Serie A after matchday 6: Inter and Lazio level on 16, Bologna's first win brings a safety line, nothing clinched

The three clubs level on 13 points at the top of Serie A are two clubs level on 16. Inter beat Parma 3-0 and Lazio beat Monza 3-1 on October 11, while Roma drew 0-0 at Como the same day and sit third on 14. Inter and Lazio have five wins and a draw each and neither has lost. The table lists Inter first on goal difference, plus ten against plus seven, and the arithmetic on this site still does not use goal difference, so the two remain one line with two names. Our September 20 piece described the same problem with three clubs in it.

Every figure here is as of the October 13 update. Sixty of the season's 380 matches have been played, and all twenty clubs are on six played with 32 left. The round ran from October 10 to October 13, Korean time, home side first: Genoa 2-1 Fiorentina on the 10th, Lecce 1-2 Bologna, Inter 3-0 Parma, Lazio 3-1 Monza, Napoli 3-0 Frosinone and Como 0-0 Roma on the 11th, Cagliari 1-1 Juventus and Sassuolo 1-1 Milan on the 12th, Atalanta 3-1 Venezia and Torino 2-1 Udinese on the 13th. The next round starts on October 17.

The title column is still empty, and the reason is that both leaders won. Inter and Lazio can each reach 112 points and nobody else can. A title clinch number has to clear every rival's maximum, and a rival who can only draw level still counts as a threat, so neither of them can clear the other's 112. One dropped result would have changed that. Keep the other nine results as they were and make Inter's match with Parma a draw, and Lazio would carry a title clinch number of 95. Make Lazio's match with Monza a draw instead, and Inter would carry the same 95. Roma's draw at Como moved them the other way: their maximum fell from 112 to 110, and Roma now carry a title tragic number, which they did not have on September 21: 32, every match they have left. Inter and Lazio are the only two clubs without one.

The top-four line came down from 111 points to 109. The same four clubs carry it: Inter and Lazio need 93 more, Roma 95, Cagliari 96, and each figure plus the points already banked is 109. The bar is one point above Milan's maximum of 108, the fourth-highest among those four clubs' rivals. The figures are not equally hard. Ninety-three from 32 matches allows one defeat or one draw, but not two draws, which make 92. Roma's 95 cannot be produced exactly, since 31 wins and a draw is 94 and the next total up is 96, so in practice Roma would have to win all 32. Cagliari's 96 is all 32 won by definition. Milan, 1-1 at Sassuolo and fifth on 12 points, are once again one point under the total the four lines point to. For Milan itself the bar is 110, because Cagliari's 109 counts among its rivals.

Cagliari's line survived the match the September pieces said could erase it. A defeat at home to Juventus would have taken Cagliari's 99, and a Juventus win would have cut Cagliari's maximum to 108. The match finished 1-1. Cagliari are fourth on 13 with a line of 96, having conceded three goals in six matches, as many as Roma and the fewest in the league. Had Juventus won, the engine gives Juventus a line of 96 and Cagliari none. Instead Juventus are sixth on 11 with a maximum of 107, and they and Como, who held Roma, again carry identical rows: no top-four clinch number, a top-four tragic number of 32, a title tragic number of 31 and a safety line of 90. Frosinone, the other club that could reach exactly the Juventus maximum on September 21, lost 3-0 at Napoli and now top out at 106.

At the bottom the safety total fell from 102 to 101, and Bologna were waiting for it. Our September 20 piece on the relegation numbers said Bologna's empty cell would fill the moment the seventeenth-highest maximum among its rivals reached 100. Four clubs that topped out at 103 lost this round, Udinese at Torino, Monza at Lazio, Parma at Inter and Fiorentina at Genoa, and each now tops out at 100. Bologna won 2-1 at Lecce, their first win of the season, which keeps their maximum at 101, exactly one above that 100. Their safety line is 96, which is all 32 remaining matches won, and their relegation tragic number is gone. A draw at Lecce would not have done it: the engine then gives Bologna no safety line and a relegation tragic number of 32.

Fourteen clubs now carry a safety line, down from seventeen, and all fourteen add up to 101: 85 for Inter and Lazio, 87 for Roma, 88 for Cagliari, 89 for Milan, 90 for Juventus and Como, 91 for Napoli and Frosinone, 92 for Atalanta, 93 for Sassuolo, 94 for Torino, 95 for Lecce and 96 for Bologna. The six without one are the five clubs on 4 points and Venezia. Udinese, Monza, Parma and Fiorentina each needed 98 on September 21 and lost this round. Genoa came the other way: the 2-1 win over Fiorentina took them from 1 point to 4 and removed their relegation tragic number, but a maximum of 100 is one short of 101. Torino were the fifth club on 4 points in September, and their win over Udinese leaves them on 7 with a line of 94.

Venezia lost 3-1 at Atalanta and have six defeats from six matches and no points. They are the only club in the league with a relegation tragic number, 31 of their 32 remaining matches, and they hold the lowest top-four tragic number, 28, and the lowest title tragic number, 27. Thirty-one is not a verdict. It says that Venezia could lose 30 more and staying up would still be arithmetically open.

Nothing is settled at either end. No club has a zero in any of the six columns, and every club's reachable range still runs from first to twentieth. Sixteen clubs carry a top-four tragic number, from Venezia's 28 to 32 for Milan, Juventus, Como, Napoli and Frosinone. The next round cannot change that either. Run all 59,049 combinations of its ten results through the engine and no clinch number reaches zero, no tragic number reaches zero, every reachable range still reads first to twentieth, and the smallest tragic number anywhere is 25.

The next round runs from October 17 to 20, Korean time, home side first: Frosinone vs Sassuolo and Venezia vs Napoli on the 17th, Roma vs Genoa, Udinese vs Lecce, Bologna vs Inter and Fiorentina vs Como on the 18th, Juventus vs Lazio and Milan vs Atalanta on the 19th, Monza vs Cagliari and Parma vs Torino on the 20th. The two leaders are both away, and those two matches can put a number in the empty title column. If Inter win at Bologna and Lazio fail to win at Juventus, Inter get one: 92 if Lazio draw, 91 if Lazio lose, or 92 if Lazio lose and Roma beat Genoa. The same holds the other way round for Lazio. A draw for one leader and a defeat for the other also produces a line of 93 for the one that drew, as long as Roma do not beat Genoa, and Roma get 93 themselves if they win while Inter and Lazio both lose. Bologna host Inter with their new line, and a Bologna win keeps it in every combination. Cagliari, at Monza on the 20th, keep their 96 in every combination by winning, and Milan, at home to Atalanta, can get a top-four line only by winning.

How to read these numbers. A clinch number is the minimum a club must still collect for an outcome to be guaranteed even if every rival wins every remaining match. A tragic number is how many more defeats make an outcome impossible even if the club wins everything else. A reachable range is the highest and the lowest finishing place still arithmetically open. On ties, a rival who can only draw level with a club is still counted as a threat to it, so our clinch can trail an official announcement by a day, while in the other direction a rival has to finish clearly above a club to eliminate it and drawing level is not enough. Goal difference, head-to-head fixtures and the official tie-breaking rules are not part of the calculation, and every line in this piece moves with other clubs' results as well as the club's own. The table is at, the remaining fixtures at, what the top four and the bottom three lead to at, every club's clinch and tragic numbers at, the method at, and a single club's lines on its own page, such as Inter's or Bologna's. To run next weekend's results through yourself, use.