Serie A standings, September 21: Roma, Inter and Lazio all level on 13 points after five rounds

Roma, Inter and Lazio are all on 13 points at the top of Serie A. Each has won four and drawn one, and none has lost. Our table prints them in that order because of goal difference, plus eleven, plus seven and plus five, but goal difference is the only thing doing the separating. The clinch and elimination math on this site does not use it, so as far as the arithmetic is concerned the three clubs are one club with three names.

Every figure here comes from the September 21 update. The fifth round is complete, all twenty clubs have played five matches, and all twenty have 33 left of a 38 match season. The fixture list is then empty until October 10.

The three leaders arrived at 13 by different routes. Roma drew 2-2 at home with Inter on September 20, which is why that pair are still joined, and Lazio won 2-0 at Venezia the same day to stay with them. Inter has scored 15, more than anyone in the division, and conceded eight, the most of any club that has not lost. Roma has scored 14 and conceded three. Lazio has scored eight, the fewest of the three, and conceded three.

Cagliari is fourth on 12 points from four wins and one defeat, and it has conceded two goals all season, the fewest in the league. Milan is fifth on 11 from three wins and two draws, the only club outside the top three that has not lost, and it beat Lecce 3-0 at home on September 21. Frosinone, Juventus and Como follow on 10 each, Como having lost 0-2 at Frosinone on September 20.

A clinch number is the number of further points that guarantees a place no matter what every rival does. Roma, Inter and Lazio each need 98 more to guarantee a top four finish. There are 99 available to them, because 33 matches at three points each is 99. Cagliari needs all 99. Those figures land on the same finishing total, 111 points, which is the bar the engine is measuring against. Milan has no clinch number at all, since reaching 111 would take 100 points from 33 matches and only 99 exist.

Nothing has closed in the other direction either. An elimination number, or tragic number, is the number of further defeats after which a place becomes impossible even if the club wins everything else. The top four have no top four elimination number. Milan's is 33, which is every match it has left, and Frosinone, Juventus and Como are on 33 as well. The smallest in the division is 30, shared by Bologna, Genoa and Venezia, and 30 defeats out of 33 is not a warning about anyone. The title column is blunter still. Not one of the twenty clubs has a title clinch number, because no total available from 33 matches would guarantee first place. The first title elimination number in the table belongs to fourth placed Cagliari at 33 defeats, and the lowest in the league is last placed Venezia's 29.

Safety works the same way from the other end. The bar for guaranteed safety is 102 points. Roma, Inter and Lazio would each need 89 more to be mathematically certain of finishing clear of the bottom three, Milan 91, and the five clubs on four points would need 98 of the 99 available. Bologna, Genoa and Venezia cannot reach 102 on their own results at all. Only those same three have a relegation elimination number, 33 further defeats for Bologna and Genoa and 32 for Venezia. The plainest summary of the whole table is this. Every one of the twenty clubs can still finish first, and every one can still finish last.

Next. The fixture list restarts on October 10 with Genoa against Fiorentina. On October 11 Roma goes to Como, Inter hosts Parma and Lazio hosts Monza, so none of the three leaders plays another. Napoli hosts Frosinone and Lecce hosts Bologna the same day. On October 12 Cagliari hosts Juventus and Sassuolo hosts Milan.

How to read these numbers. A clinch number is the minimum number of further points that guarantees a place even if every rival wins everything it has left. An elimination number is the number of further defeats after which a place is impossible even if the club wins everything else. A reachable range is the highest and lowest position a club can still finish in, and right now every range in Serie A runs from first to twentieth. Both directions resolve a tie in the direction that delays the verdict. A rival who can only draw level with us still counts as a threat when we confirm a place, and a rival has to be able to finish strictly above us before it can eliminate us, so our confirmation can arrive a day later than the official one. Goal difference, head to head records and the official tiebreakers are not part of the calculation. The full table with every club's clinch and elimination numbers is at, the fixtures at, what the top four and the bottom three lead to at, a scenario builder at, the clinch numbers on their own at, and the method at. Roma's club page is at.