Subbing in the second half

Jared Diamond of the Wall Street Journal wrote an interesting story about the beneficial nature of second-half subsitutes when a team is down. Citing the “Decision Rule” of Bret Myers, a professor of management and operations at the Villanova School of Business, Diamond wrote:

[Myers] concluded that if their team is behind, managers should make the first substitution prior to the 58th minute, the second substitution prior to the 73rd minute and the third prior to the 79th minute.

Teams that follow these guidelines improve—score at least one goal—roughly 36% of the time. Teams that don’t follow the rule improve about 18.5% of the time. He noted 1,037 instances the rule could have been applied and found that managers abide by it a little less than half the time. He also found that the timing of subs has no effect on the team ahead in the score or if the match is tied.

So, how does this stack up with Fulham? Well, according to football365 Fulham have the following record when losing at half time:

Team PLD LHT W D L F A GD GFA GAA PpG Pts
Fulham (12) 26 11 1 5 5 12 19 -7 1.09 1.72 0.72 8

Even with a seemingly low point total, we’re actually 4th overall in points per game when losing at half time behind just Arsenal, Spurs, and United. Nonetheless, the following are the 11 matches were Fulham were down at halftime and the second-half subs they made:

  • United: Dembele (61), Greening (81) and Gera (90). [Down 1-0, Fulham would draw 2-2.]
  • Wolves: Baird (45), EJ (83). [Down 1-0, Fulham would win 2-1.]
  • @Blackburn: EJ (78), Gera (89). [Down 1-0, Fulham would draw 1-1.]
  • @West Brom: AJ (59), Riise (73). [Down 2-1, Fulham would lose 2-1.]
  • Villa: Kelly (58), Andrew Johnson (59), Damien Duff (70). [Down 1-0, Fulham would draw 1-1.]
  • @Chelsea: AJ (62), Gera (79). [Down 1-0, Fulham would lose 1-0.]
  • City: Gera (45), Kamara (64). [Down 3-0, Fulham would lose 4-1.]
  • Brum: EJ (73). [Down 1-0, Fulham would draw 1-1.]
  • West Ham: EJ (54), Duff (54). [Down 2-1, Fulham would lose 3-1.]
  • @Spurs: Gera (82). [Down 1-0, Fulham would lose 1-0.]
  • @Villa: Salcido (62), Davies (68), Gudjohnsen (90). [Down 1-0, Fulham would draw 2-2.]

Hughes made a substitution in every game he was down a man, but he’s never made all three subs at or before the times Myers suggests. Nor does Diamond suggest the possibility of scoring a goal in, say, the 69th minute but still making a sub in 73rd minute. But we can still play with the data (or, at least I think so.)

Only 4 times did Hughes make a sub before the 58th minute, with a 50% scoring-at-least-one-goal success rate.

Hughes made his second sub before the 73rd minute 5 times, which resulted in at least one scored goal 4 times (80%).

Lastly, only once was the third sub made before the 79th minute, in a game that Fulham scored a goal. So that would be a 100% success rate.

So by my count, Hughes’ success rate is about 83% when following each of Myers’ guidelines. Not to shabby, eh? I wonder what Roy’s success rate would be during the 2008-09 season, back when our biggest compliant about the man was he never made subs until it was too late.

Anyway, even if all my math is complete bunk the rub is here:

Dr. Myers said the rule shows that coaches underestimate the significance of fatigue late in a match, which causes them to overvalue starters and undervalue substitutes.

Which is why I’ve always supported an additional sub or two when cup/tournament games go to extra time.

6 thoughts on “Subbing in the second half

  1. I also believe a measure of who is fit needs to be calculated into this as well. When EJ was being run out as the first sub up front, I’m not sure it would have been prudent for Hughes to bring him on before the hour mark. The one case he did was against West Ham, and we all know how that turned out (which was coincidentally the last time EJ graced the field). Not to say his contribution or lack thereof had any bearing on the result, just that depending on who is available to bring on has to have an impact on when and who is subbed.

    Thinking back to the 08-09 season as well, what were the options on the bench, Nevland, Kamara? It’s entirely possible that Woy didn’t see the fresh legs as a measurable upgrade to the tired legs already out on the field. We all know that this squad was notorious for being trim in recent times (outside of the last year and a half in my estimation).

    Is there a correlation between making all three substitutions and getting at least a point when trailing? Obviously it worked out that way every time it has happened this year…so far.

      1. Sadly, I think that was the end of the line for Johnson at the Cottage. I’m not sure if he is Prem quality and he would be better served playing in the first division with a squad where he could get minutes. All he needs is some PT, but I’m not sure if Fulham is the place for it.

  2. I don’t have the inclination to research this but my impression is that no matter how well or badly we are doing Hughes wll invariably use at least 2 and frequently all 3 subs.

    1. and if I was sarcastically inclined, I might add “in contrast to Roy who no matter how well or badly we were doing would invariably use none or at most one of our subs” – but the evidence probably does not support that cheap shot.

  3. Further to the post below, this work by Colin bears re-visiting:

    It started with this: Marlon Harewood’s ability to score lots more goals per minute on the pitch when coming on as a sub http://championshipatbest.com/another-marlon

    Then this: the effect is universal http://championshipatbest.com/strikers-bench

    Then this: AJ is much more prolific as a sub. http://championshipatbest.com/who-starts

    Colin will doubtlessly be able to expand on these numbers at some point, perhaps with a few more data points to improve reliability, but the implications if the effect really is universal are staggering: if you are a forward you will score much more often as a sub than as a starter. So managers need to bring on their subs!

    As an example, let’s expand it out a bit, using made up numbers to make a point. If you start all 38 games, average 70 minutes per game and score 10 times you’re scoring every 266 minutes (10 in 2660).

    Now, taking the point loosely, if you score (relatively) twice as often as a sub:

    You play 38 games and average 20 minutes per game. In this scenario you would score 6 goals (6 in 760).

    Wow.

    The research Timmy linked to is based on the premise that managers underestimate the effects of fatigue, and Colin’s research backs this up very well.

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