Know your odds before you roll the dice

Breeding in PhotoFinish.Live is a stochastic process but it's not random. There are rules and probabilities. Forewarned is forearmed. Any speculator needs to know their odds.

Petrocker

8/17/202410 min read

There is so much folklore in PhotoFinish.Live about breeding. Primarily this is because there is a knowledge vacuum on how breeding actually works, which is a good thing for the longevity of the game. Yes there are official blog posts on breeding, but these are, enigmatic at best and necessarily obtuse at worst. Necessarily, because if it were a code to be cracked, and min-maxed, the game would become an awful grind. I am a big fan of the breeding algorithm personally, mostly because it does what it sets out to do - which is to introduce genetic variation in the game, which is a key selling point. Is it perfect? No, no models are. Is it conquerable? I am not sure, but what I am sure of, reading discord and Twitter/X, is there are a number of players who could be better informed on the odds of success, starting with this post.

But what about breeding reports? I think breeding reports are helpful, and obviously getting access to free breeding reports gives you a tremendous advantage. There are also community tools like PhotoFinishEdge and Gap that help community members with their own interpretations of breeding reports. However, I also think that breeding reports are seductive. Those long wicks that everyone desires for a chance of a super roll, really only affect the extremes of distribution. In reality 50% of all rolls occur inside that box in the middle, and very few occur at the extreme of any joint probability distribution (which is what those box plots represent).

Official breeding reports simulate 1,000 rolls to show you the chances of what could happen. In reality you get one roll and you are stuck with it. So let's look at what people got stuck with rather than the promise of what might have been.

Upgrades and Downgrades

Before we begin a quick word on the data used in this analysis. In includes only horses that have run at least 1 race. It does not include foals yet to race or horses who have never races. The majority of the analysis is on retired horses because we can see their attributes and therefore understand what rolls they received on breeding. As a consequence, the data is always a few seasons behind what might be considered the meta right now (mid season 18 at time of writing).

Ok so let's have a look at what influence the parents' grades have on their foals' grades. To do this we simply crosstab the data to look at combinations of parent grades and the distribution of outcomes generated.

The above table shows the combination of parent grades in the first two columns and the foal's grade across the top row. Matching an A- stud with a A- mare, has to date, resulted in an A- 7/10 occasions. 23% of the time it rolls up to an A (so you have a 1/4 chance of that happening) and a small amount roll down to lower than an A-, which for purposes of space I have not detailed out. This figure also includes inbreeding, which while small in volume happens for higher grades more often.

If the mare was an A, not an A-, your chances or rolling an A grade foal would leap up to 62% and there is a 50-1 chance (2%) that you roll an A+. If the mare was an A+, that chance is noticeably higher at 27%. If you really want to match your S- mare with an A- stud, there is roughly a 1/4 chance its an A and 3/4 its an A+. In this data (and remember doesn't include all the unraced foals), there have been no S- grades and beyond by pairing these types of horses together. Now we have got the hang of the data, and what it means let's look at the broader table of results.

Let's start by looking at matched pairs - where both parents are the same (highlighted in grey), What we see is there is a 70-80% chance you get back the same grade horse. Apart from S+, there also is a pattern where it is more likely you get an up roll than a down roll. The lower the grade the higher the chance to get an up roll (where foal is a higher grade than the parents). For example if both parents are S- there is a pretty much a 1/6 chance of an up roll and a 1/12 chance of a down roll. For S+ matched with S+ there is, and bear in mind the small sample, a 0.5% chance of an SS-. Remember these are overall grades, and overall grades are created from the attribute grades.

Where parent grades are one level apart (say an A+ and an S-) there is a 90%+ chance that the foal will be either one of those grades. The chance of an upgrade on the higher grade is extremely low, generally around 1%. Don't breed your A+ mare to a cheap S- stud and expect an S grade foal. It does happen but not very often.

One of the very rare occurrences of this happening was G Wagon (A+) bred with Ono Holo (S-) to produce an S foal. Was this a random roll or are some horses more likely to roll up than others? Something to dig into on another occasion.

Where parent grades are two levels apart the most likely outcome goes back to a 70-80% chance of rolling the grade in the middle. For three levels apart, the pattern reverts to one level apart, where now the two grades in the middle account for 90% of rolls.

Clearly there are patterns to here. Note the normal-esque distributions around a mean, which is to be expected because a) these grades are a combination of the six individual attribute grades b) the breeding reports show us a joint probability function in the form of a box plot - and these results could be plotted in exactly the same way.

Before you hit up the breeding barn, or start buying up in house studs, remember the odds, and rather than try to beat them, use them to your advantage. With the current grade restricted meta, working out your chances of rolling a certain grade will help to when trying to breed champions. Say you have an amazing A+ mare you have retired. You don't want to breed up, but breed a competitive racer at either A or A+.Well an S- minus stud would mean a 60% chance of up rolling to an S-, so that's probably out. Breeding with an A+ would mean an 18% chance, which might be a risk you want to take to try to land your foal in the very top end of the A+ grade. That's why I think a table like this is useful to owners.

How do subgrades come into it?

Subgrades are when the individual attributes of a horse are either above or below the overall grade. Let's image horse A. It's an S graded horse. It's attributes are Start=SS, Speed=S-, Stamina=S+, Finish=S, Heart=S+ and Temper=S-. To calculate the subgrade we simply add up the number of grades above or below the overall grade (+3-1+1+0+1-1 = +3). Subgrades are bound to +/-5 with fives being very rare.

To make it simpler to understand the following table is just the combination of S graded parents. Each row represents the net combined subgrades of the parents. So if the stud is +3 and the mare is -2, then that breeding pair would be in the +1 row.

As you can see from the table, there is very little chance (<5%) that two S graded parents with a negative subgrade will create an S+ horse. This makes intuitative sense, horses with lower grades are less likely to roll up. Their starting points are lower and therefore the joint probability will shape out lower too. Yes long wicks are great, but outlier rolls are unlikely when your sample size is 1 (breed).

If you own a -2 S grade mare, even with a +5 subgrade stud, the best you can hope for is a +3 subgrade combination in the chart above which means you maximum chance of a S+ foal is 17%, or 1/6. Just think about that before you spend 40k on stud fees.

One of the reasons we don't have many SS- foals running around is there are (at least in my dataset) 50 plus subgrade S+ horses and 1,000 minus subgrade horses. In other grades the subgrades are normally distributed, but not at the top. Mr Wonderfull, a great champion horse is a +4 S+, extremely rare, with his best attributes in the most important places. There is no need for another theory about why some horses win and others don't. Have +subgrades and your best attributes in the right combinations.

Subgrades are vital to understanding your odds of rolling up when breeding. Community tools like PhotoFinishEdge has functionality that allow you to research potential breeds and the marketplace at a subgrade level. Obviously you can calculate subgrades for yourself easily enough - but tools like this give you a real edge particularly if you have a growing stable and lots of breeds to figure out each season. The aforementioned G Wagon is a +4 subgrade A+ stud.

The above table simplifies subgrades and just bands horses into having positive, neutral or negative subgrades. In this simplified view, in case it needed proving, illustrates that positive subgrade parents are more likely to create positive subgrade foals. This is just for S parents and S grade foals, ignoring up rolls and down rolls. When the foal is an S from S parents (in other words, all things being equal), the foal is more likely to have a positive subgrade (and therefore more likely to win on the track) if at least one parent has one too. Two positive subgrade parents have a 57% of generating a positive subgrade foal. whereas two negative subgrade parents only have a 20% chance. Your odds are three times better if you focus on positive subgrade horses.

Does it matter on the track?

Ultimately the key issue is whether these horses perform on the track. There are two things to look at here. Firstly do upgrades or downgrades perform better or worse? Is a down roll always going to be better than an average horse of the same grade? The data is quite messy, and there are many reasons for performance on the track outside of the overall grade, but we can take a look at derby ROI (winnings versus fees) and WPS%. For clarity I have reduced the table to just where the parents are the same grade.

The majority of horses run derby negative, so our baseline isn't zero here but probably -25%. I am not sure there is strong evidence here either way. Yes higher grade horses (S+ and above) are generally more profitable to run. If you look at the A+ column you see there is very little difference in ROI whether that A+ came from A parents (an upgrade), A+ parents (a sideways move) or S- parents (a downgrade). People like to look for downgrade horses thinking that they are stronger than the average horse at this level but I am not sure there is much evidence here at least to support that.

On WPS% (finish top 3) again the middle A+ column looks fairly flat You would expect top end horses to win more frequently, so again I am not sure there is compelling evidence either way. I keep an open mind on this and will look for more evidence.

Taking a similar sample of S grade horses whose parents are both S grades too, we can isolate the effect of subgrades on race track performance. Here the difference is much clearer cut. Without a doubt, subgrades of a horse drive on track performance. Given this is so clear, that +4 horses win 22% of races they enter, versus 13% for -4, and the ROI is so much higher, subgrades are what you want in your horse. You won't know until its retired whether you had them or not, but you can change the odds of acquiring better foals by paying attention to subgrades in the breeding barn.

Some rules for breeding next season

There are three things you need to think about when breeding next season:

You can't change the distribution of grades by sheer force of will. The grade of your foal is largely decided before you roll the dice. Know the odds before you pull the trigger. That S- mare of yours bred to a S+ stud will give you less than a 4% chance of rolling an S+ foal
Subgrades matter when it comes to loading the dice in your favour. The difference between a -2 and a +2 mare is massive. If your goal is to breed S+ foals, then add the subgrades of the parents up and work out the likelihood of you hitting your target. Too many people waste huge amounts of money with unrealistic expectations. There are many reasons to hit a top stud, but trying to get an S+ foal in one generation is unlikely unless you have the subgrades in your favour
Subgrades matter too in on track performance. To dominate grade restricted racing you want to drop in at the top end of the grade with a +4 horse. To do that check the statistics on what you are likely to roll and based on the parents.

Join the fun and put these insights into practice at PhotoFinish.Live and if you are considering starting your own stable please consider using my referral code: PADDOCK or just click on this link: https://signup.photofinish.live/?referralCode=PADDOCK

Please remember this is a web3 game where your spend your own money. Nothing I write about should be considered financial or investment advice.

Know your odds before you roll the dice

Upgrades and Downgrades

How do subgrades come into it?

Does it matter on the track?

Some rules for breeding next season

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