The Benefits of Being Subbed On.

I first posted about the advantages enjoyed by a sub 20+ years ago on something called usenet, before it got swamped in an avalanche of spam and became unusable.

I've added a few blogs here as well. Here's on centred around Edin Dzeko

The basic concept is very straightforward.

Goal scoring rates gradually increases as the match progresses, so if you're always getting subbed on in the 70 minute, you're playing in a very different scoring environment compared to someone who starts the match.

You've also been lounging around for an hour or so, while everyone else has been running their socks off.

That's not entirely the whole story. Game state and team talent differential also has a say.

A much better team won't be cranking up the attacking process quite as much in the first half of a tied match, compared to the final twenty minutes, if the score line status quo has been maintained.

Changing game states in tied games with a large talent differential between the teams are biggish deals, both of which we'll ignore in this post.

Working out a rough and ready goal environment for players based on when they were on the field is a fairly trivial task.

All you need is a decay factor, an initial expected scoring rate and a spreadsheet and you can easily calculate the goal expectancy (not to be confused with expected goals) for any minute in a match.

For an average team, the goal expectancy during the 80th minute is around 33% bigger than the equivalent during the 10th minute. So the frantic last ten minutes is very different to the languid first ten.

Shaq.....Once a Red & White, always a Red......

I finally got around to working out a way to quantify the "subs premium" when Shaq's offensive production for Liverpool started popping up on Twitter over Christmas.

I though, (wrongly as it mostly turned out), that his stats had been padded by playing most of his minutes late on in games as a sub.

His numbers have definitely benefitted from small sample extremes, (which may or may not be maintained), but that's another issue entirely.

He's made 14 appearances for Liverpool in the Premier League, six from the bench. Depending upon how you treat added time, that's around 760 minutes of playing time.

To see by how much Shaq's benefitted from playing when the goal environment has been cranked up, we just need to take a baseline figure for a side's goal expectancy over a full game.

Then work out the goal expectancy for each individual minute.

Add up the relevant goal expectancies tied to each minute Shaq has played.

Compare this to his theoretical goal expectancy he would have if every minute he played was equally spread across the 90+ minutes of a game.

Bottom line, Shaq's 760 minutes, equally spread over a match, based on him playing for the average Premier League team he used to grace, equates to a goal expectancy of 10.39 goals.

This compares to 10.59 goals based on the actual identity of every actual minute he's been on the field for.

His split of sub and starting appearances has benefitted him by around a 2% increase in goal scoring environment compared to par.

His numbers aren't particularly boosted by him having disproportionately large opportunities to feast on the weary, late in games.

Good buy.