The specialization points factor depends on:

1. Horse speciality.
2. Total shows entered.
3. Speciality trait.
4. The player has the The wand of horse improvement magic item.
5. The arena horse training.

In calculating the points the game will do the following:

1. It counts how many shows the horse has entered in total (including the speciality added at the arena)
2. It determines what is the speciality for the entered show.
3. It verifies if the speciality trait matches the type of the entered show. The trait bonus is:
   
   • 10% if the player is regular.
   • 20% if the player has The wand of horse improvement magic item. This item also adds a 200% base, effectively helping the horses have a double speciality. Note that the purpose of the extra 100% is to allow a second discipline, a 200% speciality will not be better than a 100% speciality.

Example:

Horse #1029054 has:

1. Trait Racing.
2. 29887 Racing shows.
3. 197879 English shows.
4.  5120 Western shows.
5. 186 Western shows.

The total amount of shows is: 29887 + 197879 + 5120 + 186 = 233072

The spec points will vary based on the type of the show entered:

1. Racing show - The trait is Racing:
   
   • When it does not have the wand:
     (5 * 233072 [total]) + (29887 [racing entered] * (29887 [racing entered] +  23307 [the trait is 10% of the total] ) * 100 [base]) / (233072 [total] * 1.5) = 1165360 + (29887*53194*100) / 349608 = 1620100
     
     • Note: Without the Racing trait, the numbers would have been 1165360 + 29887*29887*100/349608 = 1420855
     
     
   • When the player has the wand.
     (5 * 233072 [total]) + (29887 [racing entered] * (29887 [racing entered] +  46614 [the trait is 20% of the total] ) * 200 [base]) / (233072 [total] * 1.5) = 1165360 + (29887*76501*200) / 349608 = 2473330
     
2. English show
   
   • When it does not have the wand:
     (5 * 233072 [total]) + (197879 [english entered] * 197879 [english entered]  * 100 [base]) / (233072 [total] * 1.5) = 1165360 + 197879*197879*100/349608 = 12365360
     
     • Note: If the horse would have English trait, then the numbers would be: 1165360 + 197879*(197879 + 23307) * 100 / 349608 = 13684542 (a 10% increase)
   • When it has the wand:
     (5 * 233072 [total]) + (197879 [english entered] * 197879 [english entered]  * 200 [base]) / (233072 [total] * 1.5) = 1165360 + 197879*197879*200/349608 = 23565361

Notes:

• The above horse is better in English shows. Typically horses should specialize on the horse trait, for maximum results.
• The arena horse bonus applies to all the above numbers. They were calculated with 0% arena training. 100% arena training would double each of them.