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 are no  visible stat differences between non-improved 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, meaning these effects are rounded down to an integer after summation of improvement values from all equipments and applying other pre-cap modifiers(e.g. formation, engagment, yasen special attack, Type 3 Shell, WG42, chuuha/taiha modifier) but before post-cap modifiers.
 * For example, when all pre-cap modifiers are at 100% or ±0, a ★+4 Secondary Gun will give you 1×$$\sqrt{4}$$=2 according to the formula, while a ★+8 Secondary Gun also give you 1×$$\sqrt{8}$$=2.828…, but after being rounded down it still only grants 2 additional firepower.
 * However, bonuses from equipment can be stacked before being rounded down. for instance, if 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 has a 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 if they were added separately.
 * On the other hand, two ★+9 Medium Guns would give you 2*1*$$\sqrt{9}$$=6, which is same as two ★+10 Medium Guns (2*1*$$\sqrt{10}$$=6.324… (before modifiers), but if the fleet is participating in a head-on engagement battle and thus having 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.
 * The following lists the improved bonus values for a single improved equipment:
 * 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
 * It is believed that Improvements in Firepower do not help in Shelling Support Expedition, however the situation for Torpedo Support expedition is not tested. The Improvement values given by accuracy aren't tested either.

Improved Equipment Example Combination
The follwing table lists the extra firepower gain from improvement by battleships equipped with 2 main guns and 1 AP Shell during Day battle, without applying pre-cap modifiers, with the currently listed calculation formula (1.5x improvement factor for main gun and 1x for AP Shell).