Improvements

The Improvement system is displayed as a series of stars beside the equipment name. Improvement stars grant equipment hidden stat bonuses depending on the type of equipment that was improved. Improvement stars can be added to certain equipment through the Akashi's Improvement Arsenal and using Improvement Materials.

Effects

 * There's no  visible stat difference between unimproved and improved equipment.
 * Improvements on equipment have been shown to grant bonuses to stats such as firepower, torpedo, accuracy and anti-submarine damage.
 * The exact effect of improvements follow the formula of (multiplier×$$\sqrt{\bigstar}$$) according to Japanese testers.  Multipliers are listed below (AA and ASW attack's multipliers are after equipment modifier.)
 * Following table shows the improvement multipliers for certain equipment, sourced from, note that those with question marks attached are unconfirmed:
 * Other multipliers, like accuracy, evasion, Line of Sight, values for surface and AA radar, torpedo and AA attack's bonus value for various other equipment are still unconfirmed. However, it has been confirmed that Surface Radars do not increase firepower, and Machine Guns do not increase Night Battle attack power.
 * Radars are known to add LOS and Accuracy, but the multipliers are pending confirmation.
 * Accuracy multiplers for various equipments like Guns and AP Shell and Torpedo are currently believed to be 1.5 or 1.58($$\sqrt{2.5}$$), but the exact multiplier is still unknown. Effect on low morale seem to be lower, and preliminary tests suggest that Night Battle accuracy is unchanged.
 * Accuracy multiplers might either have a upper limit of 10%, or a limit that relates to type or number of equipment.
 * Accuracy multiplers for AA Radar is possible to be 1.
 * Improving Sonars help increase evasion against enemy torpedo attacks, according to official twitter.
 * Equipment Improvement effects are pre-cap modifiers.
 * These effects are rounded down to integer after summation of improvement values from all equipments and applying other precap modifier(e.g. formation, engagment, yasen special attack, Type 3 Shell, WG42, chuuha/taiha modifier) but before other postcap modifiers.
 * For instance, when all precap modifier are 100% or ±0, a ★+4 Secondary Gun give you 1×$$\sqrt{4}$$=2 according to the formula, while a ★+8 Secondary Gun also give you 1×$$\sqrt{8}$$=2.828… according to formula, but after being rounded down it is still only giving 2 additional firepower.
 * However, bonus from equipments can be stacked before being rounded down. for instance you have a ★+8 Secondary Gun which give you 2.828… additional firepower, and on the other hand you have a ★+8 Large Main Gun which give a formula value of 1.5×$$\sqrt{8}$$=4.242… additional firepower during Day Battle, using them together on the same ship would give you an additional of 7 firepower (7.071…) instead of 6 as when they are added separately.
 * On the other hand, while 2 piece of ★+9 Medium Gun give you 2*1*$$\sqrt{9}$$=6 which is same as 2 piece of ★+10 Medium Gun (2*1*$$\sqrt{10}$$=6.324… when all precap modifier do not have any effect, but for example if the fleet is participating in a head-on engagement battle and thus getting a 80% pre cap damage modifier, 2 piece of ★+9 would only give you 6*0.8=4.8 which mean 4 additional damage while 2 piece of ★+10 would give you 6.324…*0.8=5.059 which mean 5 additional damage.
 * If you only use one improved equipment on a ship, here are the improved bonus values:
 * For multipler = 1.5:
 * ★+1: +1 bonus
 * ★+2~3: +2 bonus
 * ★+4~7: +3 bonus
 * ★+8~10: +4 bonus
 * For multipler = 1.2:
 * ★+1~2: +1 bonus
 * ★+3~6: +2 bonus
 * ★+7~10: +3 bonus
 * For multipler = 1:
 * ★+1~3: +1 bonus
 * ★+4~8: +2 bonus
 * ★+9~10: +3 bonus
 * For Multipler = 0.75:
 * ★+2~7: +1 bonus
 * ★+8~10: +2 bonus
 * Sonar give bonus to evasion against torpedo when improved after 26th June 2015.
 * It is believed that Improvement in Firepower aspect can't help Shelling Support Expedition, however the situation for Torpedo Support expedition is not tested. The Improvement value given by accuracy is not tested either.
 * Improved Secondary Gun boost firepower of carriers but improved Machine Gun do not.

Improved Equipment Example Combination
The follwing table listed the extra firepower gain by battleships with 2 main gun and 1 AP Shell from improvement during Day battle, without other pre-cap modifier(No Damage, Parallel Engagement), with the currently listed calculation formula (1.5x improvement factor for main gun and 1x for AP Shell).