^{[1]}You might have been promoted this year, or not promoted… We have argued many times that the current promotion system is flawed ^{[2]} but why is there so much uncertainty in the system? Part of the explanation lies in the so-called “wave effect”. Basically, if you are in a grade with increasing population, for instance because of the arrival of a wave of colleagues promoted from the grade below, the mathematical peculiarities of Annex IB of the Staff Regulations result in a temporary increase in the quota of promotions available for that grade (see Annex 1 below for a theoretical example). Conversely, if you are in a grade with decreasing population, there will at some stage be a temporary decrease in the quota of promotions available for your grade. As a result, if you are lucky to be in “growing” grade, you might be promoted quickly just because “you are riding the front of the wave”. If you are in a “shrinking” grade, you might have to wait longer than normal to get your promotion just because you are “floating” on the “tail of the wave”.

Both situations occur in perfect compliance with the rates specified in Annex IB of the SR. The examples provided in the annex are theoretical for the sake of simplicity. However, we have seen evidence of this wave effect in the “true world”. In the past, for instance, a strong wave effect occurred as an artefact of the empty AD9 grade. Indeed, this grade did not exist before the 2004 reform of the Staff Regulations. The old A7 grade corresponded to the current AD8 grade and the old A6 grade corresponded to the current AD10 grade (if you are not convinced, check-out article 2 of Annex XIII of the SR ^{[3]}; yes, it is complex, the complexity was intentional, to fool the newcomers, but all you need to know is that the A* notation is just the same as our current AD notation). As a result, the population of the AD9 grade rapidly grew for several years while the population of the AD10 grade shrunk as many pre-2004 staff in that grade were moving to AD11 before a significant number of post-2004 staff could reach AD10. This explains why hundreds of unlucky pre-2004 AD who were not in a position to jump to the AD11 grade quickly enough got caught up in the tail of a strong wave effect. Some are still there while their comrades who were just one grade above in 2004 might have ridden a better wave to AD12 or even to AD13 by now. The final question is why DG HR did not fix Annex IB of the SR when it reformed the SR in 2014 in order to get rid of this wave effect? Could the explanation be that some of the management of DG HR and some of their friends in the unions have benefited to a large extent from the wave effect, in particular in the AD13 grade which, like the AD9 grade, was a new grade introduced by the 2004 reform?

**Annex I : Simplified example of statistical biases caused by changing populations in a given grade between 2010 and 2014**

**Scenario 1: step increase in arrivals from the grade below: from 100 arrivals from the grade below/year to 125 arrivals/year**

^{[4]}*Explanation**: initially, the population in the grade was 100, steady state. On 1.1.2010, a sudden influx of 125 officials arrives in the grade because of promotion from the grade below while 100 officials leave the grade because of their own promotion. As a result, the population in the grade becomes 325. In 2011, another 125 arrive from the grade below while 108 leave the grade through promotion (108=* ⅓ *x 325), raising the population in the grade to 342, etc. In 2011, 100 people benefit from a promotion in 3 years but an additional 8 people benefit from a fast promotion because of the favourable wave effect; in 2012 the number of fast promotions reaches the maximum of 22, in 2013 it starts decreasing to 15. Eventually, the number of promotions in the grade will reach the steady state value of 125, thereby equating the influx from the grade below and there will be no more fast promotions.*

**Scenario 2: step decrease in arrivals from the grade below: from 100 arrivals from the grade below/year to 75 arrivals/year**

^{[5]}*Explanation**: initially, the population in the grade was 100, steady state. On 1.1.2010, the influx of officials from below decreases to 75 for reasons totally independent from the merits/situation of those who are in the grade. As a result, the population in the grade decreases to 275. Next year, the population further decreases to 258 and the number of promotions decreases to 92. In 2012, the number of promotions further decreases to 78 and in 2013 to 60. As a result, 8 people are put in the slow track in 2011, a maximum of 22 people are put in the slow track in 2012. Then the number of people in the slow track starts decreasing to an eventual stabilization, in balance with the steady influx of officials coming from the grade below.*

**Assumptions:**

- For the sake of simplicity, promotions occur on 1 January of each year and there is no recruitment of new staff in the grade.
- The Commission computes promotion rates in a grade as the ratio of promotions in a given year N divided by the population in that grade on 1 January of year N-1 (this what Annex IB says).
- The number of promotions is calculated here for a ⅓ promotion rate (we should have used 0.33 but ⅓ makes the example simpler. It changes nothing to the reasoning).
- The initial population was 300 before 2010 and was steady until then 100 people were promoted from below on 1 January of each year and (100 were promoted to the grade above on the same date).
- Promotions are allocated in priority to the population that has the largest number of years of seniority on 1 January of each year (those with 4-year seniority are served first, then those with 3-year seniority, then those with 2-year seniority.

** ****Conclusion**

The varying number of staff in the grade causes statistical artefacts: being in a grade with increasing population caused by a step increase in the population coming from the grade below results in an increased likelihood to be promoted within 2 years instead of 3 years. Being in a grade with decreasing population caused by a step decrease in the population coming from the grade below results in an increased likelihood to be promoted within 4 years instead of 3 years. Here, all people are assumed to be identical, there is no difference of merit between them. The different career speeds depend only on the statistical configuration of the considered population. In other words, strictly applying the rates of annex IB does not guarantee career equivalence when populations are varying in size with time.