KairoX Tempo answers one match at a time: P(home), P(draw), P(away). A title is a property of a whole season. Getting from one to the other turns out to be free. A 1X2 triple carries two degrees of freedom, and a Dixon-Coles scoreline model at a fixed dependence parameter has exactly two free parameters, so inverting a calibrated triple into a lambda pair is a change of coordinates rather than a model fitted to another model. The worst residual across all 2,808 priced fixtures is 1.7e-16 nats of KL divergence, which is solver precision and not approximation error.

So the season simulation is Tempo's own answer, re-expressed as scorelines and played out 20,000 times per league under each league's real format, tiebreak chain included. That holds for every fixture between two teams Tempo knows. The interesting part is the fixtures it does not.

The top five in every league, with projected points and the 10th-90th percentile band around them. The bands are the part worth staring at: Manchester City's projected 74.7 points carries a range of 65 to 84, nineteen points wide, more than a third of the gap between champion and mid-table. A favourite at 51.7% is not a prediction that City finish on 75 points.

Three things in there are worth a sentence before moving on. Arsenal won the 25-26 Premier League by seven points and sit second at 35.0%, because the projection regresses hard toward the mean: across all 202 returning teams the spread of projected points per game is 0.295 against last season's realised 0.362, a regression slope of 0.73. The Austrian figure is load-bearing on a rule change, since Austria halved points at the championship split every season from 2018-19 until this one, and halving would compress the gap Salzburg and Sturm Graz build in the regular phase into something materially more open than 41.1% against 30.7%.

The third is the one to hold on to. Look at the point bands in the Championship card. Southampton, a returning team, projects 79 points in a 68-to-90 band. Wolves projects 71.8 in a band running 51 to 94, more than twice as wide. Same league, same 20,000 seasons, same accounting. The width is not a statement about Wolves; it is a statement about how little is known about Wolves, and it is the rest of this log.

Every Tempo feature is a rolling window over the league's own history: form over the last five, xG over the last ten, points gap, venue splits. A side promoted into the league has nothing to roll over, so 63 of 94 features come back NaN, and XGBoost routes NaN down a default branch at no cost. Nothing raises, nothing warns, and the number comes back with the same type, the same range and the same shape as a real one: newly-promoted Coventry, at home to Liverpool, 39.4% to win. The direction of that error is the part that matters, because a missing gap reads as no gap. The failure is biased optimistic. Across the fourteen leagues, 42 of 244 teams did not play in their league in 25-26.

The replacement is not a guess. Tempo's own Poisson component is fitted to each league-season on its own, decay off, attack and defence re-centred to mean zero, which is the gauge the parameterisation is invariant under. Teams absent the season before are the sample. That puts the prior and its destination on the same scale by construction, so there is no calibration step to argue about.

The ordering is football sense arrived at from data, which is the cheap part. The expensive part is the third row. A side relegated into a second tier is not a discounted arrival at all: it scores 12% more and concedes 11% less than the average team in the league it drops into. Second tiers are also compressed, which is why the middle pool sits so close to the origin, and the combination is what makes the second-tier projections what they are.

Two implementation details do real work. Attack and defence are drawn as whole pairs, bootstrapped from the sample, so the correlation between them survives at +0.22, +0.09 and +0.30 by pool: promoted sides are not independently bad at scoring and bad at defending. And the draw happens once per simulated season, not once per match. A promoted side that comes up flying is flying in all 34 of its games, and that persistence is what turns the prior into a strength-of-schedule effect for everyone else in the league.

One note on the spread, because it looks too wide. Fitting a single season measures realised performance, which mixes true strength with a season's luck. That is the right quantity: the simulation wants the predictive distribution of what a newcomer will actually do, not a noise-free estimate of what it is.

Shift every newcomer's prior mean by a standard deviation in each direction and rerun, with common random numbers so the differences are not swamped by Monte Carlo noise. Then do the same for a completely different worry: that Tempo is more confident about who is better than whom than it should be. That knob pulls every fixture's log-lambda a fixed fraction of the way to its venue's mean, flattening team-to-team strength while holding home advantage and the league's goals-per-game fixed, so it isolates one assumption rather than degrading the model generally.

In the eleven top flights the newcomer perturbation is a rounding error. The largest favourite move is 4.56pp, København, and the largest move for any team in any top flight is 8.82pp, Vaduz, which is itself a newcomer. Newcomers hold between 0.0% and 1.4% of all top-flight title probability, and the answers survive being substantially wrong about them.

In the three second tiers the same perturbation decides the league. Southampton goes from 21.8% to 40.3% when newcomers are a standard deviation weaker and to 3.2% when they are stronger, because the teams either side of it in the market are all relegated Premier League clubs priced entirely from the prior. In 2. Bundesliga and Segunda it is worse: the entire podium is.

Panel A of the figure is the honest bound on the headline numbers. At 25% shrinkage the top-flight favourites move a long way: PSV 75.7% to 60.4%, the largest single move in the entire sweep, Bayern 88.3% to 76.1%, Inter 57.4% to 44.3%. The reported spread integrates match outcomes and the newcomer prior; it does not contain Tempo's own parameter uncertainty, so it is a floor, and the most confident-looking figures are the ones with the most to lose.

The three second tiers barely register it. At most 3.9pp, because their strength spread is already flat and pulling a flat distribution toward its own mean does very little. So the ordering inverts: the leagues whose numbers are least sensitive to the model being overconfident are precisely the leagues whose numbers are most sensitive to an assumption the model never made.

This is the reason the finding is worth writing down rather than filing. Read the projections alone and the second tiers look like honest wide races: 6.5 to 7.5 effective contenders, no favourite above 24%, the sort of distribution that reads as appropriate humility about a competitive league. The width is real. But it is not the model expressing uncertainty about teams it has measured. It is a bootstrap over a 32-team cohort mean, wearing the model's output format.

Relegation needed no new simulation. The finishing-position distribution for every team is already in the same 20,000 seasons, so reading the bottom of the table is a change to the accounting and nothing else. It did need the real rules, which are not "bottom three" everywhere: England, Spain and Italy send three down directly, while Germany and France send two and put 16th into a two-legged play-off against the third-placed second-tier side.

That play-off needs a survival rate, and there is a measured one. The Bundesliga tie has been played 18 times since it returned in 2008-09 and the top-flight side survived 14 of them, so 16th goes down with probability 4/18, or 22.2%. Ligue 1's barrage only began in 2023-24 and has no usable base rate of its own, so it borrows the German figure. That is the one imported assumption in this section, and the direct and play-off components are reported separately so it can be discarded.

The caveat that was a rounding error on the title is the whole shortlist here. Nine of the fifteen highest-risk teams across the five leagues are promoted sides, including the top three in England, and their ±1 sd spans are enormous: Ipswich runs 25.8% to 85.8%, a sixty-point range on a single assumption. A promoted side's relegation number should be read as "roughly half, ±30", which is honest and still useful, rather than as 58.2%.

Two of the five shortlists are led by teams the model does know, and those numbers are much firmer. Lecce at 63.5% is the single highest relegation risk in the five and comes entirely from Tempo's own view of a returning team; its span is 42.1 to 75.7%, wide because its rivals for the bottom three are promoted sides, not because Lecce itself is uncertain. Angers at 57.7% in Ligue 1 is the same story with a tighter 39.9 to 67.7%. Espanyol at 38.4% and Parma at 42.2% are the other returning teams the model puts in real danger.

The play-off is worth 2 to 4 points of relegation probability and no more. Finishing 16th in Germany or France is a 10 to 16% outcome for the teams in danger, and only 22.2% of those end in relegation, so it adds roughly 2.2 to 3.6pp on top of the direct risk. It does not reorder any shortlist, which is the useful thing to know about it.

Strength shrinkage also behaves differently down here. At 25% flattening the riskiest team in each league moves 58.2% to 51.1% (Ipswich), 50.4% to 45.4% (Deportivo), 63.5% to 55.5% (Lecce), 42.1% to 38.1% (Paderborn) and 57.7% to 49.4% (Angers): smaller moves than the same knob produced at the top, and all in the same direction. Relegation risk concentrates in teams whose strength estimate is low, so flattening the table pulls them up rather than scattering them.

The three leagues where the prior dominates are also the three where the newcomers arrive from above, and their records exist. Wolves, West Ham and Burnley each played 38 Premier League matches last season. The prior throws all of that away and prices them from a 32-team cohort mean measured across four seasons and fourteen leagues.

Whether the club's own record beats the cohort is not answerable from this run, and it is not obvious which way it goes. The cohort is a tight estimate of the wrong thing: what an average relegated club does. The club's own season is a noisy estimate of the right thing, from a sample of one, in a division a tier above, before a transfer window that this experiment cannot see at all. The comparison needs running rather than reasoning about, and until it is run, the Championship number stays what it currently is: a well-calibrated statement about a cohort, formatted as a statement about Southampton.