As HSTEd explained above, the Kodama stopping services use trainsets with the same performance as the faster Hikari and Nozomi services (JR Central has standardized all services on the N700 series). This is necessary as the Kodama services have to take pathings that weave through the faster train pathings. After a Kodama service departs a certain station, it has to sprint to the next station in order for the timed overtake to occur. Once at that station, it will wait for the faster service (or two) to pass. This stop may take up to ten or eleven minutes. This process is repeated at many stations as the train makes it deliberate journey to its final destination. Highly recommended to take such a train as an introduction to the service pattern and to get a "feel" for the working timetable.
If you look at the overall Tokaido Shinkansen timetable, you have the AM and evening peaks, with a mid-day "pattern daiya" or interval timetable- not exactly a strict clockface 0, 15 or 30 min timetable, but rather a slightly more granular pattern of services repeating themselves at particular minutes on the hour. During the peaks, you will have the fastest Nozomi services "convoying" on each other to maintain a high frequency service and low headways. In the off peak, you will have 4 Nozomi, 2 Hikari and 2 Kodama services more or less alternating with each other, with a Nozomi service always at the top of the hour and the Kodama services at the half hour and towards the end of the hour. The balance of Nozomi and Hikari services fill up the remainder. This division into two distinct types of service patterns is common on Japanese railways with peaky passenger demand, such as the Tokaido Shinkansen (70% of pax are business travellers) and the many private (for profit) railways which feed suburban commuters into the urban core.