seems fairer than the single-minute peak.

Unfortunately, there is one more reason why 'peak' has sticking power. Your stats are only as good as your data.

Or that's what I expected to write. On further research: this isn't even a problem here.

British TV viewership has been monitored by Barb [Broadcasters Audience Research Board] since 1981, and Barb does tech like you wouldn't believe. They have a panel of 7000 households, who have a tracker on their TV and a special remote control. The remote has buttons to track who's in the room, who leaves, when they arrive, etc. They also have monitoring per-device and on WiFi routers so that, in this modern age, they can get data across all sorts of platforms and viewing types.

Meanwhile, -- possibly because we're an island nation -- the UK has had hourly weather readings since the mid-19th century. We sure love our weather.

So why, if we have more granular data, do we still have these imperfect metrics? Mostly simplicity, I assume. Peak viewership does, at least, capture what we feel like we want to be measuring, which I think is a sense of shared viewership.

I'm not so generous with max temperature. While it obviously reflects 'hot out, ain't it', the peaks are always set at particular stations that the majority of the country do not live near. For most of the country, the 34 degree headline is an abstract benchmark, something that needs a couple of degrees knocking off it depending on how northerly and urban (due to city heat islands) your locale.

But peak temperature is still more distant from how heat is experienced, than peak viewership is to how watching big events is experienced. External temperature of a weather station is more than one step removed from how we, humans, experience heat waves (or, in other parts of the year, cold snaps).

Shade, wind, and humidity all affect how hot we warm-blooded creatures feel, for a start. The duration of high heat, and the overnight temperature, also impacts how we experience a heat wave. We talk about heat being 'oppressive' and wanting to 'escape' it: the way that the mercury does, or doesn't, dip in an evening can really change whether that's possible.

Finally, most of us spend most of our time in buildings, the construction of which affects how hot we feel. This isn't just about machine air-conditioning: the architectural design, whether you're on a shady side or sunny side, and what floor of a tower block you live on will all affect how heat accumulates and dissipates where you are.

Fundamentally, 'peak temperature' is an answer to the wrong question. When I ask myself 'will it rain today' -- which, in Manchester, I do most non-heatwave days -- I'm not asking 'what is the peak probability of rain'. Instead, I'd look at the chance of rain during the day as a whole (or the times I'm likely to be outside).

There are a bunch of different statistical validity theory terms you could apply to all this, but my favourite is the 'fouls won' test.

If you want to know the most dangerous player on a team, you can get a not-terrible sense by looking at who is fouled the most: on Arsenal men last season it was Bukayo Saka; at Tottenham, Xavi Simons; Jack Grealish is perpetually towards the top of the Premier League list.

Is it directionally correct? Sure. Are there better ways of measuring the thing you're trying to measure? Absolutely.

Is 'max temperature' better than 'fouls won'? Yeah. But only barely.