IM Hawaii

In this series of blog posts on Kona Pro Slots, I’ve looked at Reverse Engineering The Assignment Algorithm and ideas for Different Approaches – both of these posts have been close to the facts. This post contains my views on the current algorithm, a bit of speculation on what Ironman was looking for and some bigger and smaller changes going forward. The following thoughts are my opinion, and I would love this to be a starting point for a broader discussion of how to get the best, most interesting races in Kona as possible.

On Its Own, the Assignment Algorithm Is Fair

I’ve had a detailed look at potential algorithms for assigning slots in Part 1 of this series. Here’s the graph summarizing the different approaches:

The algorithm that makes it hardest for the larger group (usually the men) to get both slots is “Hamilton Unassigned” – but it’s quite unfair as their share of slots would always be smaller than their share of starters. The next-best algorithm for the smaller group is the “Jefferson Unassigned”, and that’s the algorithm that Ironman has in all likelihood chosen to use (that’s why it’s highlighted).

I also find it reasonable that Ironman slightly tweaks the algorithm for Regional Championships as they have more fixed slots: If they used the unaltered Jefferson Unassigned, again you’d end up with a situation where the larger group’s share of slots is always smaller than their share of slots. The tweak is not very elegant, but the resulting slot assignment looks quite reasonable to me.

But Only If You Accept Proportional Assignment Based on Starters

Even if the slot assignment algorithm is fair, this doesn’t mean I like the overall system as it’s solely based on the number of starters. At first, this sounds reasonable (after all it has been used for assigning age group slots), but there should be other factors in order to determine the athletes that will likely have the biggest impact on the Kona races. (I have highlighted some of these factors such as Strength of Field or Race Performance in Part 2 of this series.)

I want to note that this discussion is a slippery slope as it can quickly deteriorate into an “X doesn’t deserve to be in Kona” type of argument that isn’t fair to anyone involved (or useful). For example, I think that Carrie Lester’s 8:44 in Arizona should have been good enough for a Kona slot – but that would have to come at the cost of TJ Tollakson who has been working hard to overcome his back problems and it’s great to see him qualify once again for Kona. But it’s hard to avoid this “men vs. women” discussion – after all the women will only get more slots if they “take” them from the men which is hardly the best way of developing our sport.

So Why Is Ironman Keeping the Algorithm Secret?

One of the criticisms leveled at Ironman is that they haven’t made much information about their slot assignment algorithm available – and the quick conclusion by some was that “Ironman must be hiding something”, even going so far as suggesting that there isn’t a real algorithm and that the unassigned slots “always go to the men”. As stated above, that is not the actual procedure (see Western Australia for a counter-example), but not being transparent has led to some confusion and frustration.

To be honest, I’m not really sure why Ironman isn’t making more information available. I can only guess that they want to avoid discussion at race sites about the slots (both for the Pros and the agegroupers) and that they want to be able to change some details whenever they see the need for it. But even in the absence of “official details”, I don’t really see “sinister motives” on Ironman’s side in keeping things private.

Has Ironman Just Been Unlucky With Arizona and Mar del Plata?

On one hand, Arizona and Mar del Plata have been very close to ending up with equal slots. (For Arizona, things shifted between the race meeting and race day, for Mar del Plata just one more woman or one less male would have made a difference.) Based on last year’s numbers Ironman probably expected equal slots: Arizona was 25–22 and Mar del Plata was 16-13, with would have clearly been equal slots.

I think that Ironman was hoping for a more equal distribution of Pro slots than in the past – maybe not providing equal slots but at least a lot closer than under the KPR system. And to a certain degree, that is what’s going to happen: Even if all the currently unassigned slots in the 2019 races go to the men, we will have at least the same number of WPROs with Kona slots as in the past.

On the other hand, the small number of starters pretty much assures that there will be some more “weirdness” in assigning the slots, similar to what we’ve seen in Arizona and Mar del Plata. This is a result of the small number of slots and the small number of racers. The “random” decisions of just one or two athletes can influence how the slots will be assigned, while that is extremely unlikely with around 50 agegroup slots and typically 2000 racers or the even larger numbers of seats and votes in context of elections.

Equal Slots Is the Cleanest Solution to This Conundrum

So what should be done moving forward? For a while there has been a push for equal slots for the Pro men and women in Kona, and I continue to believe that this is the cleanest solution on how to assign slots: When giving men and women the same number of slots we won’t have to debate the merits of this or another slot assignment algorithm. ‘Nuff said!

But I Also Have a Few More Realistic Suggestions

As “Equal Slots” would be a pretty big change for Ironman, I’m not holding my breath for this to happen in the next few seasons. (Though as Rachel Joyce has put it, I’m sure that “equality will prevail eventually”.) While I’m also not a fan of drastic changes without giving the current system to play out a bit more, here are a few ideas for minor “tweaks” intended to make the current system work a bit more smoothly:

• Announce Slot Distribution at the Pro Meeting
  In order to minimize surprises on race day, the slot distribution could be fixed on the number of Pros that sign in at the Pro Meeting. This would also give Ironman a chance to announce the slots at the Pro Meeting.
  The difference between the number of athletes at the Pro Meeting and on race morning is almost always relatively small – and I’m not sure why someone getting sick in the last few days should have an impact on how the slots fall. I also don’t think that this leaves too much room for manipulation – when someone shows up to the Pro Meeting, the extra burden of putting their toes in the water on race morning is pretty small.
• Fix the Total Number of Male and Female Slots for the Season
  Looking at the total number of Pro starters in the 2018 qualifying season (September 2017 to August 2018), I get 416 female and 772 male Pro starts. Applying those numbers to 20 unassigned slots (ten for the Regionals and another ten for Ironman races with unassigned slots) would lead to 7 female and 13 male Pro slots (pretty much regardless of the actual algorithm). When announcing the races for the upcoming season, Ironman could assign the slots to the races on the calendar, making it clear long before the races how many slots there will be for each gender.

While minimizing the surprises, implementing either of these suggestions would keep the base “proportional” system in place.  I hope that Ironman will at least discuss tweaking the system for 2020, maybe after we’ve had some more experience with the current system in the first half of 2019.

Late in 2017 Ironman announced a new system for Kona 2019 Pro Qualifying, moving to a slot-based system almost equal to the agegroup qualifying system. One aspect of the system is “unassigned slots” for some races that will be “assigned according to the ratio of starting Pro Athletes” (as stated in the official “Ironman World Championship Profession Athlete Qualification“). The specific details of the assignment algorithm is considered private by Ironman. Based on the first races and the resulting slot assignments Russell Cox (who is focused on the agegroup side, his data can be found at http://coachcox.co.uk) and I have done our best to reverse engineer this algorithm. This post looks at the available data, potential algorithms and the conclusions that can be drawn. This “algorithm post” will be followed in the next days by one looking at alternative approaches and an “opinion post”.

Data on Races With Unassigned Pro Slots

Here’s a quick look at the Pro races with unassigned slots so far:

• IM Arizona – 2 MPRO slots (based on 15 female and 32 male Pros starting the race) plus 1m+1f base slot
• IM Western Australia – 1 Pro slot each (based on 10 female and 13 male Pro starters)  plus 1m+1f base slot
• IM Mar del Plata (South American Regional Championship) – 2 MPRO slots (based on 15 female and 23 male Pro starters) plus 2m+2f base slots

In addition, Ironman has stated that they use the same algorithm for determining the slot assignment for the agegroups, so we can also cross-reference if the “suspected” algorithm also fits the agegroup slots.

Assignment Algorithms

There are a number of algorithms dealing with a similar problem to slot assignment. Typically, they come from a voting context, where a small number of indivisible “seats” (usually tens to hundreds) has to be assigned based on “votes” (usually thousands). Even though the US voting system is typically majority-based, it also has to deal with a number of “representational” issues. One example is assigning a fair number of seats in the House of Representatives (capped at 435 seats) to the States in relation to their population (total US population based on the 2010 census 308.7 million, with state populations between 37.25 Million and 0.56 Million).

This post looks in detail at the two most widely used approaches, the Hamilton and Jefferson methods using the size of the field as the basis for the slot assignment. Different approaches such as depth of field will be discussed in a follow-up post. When working off the size of the field, it seems best to apply the algorithm to the number of athletes starting the race. The number of registered athletes is often quite different from the number of athletes actually racing, especially on the Pro side. And the number of finishers isn’t finalized for some time during and after the race (especially considering DQs that might be contested for days or weeks), and DNFs often contain an element of bad mechanical luck.

Hamilton Method

The Hamilton Method, also know as Hare-Niemeyer or “Largest Remainder”, is one of the oldest systems of assigning seats. It calculates the number of votes required for a seat by dividing the total number of votes by the number of seats available and then divides the votes a party has received by this number. Another way to put this is that it multiplies the number of available seats with the fraction of votes a party has received. This calculation results in a number with an integer part and a fractional part. According to Wikipedia:

Each party is first allocated a number of seats equal to their integer. This will generally leave some seats unallocated: the parties are then ranked on the basis of the fractional remainders, and the parties with the largest remainders are each allocated one additional seat until all the seats have been allocated.

In the context of Kona slots, the Hamilton Method multiplies the number of slots with the number of starters in a group divided by the total number of starters. The algorithm is probably easier to understand with a few examples.

Hamilton Method on Unassigned Slots

The first suggested algorithm applies the Hamilton method to the number of unassigned slots. (Russ and I believe that this is the “old” method of assigning agegroup slots that was used until the summer of 2018.)

For the Pros, there are two unassigned slots. Using IM Arizona as an example, we get the following calculations:

Arizona	Starters	Quota
Men	32	1.36 (2* 32/47)
Women	15	0.64 (2* 15/47)
Total	47	2 slots

This means that the men get one slot (the integer part of their ratio), while the second slot would go to the females (as their fractional part of 0.64 is larger than 0.36). As both unassigned slots at IM Arizona went to the men, this is obviously not the algorithm that is used for the 2019 qualifying season.

If you look at this type of calculation, then the larger agegroup will have to be at least three times as large as the smaller one to get both slots (i.e. 75% of the whole Pro field):

Obviously this is a very tough requirement, and therefore not very useful to achieve “proportional slots” for the Pros when assigning only two slots. It’s also not fair that the men will always have a smaller fraction of slots than their fraction of the Pro field. It’s a bit of speculation, but I think that Ironman also felt that the system they have been using so far for assigning agegroup slots doesn’t work well for the small number of Pro slots, and that’s why they decided to change their algorithm going into the Kona 2019 qualifying season.

Hamilton Method on All Slots

Another approach would be to apply the Hamilton method on all slots while observing “minimum” slots. Again using Arizona as an example:

Arizona	Starters	Quota
Men	32	2.72 (4* 32/47)
Women	15	1.28 (4* 15/47)
Total	47	4 slots

This would result in the men getting three slots: two from the integer part of their ratio, and another one because 0.72 is larger than 0.28) – the minimums are already observed in this example. In order for the larger agegroup to get three slots, they would need more than 5/3 of the smaller agegroup or at least 62.5% of the field:

While this method gives the observed slot assignment in Arizona, IM has stated that their assignment process is based on the number of unassigned slots and not all slots. It’s also tricky to extend this algorithm to include minimum slots for the bigger number of agegoups for all cases. (For the technically minded: The minimum slots plus the integer parts may already assign more slots than available.) It’s very unlikely that this is the method used by Ironman.

Jefferson Method

The Jefferson Method (also known as D’Hondt method) uses a larger number of operations to determine the slots:

The total votes cast for each party is divided, first by 1, then by 2, then 3, up to s, the total number of seats. The winning entries are the s highest numbers in the whole grid; each party is given as many seats as there are winning entries in its row.

Similar to the Hamilton Method, it can be applied to all slots or only those that are unassigned.

Jefferson Method on Unassigned Slots

Based on the unassigned slots, here’s the resulting Jefferson grid for IM Arizona:

Arizona	Starters	1	2
Male	32	32	16
Female	15	15	7.5
Total	47	2 slots

There are two unassigned slots, and as the male starters divided by 2 is larger than the number of females starters, both “winning entries” are from the men and both slots would get assigned to the MPROs. This fits the slot assignment in Arizona.

In general, to get both unassigned slots the larger agegroup needs to have at least twice as many starters as the smaller one, i.e. at least two thirds or 66.7% of the whole Pro field:

Jefferson Method on All Slots

As for the Hamilton Method, we can also apply Jefferson Method for all available slots while observing minimums.

Arizona	Starters	1	2	3
Male	32	Auto	16	10.34
Female	15	Auto	7.5	5
Total	47	4 slots

Observing minimums is relatively straightforward in the Jefferson Method – instead of starting with the divisor 1, you start with the first divisor that is larger than the minimum. As there is one minimum slot for each, the Divisors start with 2, and again the two unassigned slots would go to the men. For Arizona, this approach would also yield the “observed” 3:1 slots, but as we know that two more WPRO starters would have changed the slots, this can’t be the actual algorithm.

In order to get both slots using this approach, the larger agegroup needs to have at least 60% of the starters:

Conclusion .. For Now

Here’s an overview of the different approaches so far:

Based on the text in the Pro Qualifying Rules (referencing “the ratio of starters to Unassigned Slots”) and the fact that the correct Arizona distribution is yielded by the Jefferson Method on Unassigned slots, I thought that I had identified the method used – that’s why it’s highlighted in the graph shown above. Russ provided further evidence from the age-group side that was supposedly using the same algorithm. (More on the agegroup side of things in Russell’s post on Age Group Kona Slot Allocation.) It also correctly predicts an even split of Pro slots for IM Western Australia. But we have not reached the end of the story yet …

Slot Assignment For Regional Championships

Regional Championships have a different number of slots: While they also have two unassigned slots, they offer two base slots each for the men and women. (IM Arizona has one slot each, plus two unassigned slots.) But as the Pro Qualifying Rules state that the slots are assigned based on “the ratio of starters to Unassigned Slots”), I was confident that there would be even slots in Mar del Plata. Here’s Jefferson Grid for Mar del Plata:

Mar del Plata	Starters	1	2
Male	23	23	11.5
Female	15	15	7.5
Total	38	2 slots

However, the actual slot assignment was that both slots went to the men, resulting in the final numbers of four slots for the men and two for the women. So we need another twist to the algorithm.

It seems reasonable that the distribution for the unassigned slots is slightly different when there are two base slots as the resulting “uneven distribution” is 3:1 (or 75%) in case of the normal races and 4:2 (or 66.7%) for the Regional Championships. If the Jefferson Method on Unassigned Slots were used, then the fraction of slots for the larger agegroup would always be lower their fraction of starters.

Jefferson Method On All Minus 2 Slots

As the Jefferson Method has been working remarkably well for the Ironman races with just one base slot each, I was looking for slight tweaks to get the right results for Mar del Plata and some of the variations. (Apparently, one more WPRO or one less MPRO would have changed things for Mar del Plata.) This “tweaking” results in the “Jefferson All Minus 2” method:

Mar del Plata	Starters	1	2	3
Male	23	Auto	11.5	7.67
Female	15	Auto	7.5	5
Total	38	4 slots (1 each minimum)

This method is equivalent to the Jefferson Method on Unassigned Slots except for the Regional Championships that offer two base slots each. (In addition, it’s the same for agegroups as there is always a minimum of one slot there.)

For the Regional Championships, there is a minimum of 60% of the field needed in order to get both unassigned slots:

Conclusion

Going forward, the “Jefferson Method on All Minus 2 Slots” will be the algorithm I’ll be using to predict how the slot assignments will look like. New results will either send me back to the drawing board, but hopefully they will strengthen the evidence that this is indeed the algorithm Ironman currently uses.

Based on this algorithm, the “inflection points” for the slot assignments are 66.7% of the Pro starters for “regular” Ironman races with unassigned slots and 60% for the Regional Championships: