The Science (and timing) of substitutions

There has been previous debate on here regarding DJ's timing of substitutions and how he tends to leave his changes very late when compared with some of the management greats (e.g. Sir Alex).

Prof. Bret Myers in the US has conducted a study on the timing of substitutions in the English, Spanish, Italian and German leagues. His findings were reported by the Wall Street Journal in February 2011. I thought that some of you may find the WSI news report and an associated Freakonomics article interesting reads.

http://online.wsj.com/article/SB1000142 ... 76930.html

http://www.freakonomics.com/2011/02/09/ ... -his-subs/

Seriously flawed statistical analysis, for obvious reasons.

Seriously flawed statistical analysis, for obvious reasons.

Can you elaborate?

How many of those substitutions were made due to injury or purely tactical?
Does it factor in the patterns of play - ie team A dominating, team B get a lucky early goal, park the bus - which indicates the substitution in itself may not have been the factor?

"Teams that follow these guidelines improve—score at least one goal—roughly 36% of the time."

So, about 2/3rds of the time, his "decision rule" has NO positive effect for the team following it.

"Teams that don't follow the rule improve about 18.5% of the time."

So, basically, there's a "natural" potential improvement; his "rule" doubles that based upon the sample size he "observed". It's still pretty much the case based upon his figures that even following his "rule", odds are, it'll have no effect.

"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."

Assuming a 50/50 split, he's based his rule upon 520 cases where the rule was followed, 520 where it wasn't. Both sample sets aren't that high to truly factor out statistical variation...

"He also found that the timing of subs has no effect on the team ahead in the score or if the match is tied."

Which tends to indicate the rule is pretty much a bogus "rule", based upon limited statistical observation a Yank felt would be interesting, to cover up his general cluelessness about football. After all, given he posits the rule has a *positive* effect upon the team following it, then observation if the rule had validity would show some increase in both the categories where he observed none.

There are simply way, way, way too many statistical variables involved within football to be able to isolate something as basic as the time of subs and quantify a rule that claims it can affect the result.

How many of those substitutions were made due to injury or purely tactical?
Does it factor in the patterns of play - ie team A dominating, team B get a lucky early goal, park the bus - which indicates the substitution in itself may not have been the factor?

"Teams that follow these guidelines improve—score at least one goal—roughly 36% of the time."

So, about 2/3rds of the time, his "decision rule" has NO positive effect for the team following it.

"Teams that don't follow the rule improve about 18.5% of the time."

So, basically, there's a "natural" potential improvement; his "rule" doubles that based upon the sample size he "observed". It's still pretty much the case based upon his figures that even following his "rule", odds are, it'll have no effect.

"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."

Assuming a 50/50 split, he's based his rule upon 520 cases where the rule was followed, 520 where it wasn't. Both sample sets aren't that high to truly factor out statistical variation...

"He also found that the timing of subs has no effect on the team ahead in the score or if the match is tied."

Which tends to indicate the rule is pretty much a bogus "rule", based upon limited statistical observation a Yank felt would be interesting, to cover up his general cluelessness about football. After all, given he posits the rule has a *positive* effect upon the team following it, then observation if the rule had validity would show some increase in both the categories where he observed none.

There are simply way, way, way too many statistical variables involved within football to be able to isolate something as basic as the time of subs and quantify a rule that claims it can affect the result.

Thanks for the well-considered analysis. I sympathise with your criticisms although I suspect that some of the apparent anomalies even themselves out.

What one can say is that the most successful and longest serving manager in British league football is known for making a number of his tactical substitutions with c.20-30 minutes or more of play remaining? Indeed, he has received criticism on a number of occasions for these decisions, some likening him to a gambler. Of course the counter-argument to this is that it is better to be decisive (and gamble) than to be indecisive.