The 27 Club

"There are known knowns, there are things we know we know. We also know there are known unknowns, that is to say there are some things we know we do not know. But there are also unknown unknowns - there are things we do not know we don't know."(Donald Rumsfeld, Feb 2002)

The relief that we didn't actually win at Fulham was palpable (enough indeed to encourage me to write a rare blog post), and now the priority can rightly return to League One matters.

Readers of my We Are Leeds? blog will recall my concern that our season was resembling theirs rather too closely from 2009/10.

Their remarkable start to the season (they had accumulated a whopping 57 points from 24 games, compared to our own impressive 54) only went downhill rapidly after their FA Cup exploits misallocated vital focus and energy.

Thus I can only commend Chris Powell's team for skilfully balancing the need to make the 7,000 travelling Addicks proud, whilst at the same time ensuring they went out of the competition.

More evidence surely of a truly great side.

Looking forward, there are now four possible outcomes for this season:

Outcome A: automatic promotion
Outcome B: promotion via play-offs
Outcome C: play-off defeat
Outcome D: finish outside top six

As a brief aside, if I asked you the following questions, what would your answer be?:

Question 1: which of the following events is more likely? Charlton suffer Outcome C (play-off defeat), or you randomly select a diamond from a full pack of cards?

Question 2: which of the following events is more likely? Charlton suffer Outcome C (play-off defeat), or a family of four has two sons?

I instinctively sense that most people would answer both questions by stating that the latter of the two options is more likely.

If so, then I fear that you are wrong for reasons I will now explain.

Calculating the true probability of Charlton's four season outcomes is virtually impossible even with massive computing power, because of the sheer number of relevant factors and influences, plus the so-called 'unknown unknowns' as Donald Rumsfeld referred to above.

As a proxy there are however numerous bookmakers willing to lay bets on some combination of Outcomes A-D.

Of the major bookmakers, seven are willing to lay odds on Charlton being promoted (whether automatically or via play-offs), and these odds range from a not-very-generous 2/7 (Stan James) to a more reasonable 4/11 (Sky Bet).

The probability equivalent of these odds for those (like me) that prefer to think in those terms are 78% and 73%.

I usually prefer to use Betfair's odds as the best proxy for actual probabilities as they better resemble a true market-driven view, and theirs are 1.39 or 72% in the above vernacular.

Given Betfair's odds are (as usual) similar but slightly better to those available on the High Street, I am comfortable taking 72% as being an excellent estimate of Charlton's actual probability of promotion.

However this 72% encompasses both Outcome A (automatic promotion) and Outcome B (promotion via play-offs).

In order to attach probabilities to all four outcomes, I need to use this 72% as the basis to strip out the probabilities of each separately, via some reasonable assumptions.

I will begin with Outcome D because it's the easiest.

Charlton are currently 16 points clear of Stevenage in 7th place.

With 22 games left, for Charlton to finish behind Stevenage we would have to experience form at least 0.72 points per game worse than the Hertfordshire side (and more for any of the other chasing clubs behind them).

This is equivalent to over 33 points on a full '46-game equivalent' basis.

Obviously such differentials in form are more likely as the number of games remaining falls, but still this appears a near-impossibility.

However as a Charlton fan used to disappointment, and in order to be intellectually 'honest', I will assign a 1% probability to Outcome D.

Now let's consider the dreaded play-offs.

If Charlton have to participate in the play-offs, then it is bound to feel like a meaningful disappointment given how long we would have spent in the top two positions.

The negative impact on dressing room sentiment and fan morale, allied with the tautological conclusion that our form must have been relatively poor in the closing weeks, are likely to offset the mere fact that our squad will likely be the strongest of the four clubs involved.

Conversely, given the way the League table is transpiring (with a large gap below 5th), the team which finishes 6th will feel as though it has a 'bonus free option' on promotion, and will feel under no pressure whatsoever (and probably play better as a result).

Putting these two views together, I am comfortable with the conclusion that each of the four play-off clubs will have an equal 25% chance of promotion.

What this means for the probability of Outcomes A-C is as follows, where PA below is the 'Probability of Outcome A' or automatic promotion:

PA + (0.25 x (0.99 - PA)) = 0.72

0.75PA + 0.2475 = 0.72

PA = 0.63 or 63%

The above equations strip out what aspect of the 72% probability of promotion is attributable to automatic promotion or Outcome A (63%), and what probability is attributable to promotion via the play-offs (9%, ie. 72% - 63%).

They do so simply by stating that the probability of promotion is equal to the probability of automatic promotion, plus the probability of promotion via the play-offs (which requires that we actually compete in the play-offs, ie. weren't promoted automatically or positioned outside the top 6!).

Thus the probability of Outcome A is 63%, and of Outcome B is 9%.

The slightly uncomfortable remaining conclusion therefore is that the probability of Charlton losing in the play-offs (Outcome C) at the end of the season is 27%, the balancing figure:

Probability of Outcome A: 63%
Probability of Outcome B: 9%
Probability of Outcome C: 27%
Probability of Outcome D: 1%

If you agree with my analysis to a decent degree, then I'd be keen to know whether these probabilities are similar to your own 'gut feeling' about the remainder of this season.

I wrote up this analysis because I instinctively feel that a 27% likelihood of more play-off heartache seems too high, yet I feel as though I've proved that it isn't.

And now every time I walk past parents of two boys (or look at my own two for that matter), I shut my eyes and see Nicky Bailey's play-off penalty disappearing into the night sky, and say, "Oh no Lord, please not again!"