Southampton’s Magic Numbers

I do not know whether the magic number concept is used in English sports.  I certainly haven’t seen it used in reference to Southampton before but I think the concept will provide some guidance as to what Southampton has left to do this season.

In American Baseball (and, less commonly, in other sports) the magic number is the combined number of wins by the team that is ahead and loses by the team that is behind necessary to guarantee that the leading team prevails.  Here is a Wikipedia article  on the subject.  The concept can be transferred to football so long as the possibility of draws is properly accounted for.  In this post I will generate Southampton’s magic numbers.  I will also look at what we need to do to qualify for European football and the Champions League and to avoid relegation--a near, but not mathematical, certainty.

MAGIC NUMBERS TEAM BY TEAM

Consider Arsenal who currently has exactly the same number of points as us.  They could, in theory win all 15 of their remaining games and end with 87 points. If they did that, we would need 88 points to finish ahead of them.  Of course, that is not possible but it does mean that our magic number is the 46 points it would take to get to 88.  If the combined total of the points we earn and the points Arsenal drops reaches 46, we are guaranteed to finish ahead of them.

In contrast, consider Leicester with only 17 points.   If they win all their remaining games they will end with 62 points.  That means our magic number to finish ahead of Leicester is 21 points.  Since it is very likely Leicester will drop 21 more points, we are effectively safe from them even though we have not mathematically clinched it yet.

Here are our magic numbers for the entire League:

Chelsea               57

Man City             52

Man U                 47

Arsenal                46

Tottenham         44

Liverpool             42

West Ham           40

Swansea              37

Stoke                    36

Newcastle            34

Everton                 30

Palace                   27

Sunderland          27

West Brom          26

Aston Villa           26

Burnley                24

Hull                       23

QPR                      23

Leicester              21

Goal differential can be ignored because these are the numbers needed to finish one point ahead of the other team.  If we can assume a favorable goal differential with any given team, the magic number for that team is one lower.

EUROPEAN QUALIFICATION

For the purposes of this article, I am assuming that fourth place qualifies for the Champions League and sixth place qualifies for the Europa League.  The latter assumption is based upon a belief that Chelsea will probably win the League Cup, but even if they do not Liverpool will at least finish in seventh place.  If Liverpool wins the League Cup and finishes eighth or lower, sixth place may not qualify depending on what happens in the FA Cup.   I am also ignoring the possibilities of English teams winning both the Europa League and the Champions League this year and both of those teams finishing outside the top four.

Magic numbers for European qualification are less clear cut than the magic numbers to beat individual teams.  Currently, our magic number to finish third is 47—the magic number to finish ahead of Manchester United.  However, that number will shift if Manchester United drops a lot of points and falls below fourth place in the table.

Currently, our magic number to guarantee finishing fourth is 46.  But this is misleading because Arsenal and Manchester United still have to play each other so one or both of them will drop points.  Effectively, the number is 45.

Our magic number to finish fifth is not really the 44 points it would take to finish ahead of Tottenham because they are playing Arsenal this weekend.  If they lose, the relevant number is the 42 points to finish ahead of Liverpool.  If they draw, the relevant number is 42, the number needed to finish ahead of both of them.  If they win then the number is 43 because Arsenal would be the team we need to beat for fifth place.  Therefore, our current effective magic number for fifth place is 43.

Sixth place is even more complicated.  Arsenal, Liverpool, Manchester United, and Tottenham all still have to play each other.  That is nine potential points for each club, but only 18 total points available for the four clubs.  If each club wins all their remaining games except against each other the highest lowest point total for the four clubs is 80 points.  We would need 39 points to finish ahead of that team so that is effectively our magic number for sixth place.

RELEGATION NUMBERS

In a Premier League season there are 380 games.  To determine how many points a club needs to avoid relegation at the start of the season, we assume that the two worst clubs lose all their games except against each other which do not matter for the purposes of this calculation.  That leaves 378 games or 1134 points.  If those points were split evenly among the remaining 18 teams that is 63 points each.  So 64 points would make a club mathematically safe from relegation.

There are three ways that number goes down during the season.  Each time one of the last two clubs in the table takes points from one of the other 18 teams, then number goes down.  Each times one of the top 18 teams draws a game, a point disappears and the number goes down.  Finally, when a team earns enough points to be mathematically safe, any extra points they earn are wasted and the number goes down. 

QPR and Leicester are 5-4-14 and 4-5-14 respectively.  QPR beat Leicester so their records against the rest of the league are 4-4-14 and 4-5-13.  This means that they have taken 24 points by winning games and 18 points by drawing games from the other clubs.  That leaves only 1092 points for the other 18 clubs.

These 18 clubs have drawn a total of 115.  However, 9 of those draws were against QPR or Leicester and have already been counted.  That leaves 106 draw results or 53 games that ended in a draw.  That is 53 more points lost leaving a total of 1039.  If those points were divided evenly among the 18 teams the result is 57.72 points per game.  Therefore, 58 points is mathematically safe while 57 points is not.

This number will continue to move down slowly in the next couple of weeks as clubs draw games and as the bottom two clubs gain points from the other clubs.  It will start to move downward more rapidly when clubs start earning points above the safety line.  If Chelsea, for example, wins their next two games they will have 59 points and the extra point will come off the total available for the other clubs.

This system of calculation breaks down once the 18^th place team can no longer reach the mathematical safety total—the total then becomes one more point than the 18^th place team can earn.   The situation becomes even more complicated when other bottom table clubs can no longer reach this safety level because you have to compensate for the points they will lose to each other.  At this point, the mathematically safe point total will drop more rapidly.  This is not yet a problem because all the bottom half teams can still reach 58 points—that won’t be true in a few more games.